§
    ¢éUg;
 ã                   ó~  — d dl Z d dlmZ d dlmZmZ d dlZd dlZd dl	m
Z
 d dlmZ d dlmZmZmZ d dlmZ d dlmZ d d	lmZ d dlmZ d dlmc mZ d d
lmZmZ ddlm Z  ddl!m"Z#m$Z% ddl&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/ ddl0m1Z1m2Z2m3Z3 ddl4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z; ddl<m=Z= d dl>m?Z? d dl@mAZA d dlBmCZC d„ ZDd„ ZE�d‡d„ZF G d„ de+¦  «        ZG eGddd¬¦  «        ZH G d„ de+¦  «        ZI eId ddd¬ ¦  «        ZJ G d!„ d"e+¦  «        ZK eKdd#¬$¦  «        ZL ejM        d%ejN        z  ¦  «        ZO ejP        eO¦  «        ZQd&„ ZRd'„ ZSd(„ ZTd)„ ZUd*„ ZVd+„ ZWd,„ ZXd-„ ZY G d.„ d/e+¦  «        ZZ eZd0¬1¦  «        Z[ G d2„ d3e+¦  «        Z\ e\dd4¬$¦  «        Z] G d5„ d6e+¦  «        Z^ e^ejN         d7z  ejN        d7z  d8¬¦  «        Z_ G d9„ d:e+¦  «        Z` e`ddd;¬¦  «        Za G d<„ d=eb¦  «        Zc G d>„ d?eA¦  «        Zdd@„ ZedA„ Zf G dB„ dCe+¦  «        Zg egdddD¬¦  «        Zh G dE„ dFe+¦  «        Zi eiddG¬$¦  «        Zj G dH„ dIe+¦  «        Zk ekdddJ¬¦  «        Zl G dK„ dLe+¦  «        Zm emddM¬$¦  «        Zn G dN„ dOe+¦  «        Zo eoddP¬$¦  «        Zp G dQ„ dRem¦  «        Zq eqddS¬$¦  «        Zr G dT„ dUe+¦  «        Zs esdV¬1¦  «        Zt G dW„ dXe+¦  «        Zu euddY¬$¦  «        Zv G dZ„ d[e+¦  «        Zw ewdd\¬$¦  «        Zx G d]„ d^e+¦  «        Zy eyejN         ejN        d_¬¦  «        Zz G d`„ dae+¦  «        Z{ e{db¬1¦  «        Z| G dc„ dde+¦  «        Z} e}de¬1¦  «        Z~ G df„ dge+¦  «        Z eddh¬$¦  «        Z€ G di„ dje+¦  «        Z� e�dk¬1¦  «        Z‚dl„ Zƒ G dm„ dne+¦  «        Z„ e„ddo¬$¦  «        Z… G dp„ dqe+¦  «        Z† e†ddr¬$¦  «        Z‡ G ds„ dte+¦  «        Zˆ eˆddu¬$¦  «        Z‰ G dv„ dwe+¦  «        ZŠ eŠddx¬$¦  «        Z‹ G dy„ dze+¦  «        ZŒ eŒdd{¬$¦  «        Z� G d|„ d}e+¦  «        ZŽ eŽdd~¬$¦  «        Z� G d„ d€e+¦  «        Z� e�dd�¬$¦  «        Z‘ G d‚„ dƒe+¦  «        Z’ e’d„¬1¦  «        Z“ G d…„ d†e+¦  «        Z” e”dd‡¬ˆ¦  «        Z• G d‰„ dŠe+¦  «        Z– e–d‹¬1¦  «        Z— G dŒ„ d�e+¦  «        Z˜ e˜ddŽ¬$¦  «        Z™ G d�„ d�e+¦  «        Zš ešdd‘¬$¦  «        Z› G d’„ d“e+¦  «        Zœ eœd”¬1¦  «        Z�d•„ Zž G d–„ d—e+¦  «        ZŸ eŸdd˜¬$¦  «        Z  G d™„ dšeŸ¦  «        Z¡ e¡dd›¬$¦  «        Z¢ G dœ„ d�e+¦  «        Z£ e£ddž¬$¦  «        Z¤ G dŸ„ d e+¦  «        Z¥ e¥dd¡¬$¦  «        Z¦ G d¢„ d£e+¦  «        Z§ e§d¤¬1¦  «        Z¨ G d¥„ d¦e+¦  «        Z© e©dd§¬$¦  «        Zªd¨„ Z« G d©„ dªe+¦  «        Z¬ e¬d«¬1¦  «        Z­ G d¬„ d­e+¦  «        Z® e®d®¬1¦  «        Z¯ G d¯„ d°e+¦  «        Z° e°dd±¬$¦  «        Z± G d²„ d³e+¦  «        Z² e²dd´¬$¦  «        Z³ G dµ„ d¶e+¦  «        Z´ e´dd·¬$¦  «        Zµ G d¸„ d¹e+¦  «        Z¶ e¶dº¬1¦  «        Z· G d»„ d¼e+¦  «        Z¸ e¸ddd½¬¦  «        Z¹ G d¾„ d¿e+¦  «        Zº eºddÀ¬$¦  «        Z» G dÁ„ dÂe+¦  «        Z¼ e¼ddÃ¬$¦  «        Z½ G dÄ„ dÅe+¦  «        Z¾ e¾ddÆ¬$¦  «        Z¿ G dÇ„ dÈe+¦  «        ZÀ eÀdÉ¬1¦  «        ZÁ G dÊ„ dËe+¦  «        ZÂ eÂd dÌ¬$¦  «        ZÃ G dÍ„ dÎe+¦  «        ZÄ eÄdÏ¬1¦  «        ZÅ G dÐ„ dÑe+¦  «        ZÆ eÆdddÒ¬¦  «        ZÇ G dÓ„ dÔe+¦  «        ZÈ eÈdÕ¬1¦  «        ZÉ G dÖ„ d×e+¦  «        ZÊ eÊdØ¬1¦  «        ZË G dÙ„ dÚe+¦  «        ZÌ eÌdÛ¬1¦  «        ZÍdÜ„ ZÎ G dÝ„ dÞe+¦  «        ZÏ eÏddß¬$¦  «        ZÐ G dà„ dáe+¦  «        ZÑ eÑddâ¬ˆ¦  «        ZÒ G dã„ däe+¦  «        ZÓ eÓdå¬1¦  «        ZÔ G dæ„ dçe+¦  «        ZÕ eÕdè¬1¦  «        ZÖ G dé„ dêe+¦  «        Z× e×ddë¬$¦  «        ZØdì„ ZÙ G dí„ dîe+¦  «        ZÚ eÚddï¬$¦  «        ZÛ G dð„ dñe+¦  «        ZÜ eÜddò¬$¦  «        ZÝ G dó„ dôe+¦  «        ZÞ eÞddõ¬$¦  «        Zß G dö„ d÷e+¦  «        Zà eàddø¬$¦  «        Zá G dù„ dúe+¦  «        Zâ eâdû¬1¦  «        Zã G dü„ dýe+¦  «        Zä eäddþ¬$¦  «        Zå G dÿ„ �d e+¦  «        Zæ eæ�d¬1¦  «        Zç G �d„ �de+¦  «        Zè eèd�d¬$¦  «        Zé�d„ Zê G �d„ �de+¦  «        Zë eëd�d¬$¦  «        Zì G �d	„ �d
e+¦  «        Zí eíd�d¬$¦  «        Zî G �d„ �de+¦  «        Zï eï�d¬1¦  «        Zð G �d„ �de+¦  «        Zñ eñ�d¬1¦  «        Zò G �d„ �de+¦  «        Zó eód�d¬$¦  «        Zô G �d„ �de+¦  «        Zõ eõd�d¬$¦  «        Zö G �d„ �de+¦  «        Z÷ e÷�d¬1¦  «        Zø G �d„ �de+¦  «        Zù eùdd�d¬¦  «        Zú G �d„ �de+¦  «        Zû eûd�d ¬$¦  «        Zü G �d!„ �d"e+¦  «        Zý eý�d#¬1¦  «        Zþ G �d$„ �d%e+¦  «        Zÿ eÿ�d&d�d'¬¦  «        �Z  G �d(„ �d)e+¦  «        �Z �ed�d*¬$¦  «        �Z G �d+„ �d,e+¦  «        �Z �e�d-¬1¦  «        �Z �e�d.¬1¦  «        �Z G �d/„ �d0e+¦  «        �Z �ed�d1¬$¦  «        �Z G �d2„ �d3e+¦  «        �Z �e�d4¬1¦  «        �Z	 G �d5„ �d6e+¦  «        �Z
 �e
d�d7¬$¦  «        �Z G �d8„ �d9e+¦  «        �Z �e�d&d�d:¬¦  «        �Z G �d;„ �d<e+¦  «        �Z �e�d=¬1¦  «        �Z G �d>„ �d?e+¦  «        �Z �e�d@¬1¦  «        �Z G �dA„ �dBe+¦  «        �Z�dC�Z G �dD„ �dE�e¦  «        �Z �edd�dF¬¦  «        �Z �edd�dG¬¦  «        �Zg �dH¢�Z G �dI„ �dJ¦  «        �Z�eD ]�Z �e�e�e �e�e¦  «        ¦  «         Œ G �dK„ �dLe+¦  «        �Z �edd�dM¬¦  «        �Z G �dN„ �dOe+¦  «        �Z �ed�dP¬$¦  «        �Z�dQ„ �Z�dR„ �Z �dS„ �Z! G �dT„ �dUe+¦  «        �Z" �e"�dVd�¬W¦  «        �Z# G �dX„ �dYe+¦  «        �Z$ �e$d�dZ¬$¦  «        �Z% G �d[„ �d\e+¦  «        �Z& �e&�d]¬1¦  «        �Z' G �d^„ �d_ec¦  «        �Z( G �d`„ �dae+¦  «        �Z) �e)dd�db¬¦  «        �Z* G �dc„ �dde+¦  «        �Z+ �e+�de¬1¦  «        �Z, �e+ejN         ejN        �df¬¦  «        �Z- G �dg„ �dhe¼¦  «        �Z. �e.d�di¬$¦  «        �Z/ G �dj„ �dke+¦  «        �Z0 �e0dd%ejN        z  �dl¬¦  «        �Z1 G �dm„ �dne+¦  «        �Z2 �e2�do¬1¦  «        �Z3 G �dp„ �dqe+¦  «        �Z4 �e4d �dr¬$¦  «        �Z5 G �ds„ �dte+¦  «        �Z6 �e6�du�dv�¬w¦  «        �Z7�dx„ �Z8 G �dy„ �dze+¦  «        �Z9 �e9�d{�d|dd�¬}¦  «        �Z: G �d~„ �de+¦  «        �Z; G �d€„ �d�e+¦  «        �Z< �e<�d‚d e�j=        �¬ƒ¦  «        �Z> G �d„„ �d…e+¦  «        �Z? �e?d�d†¬$¦  «        �Z@ �eA �eB¦   «         � C                    ¦   «         � D                    ¦   «         ¦  «        �ZE e(�eEe+¦  «        \  �ZF�ZG�eF�eGz   �dgz   �ZHdS (ˆ  é    N)ÚIterable)ÚwrapsÚcached_property©Ú
Polynomial)ÚBSpline)Úextend_notes_in_docstringÚreplace_notes_in_docstringÚinherit_docstring_from)ÚLowLevelCallable)Úoptimize)Ú	integrate)Ú_lazyselectÚ
_lazywhereé   )Ú_stats)Útukeylambda_varianceÚtukeylambda_kurtosis)	Ú_vectorize_rvs_over_shapesÚget_distribution_namesÚ	_kurtosisÚ_isintegralÚrv_continuousÚ_skewÚ_get_fixed_fit_valueÚ_check_shapeÚ
_ShapeInfo)ÚkolmognÚkolmognpÚkolmogni)Ú_XMINÚ_LOGXMINÚ_EULERÚ_ZETA3Ú_SQRT_PIÚ_SQRT_2_OVER_PIÚ_LOG_SQRT_2_OVER_PI)ÚCensoredData)Úroot_scalar)ÚFitErrorc                 óÞ   — |                       dd¦  «         |                       dd¦  «         |                       dd¦  «         |                       dd¦  «         | rt          d| z  ¦  «        ‚dS )a†  
    Remove the optimizer-related keyword arguments 'loc', 'scale' and
    'optimizer' from `kwds`.  Then check that `kwds` is empty, and
    raise `TypeError("Unknown arguments: %s." % kwds)` if it is not.

    This function is used in the fit method of distributions that override
    the default method and do not use the default optimization code.

    `kwds` is modified in-place.
    ÚlocNÚscaleÚ	optimizerÚmethodzUnknown arguments: %s.)ÚpopÚ	TypeError)Úkwdss    ú]/var/www/surfInsights/venv3-11/lib/python3.11/site-packages/scipy/stats/_continuous_distns.pyÚ_remove_optimizer_parametersr4   '   sz   € ð 	‡H‚HˆU�DÑÔÐØ‡H‚HˆW�dÑÔÐØ‡H‚Hˆ[˜$ÑÔÐØ‡H‚HˆX�tÑÔÐØð 9ÝÐ0°4Ñ7Ñ8Ô8Ð8ð9ð 9ó    c                 ó<   ‡ — t          ‰ ¦  «        ˆ fd„¦   «         }|S )Nc                 óB  •— |                      dd¦  «                             ¦   «         }t          |t          ¦  «        }|dk    s|rD|                     ¦   «         dk    r, t          t          | ¦  «        | ¦  «        j        |g|¢R i |¤ŽS |r|j        } ‰| |g|¢R i |¤ŽS )Nr/   ÚmleÚmmr   )	ÚgetÚlowerÚ
isinstancer(   Únum_censoredÚsuperÚtypeÚfitÚ_uncensored)ÚselfÚdataÚargsr2   r/   ÚcensoredÚfuns         €r3   Úwrapperz _call_super_mom.<locals>.wrapper>   s»   ø€ à—’˜( EÑ*Ô*×0Ò0Ñ2Ô2ˆÝ˜d¥LÑ1Ô1ˆØ�TŠ>ˆ>˜hˆ>¨4×+<Ò+<Ñ+>Ô+>ÀÒ+BÐ+BØ.•5�˜d™œ TÑ*Ô*Ô.¨tÐC°dÐCÐCÐC¸dÐCÐCÐCàð (ð Ô'�Ø�3�t˜TÐ1 DÐ1Ð1Ð1¨DÐ1Ð1Ð1r5   )r   )rF   rG   s   ` r3   Ú_call_super_momrH   :   s5   ø€ õ ˆ3�Z„Zð2ð 2ð 2ð 2ñ „Zð2ð €Nr5   c                 ó¸   ‡ — |p|dz
  }||z
  }ˆ fd„} |||¦  «        s;|dz  }||z
  }d}t          j        |¦  «        rt          |¦  «        ‚ |||¦  «        ¯;|S )Nr   c                 ó|   •— t          j         ‰| ¦  «        ¦  «        t          j         ‰|¦  «        ¦  «        k    S ©N©ÚnpÚsign)ÚlbrackÚrbrackrF   s     €r3   Úinterval_contains_rootz1_get_left_bracket.<locals>.interval_contains_rootV   s2   ø€ åŒw�s�s˜6‘{”{Ñ#Ô#¥r¤w¨s¨s°6©{¬{Ñ';Ô';Ò;Ð;r5   é   zVThe solver could not find a bracket containing a root to an MLE first order condition.)rM   ÚisinfÚFitSolverError)rF   rP   rO   ÚdiffrQ   Úmsgs   `     r3   Ú_get_left_bracketrW   O   s¡   ø€ àÐ!�v ‘z€FØ�F‰?€Dð<ð <ð <ð <ð <ð %Ð$ V¨VÑ4Ô4ð &Ø�‰	ˆØ˜$‘ˆð7ˆåŒ8�FÑÔð 	&Ý  Ñ%Ô%Ð%ð %Ð$ V¨VÑ4Ô4ð &ð €Mr5   c                   ó<   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	S )
Ú	ksone_genaá  Kolmogorov-Smirnov one-sided test statistic distribution.

    This is the distribution of the one-sided Kolmogorov-Smirnov (KS)
    statistics :math:`D_n^+` and :math:`D_n^-`
    for a finite sample size ``n >= 1`` (the shape parameter).

    %(before_notes)s

    See Also
    --------
    kstwobign, kstwo, kstest

    Notes
    -----
    :math:`D_n^+` and :math:`D_n^-` are given by

    .. math::

        D_n^+ &= \text{sup}_x (F_n(x) - F(x)),\\
        D_n^- &= \text{sup}_x (F(x) - F_n(x)),\\

    where :math:`F` is a continuous CDF and :math:`F_n` is an empirical CDF.
    `ksone` describes the distribution under the null hypothesis of the KS test
    that the empirical CDF corresponds to :math:`n` i.i.d. random variates
    with CDF :math:`F`.

    %(after_notes)s

    References
    ----------
    .. [1] Birnbaum, Z. W. and Tingey, F.H. "One-sided confidence contours
       for probability distribution functions", The Annals of Mathematical
       Statistics, 22(4), pp 592-596 (1951).

    Examples
    --------
    >>> import numpy as np
    >>> from scipy.stats import ksone
    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots(1, 1)

    Display the probability density function (``pdf``):

    >>> n = 1e+03
    >>> x = np.linspace(ksone.ppf(0.01, n),
    ...                 ksone.ppf(0.99, n), 100)
    >>> ax.plot(x, ksone.pdf(x, n),
    ...         'r-', lw=5, alpha=0.6, label='ksone pdf')

    Alternatively, the distribution object can be called (as a function)
    to fix the shape, location and scale parameters. This returns a "frozen"
    RV object holding the given parameters fixed.

    Freeze the distribution and display the frozen ``pdf``:

    >>> rv = ksone(n)
    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
    >>> ax.legend(loc='best', frameon=False)
    >>> plt.show()

    Check accuracy of ``cdf`` and ``ppf``:

    >>> vals = ksone.ppf([0.001, 0.5, 0.999], n)
    >>> np.allclose([0.001, 0.5, 0.999], ksone.cdf(vals, n))
    True

    c                 ó@   — |dk    |t          j        |¦  «        k    z  S ©Nr   ©rM   Úround©rB   Úns     r3   Ú	_argcheckzksone_gen._argcheckª   ó   € Ø�Q’˜1¥¤¨¡¤Ò+Ñ,Ð,r5   c                 ó@   — t          dddt          j        fd¦  «        gS ©Nr_   Tr   ©TF©r   rM   Úinf©rB   s    r3   Ú_shape_infozksone_gen._shape_info­   ó   € Ý˜3  q­"¬& k°=ÑAÔAÐBÐBr5   c                 ó.   — t          j        ||¦  «         S rK   )ÚscuÚ	_smirnovp©rB   Úxr_   s      r3   Ú_pdfzksone_gen._pdf°   s   € Ý”˜a Ñ#Ô#Ð#Ð#r5   c                 ó,   — t          j        ||¦  «        S rK   )rk   Ú	_smirnovcrm   s      r3   Ú_cdfzksone_gen._cdf³   s   € ÝŒ}˜Q Ñ"Ô"Ð"r5   c                 ó,   — t          j        ||¦  «        S rK   )ÚscÚsmirnovrm   s      r3   Ú_sfzksone_gen._sf¶   s   € ÝŒz˜!˜QÑÔÐr5   c                 ó,   — t          j        ||¦  «        S rK   )rk   Ú
_smirnovci©rB   Úqr_   s      r3   Ú_ppfzksone_gen._ppf¹   s   € ÝŒ~˜a Ñ#Ô#Ð#r5   c                 ó,   — t          j        ||¦  «        S rK   )rt   Úsmirnoviry   s      r3   Ú_isfzksone_gen._isf¼   ó   € ÝŒ{˜1˜aÑ Ô Ð r5   N)Ú__name__Ú
__module__Ú__qualname__Ú__doc__r`   rh   ro   rr   rv   r{   r~   © r5   r3   rY   rY   f   s�   € € € € € ðBð BðF-ð -ð -ðCð Cð Cð$ð $ð $ð#ð #ð #ð ð  ð  ð$ð $ð $ð!ð !ð !ð !ð !r5   rY   ç        ç      ð?Úksone)ÚaÚbÚnamec                   óB   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
S )Ú	kstwo_genad  Kolmogorov-Smirnov two-sided test statistic distribution.

    This is the distribution of the two-sided Kolmogorov-Smirnov (KS)
    statistic :math:`D_n` for a finite sample size ``n >= 1``
    (the shape parameter).

    %(before_notes)s

    See Also
    --------
    kstwobign, ksone, kstest

    Notes
    -----
    :math:`D_n` is given by

    .. math::

        D_n = \text{sup}_x |F_n(x) - F(x)|

    where :math:`F` is a (continuous) CDF and :math:`F_n` is an empirical CDF.
    `kstwo` describes the distribution under the null hypothesis of the KS test
    that the empirical CDF corresponds to :math:`n` i.i.d. random variates
    with CDF :math:`F`.

    %(after_notes)s

    References
    ----------
    .. [1] Simard, R., L'Ecuyer, P. "Computing the Two-Sided
       Kolmogorov-Smirnov Distribution",  Journal of Statistical Software,
       Vol 39, 11, 1-18 (2011).

    Examples
    --------
    >>> import numpy as np
    >>> from scipy.stats import kstwo
    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots(1, 1)

    Display the probability density function (``pdf``):

    >>> n = 10
    >>> x = np.linspace(kstwo.ppf(0.01, n),
    ...                 kstwo.ppf(0.99, n), 100)
    >>> ax.plot(x, kstwo.pdf(x, n),
    ...         'r-', lw=5, alpha=0.6, label='kstwo pdf')

    Alternatively, the distribution object can be called (as a function)
    to fix the shape, location and scale parameters. This returns a "frozen"
    RV object holding the given parameters fixed.

    Freeze the distribution and display the frozen ``pdf``:

    >>> rv = kstwo(n)
    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
    >>> ax.legend(loc='best', frameon=False)
    >>> plt.show()

    Check accuracy of ``cdf`` and ``ppf``:

    >>> vals = kstwo.ppf([0.001, 0.5, 0.999], n)
    >>> np.allclose([0.001, 0.5, 0.999], kstwo.cdf(vals, n))
    True

    c                 ó@   — |dk    |t          j        |¦  «        k    z  S r[   r\   r^   s     r3   r`   zkstwo_gen._argcheck  ra   r5   c                 ó@   — t          dddt          j        fd¦  «        gS rc   re   rg   s    r3   rh   zkstwo_gen._shape_info	  ri   r5   c                 ób   — dt          |t          ¦  «        s|nt          j        |¦  «        z  dfS ©Nç      à?r†   )r<   r   rM   Ú
asanyarrayr^   s     r3   Ú_get_supportzkstwo_gen._get_support  s4   € Ø�j¨­HÑ5Ô5ÐK�Q�Q½2¼=ÈÑ;KÔ;KÑLØðð 	r5   c                 ó"   — t          ||¦  «        S rK   )r   rm   s      r3   ro   zkstwo_gen._pdf  s   € Ý˜˜1‰~Œ~Ðr5   c                 ó"   — t          ||¦  «        S rK   ©r   rm   s      r3   rr   zkstwo_gen._cdf  s   € Ý�q˜!‰}Œ}Ðr5   c                 ó&   — t          ||d¬¦  «        S ©NF©Úcdfr–   rm   s      r3   rv   zkstwo_gen._sf  s   € Ý�q˜! Ð'Ñ'Ô'Ð'r5   c                 ó&   — t          ||d¬¦  «        S )NTr™   ©r    ry   s      r3   r{   zkstwo_gen._ppf  s   € Ý˜˜1 $Ð'Ñ'Ô'Ð'r5   c                 ó&   — t          ||d¬¦  «        S r˜   rœ   ry   s      r3   r~   zkstwo_gen._isf  s   € Ý˜˜1 %Ð(Ñ(Ô(Ð(r5   N)r€   r�   r‚   rƒ   r`   rh   r“   ro   rr   rv   r{   r~   r„   r5   r3   rŒ   rŒ   Ã   sœ   € € € € € ðAð AðD-ð -ð -ðCð Cð Cðð ð ðð ð ðð ð ð(ð (ð (ð(ð (ð (ð)ð )ð )ð )ð )r5   rŒ   Úkstwo)Úmomtyperˆ   r‰   rŠ   c                   ó6   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	dS )	Úkstwobign_gena  Limiting distribution of scaled Kolmogorov-Smirnov two-sided test statistic.

    This is the asymptotic distribution of the two-sided Kolmogorov-Smirnov
    statistic :math:`\sqrt{n} D_n` that measures the maximum absolute
    distance of the theoretical (continuous) CDF from the empirical CDF.
    (see `kstest`).

    %(before_notes)s

    See Also
    --------
    ksone, kstwo, kstest

    Notes
    -----
    :math:`\sqrt{n} D_n` is given by

    .. math::

        D_n = \text{sup}_x |F_n(x) - F(x)|

    where :math:`F` is a continuous CDF and :math:`F_n` is an empirical CDF.
    `kstwobign`  describes the asymptotic distribution (i.e. the limit of
    :math:`\sqrt{n} D_n`) under the null hypothesis of the KS test that the
    empirical CDF corresponds to i.i.d. random variates with CDF :math:`F`.

    %(after_notes)s

    References
    ----------
    .. [1] Feller, W. "On the Kolmogorov-Smirnov Limit Theorems for Empirical
       Distributions",  Ann. Math. Statist. Vol 19, 177-189 (1948).

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   zkstwobign_gen._shape_infoI  ó   € Øˆ	r5   c                 ó,   — t          j        |¦  «         S rK   )rk   Ú_kolmogp©rB   rn   s     r3   ro   zkstwobign_gen._pdfL  s   € Ý”˜Q‘”ÐÐr5   c                 ó*   — t          j        |¦  «        S rK   )rk   Ú_kolmogcr¦   s     r3   rr   zkstwobign_gen._cdfO  s   € ÝŒ|˜A‰ŒÐr5   c                 ó*   — t          j        |¦  «        S rK   )rt   Ú
kolmogorovr¦   s     r3   rv   zkstwobign_gen._sfR  s   € ÝŒ}˜QÑÔÐr5   c                 ó*   — t          j        |¦  «        S rK   )rk   Ú	_kolmogci©rB   rz   s     r3   r{   zkstwobign_gen._ppfU  s   € ÝŒ}˜QÑÔÐr5   c                 ó*   — t          j        |¦  «        S rK   )rt   Úkolmogir­   s     r3   r~   zkstwobign_gen._isfX  s   € ÝŒz˜!‰}Œ}Ðr5   N)
r€   r�   r‚   rƒ   rh   ro   rr   rv   r{   r~   r„   r5   r3   r¡   r¡   $  sy   € € € € € ð#ð #ðHð ð ð ð  ð  ðð ð ð ð  ð  ð ð  ð  ðð ð ð ð r5   r¡   Ú	kstwobign)rˆ   rŠ   rR   c                 óH   — t          j        | dz   dz  ¦  «        t          z  S ©NrR   ç       @)rM   ÚexpÚ_norm_pdf_C©rn   s    r3   Ú	_norm_pdfr·   h  s!   € ÝŒ6�1�a‘4�%˜‘)ÑÔ�{Ñ*Ð*r5   c                 ó$   — | dz   dz  t           z
  S r²   )Ú_norm_pdf_logCr¶   s    r3   Ú_norm_logpdfrº   l  s   € Øˆq‰Dˆ5�3‰;�Ñ'Ð'r5   c                 ó*   — t          j        | ¦  «        S rK   )rt   Úndtrr¶   s    r3   Ú	_norm_cdfr½   p  s   € ÝŒ7�1‰:Œ:Ðr5   c                 ó*   — t          j        | ¦  «        S rK   )rt   Úlog_ndtrr¶   s    r3   Ú_norm_logcdfrÀ   t  s   € ÝŒ;�q‰>Œ>Ðr5   c                 ó*   — t          j        | ¦  «        S rK   )rt   Úndtri©rz   s    r3   Ú	_norm_ppfrÄ   x  s   € ÝŒ8�A‰;Œ;Ðr5   c                 ó"   — t          |  ¦  «        S rK   ©r½   r¶   s    r3   Ú_norm_sfrÇ   |  s   € Ý�a�R‰=Œ=Ðr5   c                 ó"   — t          |  ¦  «        S rK   ©rÀ   r¶   s    r3   Ú_norm_logsfrÊ   €  s   € Ý˜˜ÑÔÐr5   c                 ó"   — t          | ¦  «         S rK   ©rÄ   rÃ   s    r3   Ú	_norm_isfrÍ   „  s   € Ý�a‰LŒLˆ=Ðr5   c                   óž   — e Zd ZdZd„ Zdd„Zd„ Zd„ Zd„ Zd„ Z	d	„ Z
d
„ Zd„ Zd„ Zd„ Zd„ Ze eed¬¦  «        d„ ¦   «         ¦   «         Zd„ ZdS )Únorm_gena�  A normal continuous random variable.

    The location (``loc``) keyword specifies the mean.
    The scale (``scale``) keyword specifies the standard deviation.

    %(before_notes)s

    Notes
    -----
    The probability density function for `norm` is:

    .. math::

        f(x) = \frac{\exp(-x^2/2)}{\sqrt{2\pi}}

    for a real number :math:`x`.

    %(after_notes)s

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   znorm_gen._shape_infoŸ  r£   r5   Nc                 ó,   — |                      |¦  «        S rK   )Ústandard_normal©rB   ÚsizeÚrandom_states      r3   Ú_rvsznorm_gen._rvs¢  s   € Ø×+Ò+¨DÑ1Ô1Ð1r5   c                 ó    — t          |¦  «        S rK   ©r·   r¦   s     r3   ro   znorm_gen._pdf¥  s   € å˜‰|Œ|Ðr5   c                 ó    — t          |¦  «        S rK   ©rº   r¦   s     r3   Ú_logpdfznorm_gen._logpdf©  ó   € Ý˜A‰ŒÐr5   c                 ó    — t          |¦  «        S rK   rÆ   r¦   s     r3   rr   znorm_gen._cdf¬  ó   € Ý˜‰|Œ|Ðr5   c                 ó    — t          |¦  «        S rK   rÉ   r¦   s     r3   Ú_logcdfznorm_gen._logcdf¯  rÜ   r5   c                 ó    — t          |¦  «        S rK   ©rÇ   r¦   s     r3   rv   znorm_gen._sf²  s   € Ý˜‰{Œ{Ðr5   c                 ó    — t          |¦  «        S rK   )rÊ   r¦   s     r3   Ú_logsfznorm_gen._logsfµ  s   € Ý˜1‰~Œ~Ðr5   c                 ó    — t          |¦  «        S rK   rÌ   r­   s     r3   r{   znorm_gen._ppf¸  rÞ   r5   c                 ó    — t          |¦  «        S rK   ©rÍ   r­   s     r3   r~   znorm_gen._isf»  rÞ   r5   c                 ó   — dS )N)r…   r†   r…   r…   r„   rg   s    r3   r   znorm_gen._stats¾  ó   € Ø!Ð!r5   c                 óP   — dt          j        dt           j        z  ¦  «        dz   z  S ©Nr‘   rR   r   ©rM   ÚlogÚpirg   s    r3   Ú_entropyznorm_gen._entropyÁ  s    € Ø•B”F˜1�RœU™7‘O”O AÑ%Ñ&Ð&r5   a}          For the normal distribution, method of moments and maximum likelihood
        estimation give identical fits, and explicit formulas for the estimates
        are available.
        This function uses these explicit formulas for the maximum likelihood
        estimation of the normal distribution parameters, so the
        `optimizer` and `method` arguments are ignored.

©Únotesc                 óÌ  — |                      dd ¦  «        }|                      dd ¦  «        }t          |¦  «         |�|�t          d¦  «        ‚t          j        |¦  «        }t          j        |¦  «                             ¦   «         st          d¦  «        ‚|€|                     ¦   «         }n|}|€-t          j        ||z
  dz                       ¦   «         ¦  «        }n|}||fS )NÚflocÚfscaleú3All parameters fixed. There is nothing to optimize.ú$The data contains non-finite values.rR   )	r0   r4   Ú
ValueErrorrM   ÚasarrayÚisfiniteÚallÚmeanÚsqrt)rB   rC   r2   ró   rô   r,   r-   s          r3   r@   znorm_gen.fitÄ  sí   € ð �xŠx˜ Ñ%Ô%ˆØ—’˜( DÑ)Ô)ˆå$ TÑ*Ô*Ð*àÐ Ð 2õ ð )ñ *ô *ð *õ Œz˜$ÑÔˆåŒ{˜4Ñ Ô ×$Ò$Ñ&Ô&ð 	EÝÐCÑDÔDÐDàˆ<Ø—)’)‘+”+ˆCˆCàˆCàˆ>Ý”G˜d S™j¨1™_×2Ò2Ñ4Ô4Ñ5Ô5ˆEˆEàˆEà�EˆzÐr5   c                 óF   — |dz  dk    rt          j        |dz
  ¦  «        S dS )zŽ
        @returns Moments of standard normal distribution for integer n >= 0

        See eq. 16 of https://arxiv.org/abs/1209.4340v2
        rR   r   r   r…   )rt   Ú
factorial2r^   s     r3   Ú_munpznorm_gen._munpê  s*   € ð ˆq‰5�AŠ:ˆ:Ý”=  Q¡Ñ'Ô'Ð'à�2r5   ©NN)r€   r�   r‚   rƒ   rh   rÖ   ro   rÛ   rr   rà   rv   rä   r{   r~   r   rï   rH   r
   r   r@   rÿ   r„   r5   r3   rÏ   rÏ   ˆ  s,  € € € € € ðð ð,ð ð ð2ð 2ð 2ð 2ðð ð ðð ð ðð ð ðð ð ðð ð ðð ð ðð ð ðð ð ð"ð "ð "ð'ð 'ð 'ð ØÐ ð 6?ð @ñ @ô @ðð ñ@ô @ñ „_ðð<	ð 	ð 	ð 	ð 	r5   rÏ   Únorm)rŠ   c                   óD   — e Zd ZdZej        Zd„ Zd„ Zd„ Z	d„ Z
d„ Zd„ ZdS )	Ú	alpha_gena&  An alpha continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `alpha` ([1]_, [2]_) is:

    .. math::

        f(x, a) = \frac{1}{x^2 \Phi(a) \sqrt{2\pi}} *
                  \exp(-\frac{1}{2} (a-1/x)^2)

    where :math:`\Phi` is the normal CDF, :math:`x > 0`, and :math:`a > 0`.

    `alpha` takes ``a`` as a shape parameter.

    %(after_notes)s

    References
    ----------
    .. [1] Johnson, Kotz, and Balakrishnan, "Continuous Univariate
           Distributions, Volume 1", Second Edition, John Wiley and Sons,
           p. 173 (1994).
    .. [2] Anthony A. Salvia, "Reliability applications of the Alpha
           Distribution", IEEE Transactions on Reliability, Vol. R-34,
           No. 3, pp. 251-252 (1985).

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS ©Nrˆ   Fr   ©FFre   rg   s    r3   rh   zalpha_gen._shape_info  ó   € Ý˜3 ¨­2¬6 {°NÑCÔCÐDÐDr5   c                 ó^   — d|dz  z  t          |¦  «        z  t          |d|z  z
  ¦  «        z  S ©Nr†   rR   )r½   r·   ©rB   rn   rˆ   s      r3   ro   zalpha_gen._pdf  s0   € à�A�q‘D‰z�) A™,œ,Ñ&¥y°°3°q±5±Ñ'9Ô'9Ñ9Ð9r5   c                 ó    — dt          j        |¦  «        z  t          |d|z  z
  ¦  «        z   t          j        t          |¦  «        ¦  «        z
  S )Néþÿÿÿr†   )rM   rí   rº   r½   r
  s      r3   rÛ   zalpha_gen._logpdf"  s>   € Ø•"”&˜‘)”)‰|�l¨1¨S°©U©7Ñ3Ô3Ñ3µb´f½YÀq¹\¼\Ñ6JÔ6JÑJÐJr5   c                 óL   — t          |d|z  z
  ¦  «        t          |¦  «        z  S ©Nr†   rÆ   r
  s      r3   rr   zalpha_gen._cdf%  s#   € Ý˜˜3˜q™5™Ñ!Ô!¥I¨a¡L¤LÑ0Ð0r5   c           
      óp   — dt          j        |t          |t          |¦  «        z  ¦  «        z
  ¦  «        z  S r  )rM   rø   rÄ   r½   ©rB   rz   rˆ   s      r3   r{   zalpha_gen._ppf(  s.   € Ø•2”:˜a¥)¨A­i¸©l¬l©NÑ";Ô";Ñ;Ñ<Ô<Ñ<Ð<r5   c                 óD   — t           j        gdz  t           j        gdz  z   S ©NrR   ©rM   rf   Únan©rB   rˆ   s     r3   r   zalpha_gen._stats+  s   € Ý”ˆx˜‰z�RœV˜H Q™JÑ&Ð&r5   N)r€   r�   r‚   rƒ   r   Ú_open_support_maskÚ_support_maskrh   ro   rÛ   rr   r{   r   r„   r5   r3   r  r  ù  sˆ   € € € € € ðð ð> "Ô4€MðEð Eð Eð:ð :ð :ðKð Kð Kð1ð 1ð 1ð=ð =ð =ð'ð 'ð 'ð 'ð 'r5   r  Úalphac                   ó<   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	S )
Ú
anglit_gena  An anglit continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `anglit` is:

    .. math::

        f(x) = \sin(2x + \pi/2) = \cos(2x)

    for :math:`-\pi/4 \le x \le \pi/4`.

    %(after_notes)s

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   zanglit_gen._shape_infoF  r£   r5   c                 ó0   — t          j        d|z  ¦  «        S r  )rM   Úcosr¦   s     r3   ro   zanglit_gen._pdfI  s   € åŒv�a˜‘c‰{Œ{Ðr5   c                 óP   — t          j        |t           j        dz  z   ¦  «        dz  S ©Né   r³   ©rM   Úsinrî   r¦   s     r3   rr   zanglit_gen._cdfM  s!   € ÝŒv�a�œ˜a™‘iÑ Ô  #Ñ%Ð%r5   c                 óP   — t          j        |t           j        dz  z   ¦  «        dz  S r  )rM   r  rî   r¦   s     r3   rv   zanglit_gen._sfP  s!   € ÝŒv�a�"œ% !™)‘mÑ$Ô$¨Ñ+Ð+r5   c                 ón   — t          j        t          j        |¦  «        ¦  «        t           j        dz  z
  S ©Nr   )rM   Úarcsinrü   rî   r­   s     r3   r{   zanglit_gen._ppfS  s%   € ÝŒy�œ ™œÑ$Ô$¥R¤U¨1¡WÑ,Ð,r5   c                 ó®   — dt           j        t           j        z  dz  dz
  ddt           j        dz  dz
  z  t           j        t           j        z  dz
  dz  z  fS )	Nr…   é   r‘   r  r   é`   é   rR   ©rM   rî   rg   s    r3   r   zanglit_gen._statsV  sH   € Ø•B”E�"œ%‘K ‘N 3Ñ&¨¨Rµ´¸±¸B±Ñ-?ÅÄÅrÄuÁÈQÁÐQRÑ@RÑ-RÐRÐRr5   c                 ó0   — dt          j        d¦  «        z
  S ©Nr   rR   ©rM   rí   rg   s    r3   rï   zanglit_gen._entropyY  ó   € Ø•”˜‘”‰{Ðr5   N)r€   r�   r‚   rƒ   rh   ro   rr   rv   r{   r   rï   r„   r5   r3   r  r  2  sŠ   € € € € € ðð ð&ð ð ðð ð ð&ð &ð &ð,ð ,ð ,ð-ð -ð -ðSð Sð Sðð ð ð ð r5   r  r   Úanglitc                   ó6   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	dS )	Úarcsine_gena  An arcsine continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `arcsine` is:

    .. math::

        f(x) = \frac{1}{\pi \sqrt{x (1-x)}}

    for :math:`0 < x < 1`.

    %(after_notes)s

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   zarcsine_gen._shape_infot  r£   r5   c                 ó´   — t          j        d¬¦  «        5  dt           j        z  t          j        |d|z
  z  ¦  «        z  cd d d ¦  «         S # 1 swxY w Y   d S )NÚignore©Údivider†   r   )rM   Úerrstaterî   rü   r¦   s     r3   ro   zarcsine_gen._pdfw  s™   € åŒ[ Ð)Ñ)Ô)ð 	.ð 	.Ø•r”u‘9�RœW Q¨¨!©¡WÑ-Ô-Ñ-ð	.ð 	.ð 	.ð 	.ñ 	.ô 	.ð 	.ð 	.ð 	.ð 	.ð 	.ð 	.øøøð 	.ð 	.ð 	.ð 	.ð 	.ð 	.ó   –*AÁAÁAc                 ón   — dt           j        z  t          j        t          j        |¦  «        ¦  «        z  S ©Nr³   )rM   rî   r&  rü   r¦   s     r3   rr   zarcsine_gen._cdf|  s%   € Ø•2”5‰y�œ¥2¤7¨1¡:¤:Ñ.Ô.Ñ.Ð.r5   c                 óP   — t          j        t           j        dz  |z  ¦  «        dz  S r;  r!  r­   s     r3   r{   zarcsine_gen._ppf  s!   € ÝŒv•b”e˜C‘i ‘kÑ"Ô" CÑ'Ð'r5   c                 ó   — d}d}d}d}||||fS )Nr‘   g      À?r   ç      ø¿r„   ©rB   ÚmuÚmu2Úg1Úg2s        r3   r   zarcsine_gen._stats‚  s$   € ØˆØˆØˆØˆØ�3˜˜BˆÐr5   c                 ó   — dS )Ng‘Á”°•ëÎ¿r„   rg   s    r3   rï   zarcsine_gen._entropy‰  s   € Ø&Ð&r5   N©
r€   r�   r‚   rƒ   rh   ro   rr   r{   r   rï   r„   r5   r3   r2  r2  `  sx   € € € € € ðð ð&ð ð ð.ð .ð .ð
/ð /ð /ð(ð (ð (ðð ð ð'ð 'ð 'ð 'ð 'r5   r2  Úarcsinec                   ó   — e Zd ZdZd„ ZdS )ÚFitDataErrorz=Raised when input data is inconsistent with fixed parameters.c                 ó*   — d|›d|›d|›d�f| _         d S )Nz>Invalid values in `data`.  Maximum likelihood estimation with z requires that z < (x - loc)/scale  < z for each x in `data`.©rD   )rB   Údistrr;   Úuppers       r3   Ú__init__zFitDataError.__init__•  sH   € ðBØ$ðBð BØ7<ðBð Bà"'ðBð Bð Bð
ˆŒ	ˆ	ˆ	r5   N©r€   r�   r‚   rƒ   rM  r„   r5   r3   rH  rH  �  s)   € € € € € ØGÐGð
ð 
ð 
ð 
ð 
r5   rH  c                   ó   — e Zd ZdZd„ ZdS )rT   zN
    Raised when a solver fails to converge while fitting a distribution.
    c                 óL   — d}||                      dd¦  «        z  }|f| _        d S )Nz1Solver for the MLE equations failed to converge: ú
Ú )ÚreplacerD   )rB   ÚmesgÚemsgs      r3   rM  zFitSolverError.__init__£  s,   € ØBˆØ�—’˜T 2Ñ&Ô&Ñ&ˆØ�GˆŒ	ˆ	ˆ	r5   NrN  r„   r5   r3   rT   rT   �  s-   € € € € € ðð ð
ð ð ð ð r5   rT   c                 óp   — t          j        | |z   ¦  «        }||| t          j        | ¦  «        z   z  z
  }|S rK   ©rt   Úpsi)rˆ   r‰   r_   Ús1ÚpsiabÚfuncs         r3   Ú_beta_mle_ar\  ©  s8   € õ ŒF�1�q‘5‰MŒM€EØ��e�V�bœf Q™iœiÑ'Ñ(Ñ(€DØ€Kr5   c                 ó¶   — | \  }}t          j        ||z   ¦  «        }||| t          j        |¦  «        z   z  z
  ||| t          j        |¦  «        z   z  z
  g}|S rK   rW  )Úthetar_   rY  Ús2rˆ   r‰   rZ  r[  s           r3   Ú_beta_mle_abr`  ²  sb   € ð �D€A€qÝŒF�1�q‘5‰MŒM€EØ��u�f�rœv a™yœyÑ(Ñ)Ñ)Ø��u�f�rœv a™yœyÑ(Ñ)Ñ)ð+€Dà€Kr5   c                   ó    ‡ — e Zd ZdZd„ Zdd„Zd„ Zd„ Zd„ Zd„ Z	d	„ Z
d
„ Zd„ Zˆ fd„Ze eed¬¦  «        ˆ fd„¦   «         ¦   «         Zd„ Zˆ xZS )Úbeta_genaì  A beta continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `beta` is:

    .. math::

        f(x, a, b) = \frac{\Gamma(a+b) x^{a-1} (1-x)^{b-1}}
                          {\Gamma(a) \Gamma(b)}

    for :math:`0 <= x <= 1`, :math:`a > 0`, :math:`b > 0`, where
    :math:`\Gamma` is the gamma function (`scipy.special.gamma`).

    `beta` takes :math:`a` and :math:`b` as shape parameters.

    %(after_notes)s

    %(example)s

    c                 ó‚   — t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }||gS ©Nrˆ   Fr   r  r‰   re   ©rB   ÚiaÚibs      r3   rh   zbeta_gen._shape_infoØ  ó=   € Ý˜˜U Q­¬ K°Ñ@Ô@ˆÝ˜˜U Q­¬ K°Ñ@Ô@ˆØ�Bˆxˆr5   Nc                 ó0   — |                      |||¦  «        S rK   ©Úbeta)rB   rˆ   r‰   rÔ   rÕ   s        r3   rÖ   zbeta_gen._rvsÝ  s   € Ø× Ò   A tÑ,Ô,Ð,r5   c                 óŒ   — t          j        d¬¦  «        5  t          j        |||¦  «        cd d d ¦  «         S # 1 swxY w Y   d S ©Nr5  ©Úover)rM   r8  rk   Ú	_beta_pdf©rB   rn   rˆ   r‰   s       r3   ro   zbeta_gen._pdfà  sŒ   € õ Œ[˜hÐ'Ñ'Ô'ð 	*ð 	*Ý”=  A qÑ)Ô)ð	*ð 	*ð 	*ð 	*ñ 	*ô 	*ð 	*ð 	*ð 	*ð 	*ð 	*ð 	*øøøð 	*ð 	*ð 	*ð 	*ð 	*ð 	*ó   –9¹=Á =c                 óš   — t          j        |dz
  | ¦  «        t          j        |dz
  |¦  «        z   }|t          j        ||¦  «        z  }|S r  )rt   Úxlog1pyÚxlogyÚbetaln)rB   rn   rˆ   r‰   ÚlPxs        r3   rÛ   zbeta_gen._logpdfç  sG   € ÝŒj˜˜S™ 1 "Ñ%Ô%­¬°°S±¸!Ñ(<Ô(<Ñ<ˆØ�rŒy˜˜A‰ŒÑˆØˆ
r5   c                 ó.   — t          j        |||¦  «        S rK   )rt   Úbetaincrq  s       r3   rr   zbeta_gen._cdfì  s   € ÝŒz˜!˜Q Ñ"Ô"Ð"r5   c                 ó.   — t          j        |||¦  «        S rK   )rt   Úbetainccrq  s       r3   rv   zbeta_gen._sfï  s   € ÝŒ{˜1˜a Ñ#Ô#Ð#r5   c                 ó.   — t          j        |||¦  «        S rK   )rt   Úbetainccinvrq  s       r3   r~   zbeta_gen._isfò  s   € ÝŒ~˜a  AÑ&Ô&Ð&r5   c                 ó.   — t          j        |||¦  «        S rK   )rk   Ú	_beta_ppf©rB   rz   rˆ   r‰   s       r3   r{   zbeta_gen._ppfõ  s   € ÝŒ}˜Q  1Ñ%Ô%Ð%r5   c                 ó&  — ||z   }||z  }||z  |dz  |dz   z  z  }d||z
  z  t          j        |dz   ¦  «        z  |dz   t          j        ||z  ¦  «        z  z  }d||z
  dz  |dz   z  ||z  |dz   z  z
  z  }||z  |dz   z  |dz   z  }||z  }	||||	fS )NrR   r   é   é   ©rM   rü   )
rB   rˆ   r‰   Úa_plus_bÚ
_beta_meanÚ_beta_varianceÚ_beta_skewnessÚ_beta_kurtosis_excess_nÚ_beta_kurtosis_excess_dÚ_beta_kurtosis_excesss
             r3   r   zbeta_gen._statsø  sÝ   € Ø�q‘5ˆØ�x‘Zˆ
Ø˜1™ ¨!¡¨x¸!©|Ñ <Ñ=ˆØ  A¡™;­¬°¸A±Ñ)>Ô)>Ñ>Ø$ q™L­B¬G°A¸±E©N¬NÑ:ñ<ˆà"#¨¨A©°¡z°XÀ±\Ñ'BØ'(¨1¡u°¸1±Ñ'=ñ(>ñ #?Ðà"# a¡%¨8°a©<Ñ"8¸HÀq¹LÑ"IÐØ 7Ð:QÑ QÐàØØØ!ð	#ð 	#r5   c                 ó  •‡‡— t          |t          ¦  «        r|                     ¦   «         }t          |¦  «        Št	          |¦  «        Šˆˆfd„}t          j        |d¦  «        \  }}t          ¦   «                              |||f¬¦  «        S )Nc                 óF  •— | \  }}d||z
  z  t          j        ||z   dz   ¦  «        z  ||z   dz   z  t          j        ||z  ¦  «        z  }|dz  |dz  d|z  dz
  z  z
  |dz  |dz   z  z   d|z  |z  |dz   z  z
  }|||z  ||z   dz   z  ||z   dz   z  z  }|dz  }|‰z
  |‰z
  gS )NrR   r   rƒ  r‚  r„  )rn   rˆ   r‰   ÚskÚkurB  rC  s        €€r3   r[  z beta_gen._fitstart.<locals>.func  sÔ   ø€ Ø‰DˆAˆqØ�A�a‘C‘�œ  Q¡¨¡Ñ+Ô+Ñ+¨q°1©u°q©yÑ9½B¼GÀAÀaÁC¹L¼LÑHˆBØ�A‘˜˜1™˜a ™c !™e™Ñ$ q¨!¡t¨Q¨q©S¡zÑ1°A°a±C¸±E¸1¸Q¹3±KÑ?ˆBØ�!�A‘#�q˜‘s˜1‘u‘+˜q ™s 1™uÑ%Ñ%ˆBØ�!‰GˆBØ�r‘E˜2˜b™5�>Ð!r5   )r†   r†   rJ  )	r<   r(   Ú	_uncensorr   r   r   Úfsolver>   Ú	_fitstart)rB   rC   r[  rˆ   r‰   rB  rC  Ú	__class__s        @@€r3   r’  zbeta_gen._fitstart  s’   øøø€ Ý�d�LÑ)Ô)ð 	$Ø—>’>Ñ#Ô#ˆDå�4‰[Œ[ˆÝ�t‰_Œ_ˆð	"ð 	"ð 	"ð 	"ð 	"ð 	"õ Œ˜t ZÑ0Ô0‰ˆˆ1Ý‰wŒw× Ò  ¨Q°¨FÐ Ñ3Ô3Ð3r5   zÓ        In the special case where `method="MLE"` and
        both `floc` and `fscale` are given, a
        `ValueError` is raised if any value `x` in `data` does not satisfy
        `floc < x < floc + fscale`.

rð   c           	      óª  •— |                      dd ¦  «        }|                      dd ¦  «        }|�|€ t          ¦   «         j        |g|¢R i |¤ŽS |                     dd ¦  «         |                     dd ¦  «         t	          |g d¢¦  «        }t	          |g d¢¦  «        }t          |¦  «         |�|�t          d¦  «        ‚t          j        |¦  «         	                    ¦   «         st          d¦  «        ‚t          j
        |¦  «        |z
  |z  }t          j        |dk    ¦  «        st          j        |dk    ¦  «        rt          d	|||z   ¬
¦  «        ‚|                     ¦   «         }|€|�—|�|}	d|z
  }d|z
  }n|}	|	|z  d|z
  z  }
t          j        t           |
|	t#          |¦  «        t          j        |¦  «                             ¦   «         fd¬¦  «        \  }}}}|dk    rt)          |¬¦  «        ‚|d         }
|�|	|
}	}
nËt          j        |¦  «                             ¦   «         }t+          j        | ¦  «                             ¦   «         }|d|z
  z  |                     d¬¦  «        z  dz
  }||z  }
d|z
  |z  }	t          j        t0          |
|	gt#          |¦  «        ||fd¬¦  «        \  }}}}|dk    rt)          |¬¦  «        ‚|\  }
}	|
|	||fS )Nró   rô   ©Úf0ÚfaÚfix_a)Úf1ÚfbÚfix_brõ   rö   r   r   rk  ©r;   rL  T)rD   Úfull_output)rT  )Úddof)r:   r>   r@   r0   r   r4   r÷   rM   rù   rú   ÚravelÚanyrH  rû   r   r‘  r\  Úlenrí   ÚsumrT   rt   Úlog1pÚvarr`  )rB   rC   rD   r2   ró   rô   r–  r™  Úxbarr‰   rˆ   r^  ÚinfoÚierrT  rY  r_  Úfacr“  s                     €r3   r@   zbeta_gen.fit  s'  ø€ ð �xŠx˜ Ñ%Ô%ˆØ—’˜( DÑ)Ô)ˆàˆ<˜6˜>à•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3ð 	�Š�˜ÑÔÐØ�Š�˜4Ñ Ô Ð å! $Ð(=Ð(=Ð(=Ñ>Ô>ˆÝ! $Ð(=Ð(=Ð(=Ñ>Ô>ˆå$ TÑ*Ô*Ð*àˆ>˜b˜nåð )ñ *ô *ð *õ Œ{˜4Ñ Ô ×$Ò$Ñ&Ô&ð 	EÝÐCÑDÔDÐDõ ”˜‘” Ñ%¨Ñ/ˆÝŒ6�$˜!’)ÑÔð 	H¥¤ t¨q¢yÑ 1Ô 1ð 	HÝ˜v¨T¸À¹ÐGÑGÔGÐGà�yŠy‰{Œ{ˆàˆ>˜R˜^ð ˆ~ð �Ø˜4‘x�Ø˜4‘x��à�ð �D‘˜A ™HÑ%ˆAõ &.¤_Ý˜QØ�˜T™œ¥B¤F¨4¡L¤L×$4Ò$4Ñ$6Ô$6Ð7Ø ð&ñ &ô &Ñ"ˆE�4˜˜dð
 �aŠxˆxÝ$¨$Ð/Ñ/Ô/Ð/Ø�a”ˆAàˆ~ð ˜!�1�øõ ”˜‘”×!Ò!Ñ#Ô#ˆBÝ”˜4˜%‘”×$Ò$Ñ&Ô&ˆBð ˜!˜d™(Ñ# d§h¢h°A hÑ&6Ô&6Ñ6¸Ñ:ˆCØ�s‘
ˆAØ�T‘˜SÑ ˆAõ &.¤_Ý˜q !˜fÝ˜$‘i”i  RÐ(Ø ð&ñ &ô &Ñ"ˆE�4˜˜dð
 �aŠxˆxÝ$¨$Ð/Ñ/Ô/Ð/Ø‰DˆAˆqà�!�T˜6Ð!Ð!r5   c                 ó
  — d„ }d„ }d„ }d„ }|dk    r|dk    r |||¦  «        S |dk    r$||z
  dk    r| ||¦  «        k    r |||¦  «        S |dk    r$||z
  dk    r| ||¦  «        k    r |||¦  «        S  |||¦  «        S )Nc                 óÚ   — t          j        | |¦  «        | dz
  t          j        | ¦  «        z  z
  |dz
  t          j        |¦  «        z  z
  | |z   dz
  t          j        | |z   ¦  «        z  z   S r-  )rt   rv  rX  ©rˆ   r‰   s     r3   Úregularz"beta_gen._entropy.<locals>.regular…  sf   € Ý”I˜a ‘O”O q¨1¡uµ´°q±	´	Ñ&9Ñ9Ø˜‘U�bœf Q™iœiÑ'ñ(Ø+,¨q©5°1©9½¼¸qÀ1¹u¹¼Ñ*EñFð Gr5   c                 óœ  — | |z   }dt          j        dt           j        z  ¦  «        t          j        | ¦  «        z   t          j        |¦  «        z   dt          j        |¦  «        z  z
  dz   z  }d|z  d|dz  z  z   |dz  z   d|d	z  z  z
  }d
| z  d| dz  z  z
  | dz  z
  | d	z  z   }d
|z  d|dz  z  z
  |dz  z
  |d	z  z   }|||z   |z   dz  z   S )Nr‘   rR   rƒ  r   én   é   ç       Àç      Àç      ÀiÎÿÿÿé
   éx   rì   )rˆ   r‰   Úsum_abÚlog_termÚt1Út2Út3s          r3   Úasymptotic_ab_largez.beta_gen._entropy.<locals>.asymptotic_ab_large‰  sí   € Ø˜‘UˆFØÝ”�q�œ‘w‘”¥"¤&¨¡)¤)Ñ+­b¬f°Q©i¬iÑ7¸!½B¼FÀ6¹N¼NÑ:JÑJÈQÑNñˆHð �V‘˜b ¨¡™oÑ-°¸±Ñ<¸qÀÈÁ¹~ÑMˆBØ�Q‘˜˜A˜t™G™Ñ# a¨¡gÑ-°°4±Ñ7ˆBØ�Q‘˜˜A˜t™G™Ñ# a¨¡gÑ-°°4±Ñ7ˆBØ˜r B™w¨™|¨sÑ2Ñ2Ð2r5   c                 óü  — | |z   }t          j        | ¦  «        | dz
  t          j        | ¦  «        z  z
  }dd|z  z  dd|z  z  z   |dz  dz  z
  |dz  dz  z
  |dz  dz  z   |d	z  d
z  z   |dz  d
z  z
  d|z  z   dd|z  z  z
  |dz  dz  z   |dz  dz  z   |dz  dz  z
  |d	z  d
z  z
  |dz  dz  z   }|t          j        | |z  ¦  «        z  t          j        |¦  «        z   dt          j        |¦  «        z  z
  }||z   |z   S )Nr   éÿÿÿÿrR   é   r°  r±  r´  r²  ç      Àéü   ç      Àr‚  é<   é~   )rt   ÚgammalnrX  rM   r£  rí   )rˆ   r‰   rµ  r·  r¸  r¶  s         r3   Úasymptotic_b_largez-beta_gen._entropy.<locals>.asymptotic_b_large“  sM  € Ø˜‘UˆFÝ”˜A‘” ! a¡%­2¬6°!©9¬9Ñ!4Ñ4ˆBà�Q�q‘S‘	˜A˜r !™t™HÑ$ q¨$¡w¨r¡zÑ1°A°t±G¸C±KÑ?À!ÀTÁ'È#Á+ÑMØ�T‘'˜#‘+ñØ ! 4¡¨¡ñ,Ø./°©hñ7Ø9:¸B¸v¹I¹ñGà˜$‘,˜q‘.ñ!à#)¨4¡<°Ñ#3ñ4à6<¸d±lÀ2±oñFð ˜$‘,˜sÑ"ñ#ð &,¨T¡\°#Ñ%5ñ6ð ð �bœh q¨¡s™mœmÑ+­b¬f°Q©i¬iÑ7¸!½B¼FÀ6¹N¼NÑ:JÑJˆHØ˜‘7˜XÑ%Ð%r5   c                 óž   — | dk    rdS t          j        | ¦  «        }t          |¦  «        }t          | d|z  z  ¦  «        dz   }|dd|z   z  z  S )Nr†   iè  r³  rR   é   )rM   Úlog10Úint)ÚvÚjÚdigitsÚds       r3   Úthreshold_largez*beta_gen._entropy.<locals>.threshold_largeŸ  sU   € Ø�CŠxˆxØ�tå”˜‘”ˆAÝ˜‘V”VˆFÝ�A˜˜f™Ñ$Ñ%Ô%¨Ñ)ˆAØ�R˜!˜a™%‘[‘=Ð r5   g    ÀëRAg    (±RAg    €„.Ar„   )rB   rˆ   r‰   r¬  rº  rÄ  rÍ  s          r3   rï   zbeta_gen._entropy„  sï   € ð	Gð 	Gð 	Gð	3ð 	3ð 	3ð
	&ð 
	&ð 
	&ð	!ð 	!ð 	!ð �Š;ˆ;˜1 š;˜;Ø&Ð& q¨!Ñ,Ô,Ð,Ø�%ŠZˆZ˜A ™E SšL˜L¨Q°/°/À!Ñ2DÔ2DÒ-DÐ-DØ%Ð% a¨Ñ+Ô+Ð+Ø�%ŠZˆZ˜A ™E SšL˜L¨Q°/°/À!Ñ2DÔ2DÒ-DÐ-DØ%Ð% a¨Ñ+Ô+Ð+à�7˜1˜a‘=”=Ð r5   r   )r€   r�   r‚   rƒ   rh   rÖ   ro   rÛ   rr   rv   r~   r{   r   r’  rH   r	   r   r@   rï   Ú__classcell__©r“  s   @r3   rb  rb  À  s.  ø€ € € € € ðð ð.ð ð ð
-ð -ð -ð -ð*ð *ð *ðð ð ð
#ð #ð #ð$ð $ð $ð'ð 'ð 'ð&ð &ð &ð#ð #ð #ð 4ð 4ð 4ð 4ð 4ð" ØÐ˜}ð 5+ð ,ñ ,ô ,ð
c"ð c"ð c"ð c"ñ,ô ,ñ „_ðc"ðJ+!ð +!ð +!ð +!ð +!ð +!ð +!r5   rb  rk  c                   óR   — e Zd ZdZej        Zd„ Zdd„Zd„ Z	d„ Z
d„ Zd„ Zd	„ Zd
„ ZdS )Úbetaprime_gena«  A beta prime continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `betaprime` is:

    .. math::

        f(x, a, b) = \frac{x^{a-1} (1+x)^{-a-b}}{\beta(a, b)}

    for :math:`x >= 0`, :math:`a > 0`, :math:`b > 0`, where
    :math:`\beta(a, b)` is the beta function (see `scipy.special.beta`).

    `betaprime` takes ``a`` and ``b`` as shape parameters.

    The distribution is related to the `beta` distribution as follows:
    If :math:`X` follows a beta distribution with parameters :math:`a, b`,
    then :math:`Y = X/(1-X)` has a beta prime distribution with
    parameters :math:`a, b` ([1]_).

    The beta prime distribution is a reparametrized version of the
    F distribution.  The beta prime distribution with shape parameters
    ``a`` and ``b`` and ``scale = s`` is equivalent to the F distribution
    with parameters ``d1 = 2*a``, ``d2 = 2*b`` and ``scale = (a/b)*s``.
    For example,

    >>> from scipy.stats import betaprime, f
    >>> x = [1, 2, 5, 10]
    >>> a = 12
    >>> b = 5
    >>> betaprime.pdf(x, a, b, scale=2)
    array([0.00541179, 0.08331299, 0.14669185, 0.03150079])
    >>> f.pdf(x, 2*a, 2*b, scale=(a/b)*2)
    array([0.00541179, 0.08331299, 0.14669185, 0.03150079])

    %(after_notes)s

    References
    ----------
    .. [1] Beta prime distribution, Wikipedia,
           https://en.wikipedia.org/wiki/Beta_prime_distribution

    %(example)s

    c                 ó‚   — t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }||gS rd  re   re  s      r3   rh   zbetaprime_gen._shape_infoç  rh  r5   Nc                 ó€   — t                                |||¬¦  «        }t                                |||¬¦  «        }||z  S ©N©rÔ   rÕ   )ÚgammaÚrvs)rB   rˆ   r‰   rÔ   rÕ   Úu1Úu2s          r3   rÖ   zbetaprime_gen._rvsì  s9   € Ý�YŠY�q˜t°,ˆYÑ?Ô?ˆÝ�YŠY�q˜t°,ˆYÑ?Ô?ˆØ�B‰wˆr5   c                 óT   — t          j        |                      |||¦  «        ¦  «        S rK   ©rM   r´   rÛ   rq  s       r3   ro   zbetaprime_gen._pdfñ  ó"   € åŒv�d—l’l 1 a¨Ñ+Ô+Ñ,Ô,Ð,r5   c                 ó�   — t          j        |dz
  |¦  «        t          j        ||z   |¦  «        z
  t          j        ||¦  «        z
  S r  )rt   ru  rt  rv  rq  s       r3   rÛ   zbetaprime_gen._logpdfõ  s<   € ÝŒx˜˜C™ Ñ#Ô#¥b¤j°°Q±¸Ñ&:Ô&:Ñ:½R¼YÀqÈ!¹_¼_ÑLÐLr5   c                 ó:   — t          |dk    |||gd„ d„ ¬¦  «        S )Nr   c                 óF   — t                                dd| z   z  ||¦  «        S r[   ©rk  rv   ©Úx_Úa_Úb_s      r3   ú<lambda>z$betaprime_gen._cdf.<locals>.<lambda>  s   € �tŸxšx¨¨1¨R©4©°"°bÑ9Ô9€ r5   c                 óF   — t                                | d| z   z  ||¦  «        S r[   ©rk  rr   rá  s      r3   rå  z$betaprime_gen._cdf.<locals>.<lambda>  s   € ¥$§)¢)¨B°°"±©I°r¸2Ñ">Ô">€ r5   ©Úf2©r   rq  s       r3   rr   zbetaprime_gen._cdfø  s:   € õ Ø�ŠE�A�q˜!�9Ø9Ð9Ø>Ð>ð@ñ @ô @ð 	@r5   c                 ó:   — t          |dk    |||gd„ d„ ¬¦  «        S )Nr   c                 óF   — t                                dd| z   z  ||¦  «        S r[   rç  rá  s      r3   rå  z#betaprime_gen._sf.<locals>.<lambda>  s   € �tŸyšy¨¨A¨b©D©°2°rÑ:Ô:€ r5   c                 óF   — t                                | d| z   z  ||¦  «        S r[   rà  rá  s      r3   rå  z#betaprime_gen._sf.<locals>.<lambda>	  s   € ¥$§(¢(¨2¨q°©t©9°b¸"Ñ"=Ô"=€ r5   rè  rê  rq  s       r3   rv   zbetaprime_gen._sf  s4   € ÝØ�ŠE�A�q˜!�9Ø:Ð:Ø=Ð=ð
ñ 
ô 
ð 	
r5   c                 ój  — t          j        |||¦  «        \  }}}t          j                             |||¦  «        }t          j        d¬¦  «        5  |d|z
  z  }d d d ¦  «         n# 1 swxY w Y   |dk    }dt          j                             ||         ||         ||         ¦  «        z  dz
  ||<   |S )Nr5  r6  r   g§èH.ÿï?)rM   Úbroadcast_arraysÚstatsrk  r{   r8  r~   )rB   Úprˆ   r‰   ÚrÚoutÚis          r3   r{   zbetaprime_gen._ppf  sé   € ÝÔ% a¨¨AÑ.Ô.‰ˆˆ1ˆaõ ŒJ�OŠO˜A˜q !Ñ$Ô$ˆÝŒ[ Ð)Ñ)Ô)ð 	ð 	Ø�q˜1‘u‘+ˆCð	ð 	ð 	ñ 	ô 	ð 	ð 	ð 	ð 	ð 	ð 	øøøð 	ð 	ð 	ð 	à�ŠZˆØ•5”:—?’? 1 Q¤4¨¨1¬¨q°¬tÑ4Ô4Ñ4°qÑ8ˆˆA‰Øˆ
s   Á	A&Á&A*Á-A*c                 óP   ‡— t          |‰k    ||fˆfd„t          j        ¬¦  «        S )Nc                 óp   •‡ ‡— t          j        ˆ ˆfd„t          d‰dz   ¦  «        D ¦   «         d¬¦  «        S )Nc                 ó,   •— g | ]}‰|z   d z
  ‰|z
  z  ‘ŒS ©r   r„   )Ú.0rô  rˆ   r‰   s     €€r3   ú
<listcomp>z9betaprime_gen._munp.<locals>.<lambda>.<locals>.<listcomp>  s)   ø€ Ð!GÐ!GÐ!G°A 1 Q¡3 q¡5¨1¨Q©3¡-Ð!GÐ!GÐ!Gr5   r   r   ©Úaxis)rM   ÚprodÚrange)rˆ   r‰   r_   s   ``€r3   rå  z%betaprime_gen._munp.<locals>.<lambda>  s<   øøø€ �œÐ!GÐ!GÐ!GÐ!GÐ!G½¸qÀ!ÀAÁ#¹¼Ð!GÑ!GÔ!GÈaÐPÑPÔP€ r5   ©Ú	fillvalue©r   rM   rf   )rB   r_   rˆ   r‰   s    `  r3   rÿ   zbetaprime_gen._munp  s8   ø€ ÝØ�ŠE�A�q�6ØPÐPÐPÐPÝ”fðñ ô ð 	r5   r   )r€   r�   r‚   rƒ   r   r  r  rh   rÖ   ro   rÛ   rr   rv   r{   rÿ   r„   r5   r3   rÑ  rÑ  µ  s¬   € € € € € ð.ð .ð^ "Ô4€Mðð ð ð
ð ð ð ð
-ð -ð -ðMð Mð Mð@ð @ð @ð
ð 
ð 
ðð ð ðð ð ð ð r5   rÑ  Ú	betaprimec                   ó8   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd
d„Zd„ Z	d	S )Úbradford_genab  A Bradford continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `bradford` is:

    .. math::

        f(x, c) = \frac{c}{\log(1+c) (1+cx)}

    for :math:`0 <= x <= 1` and :math:`c > 0`.

    `bradford` takes ``c`` as a shape parameter for :math:`c`.

    %(after_notes)s

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS ©NÚcFr   r  re   rg   s    r3   rh   zbradford_gen._shape_info:  r  r5   c                 óB   — |||z  dz   z  t          j        |¦  «        z  S r  ©rt   r£  ©rB   rn   r  s      r3   ro   zbradford_gen._pdf=  s!   € à�A�a‘C˜#‘I‰¥¤¨!¡¤Ñ,Ð,r5   c                 óZ   — t          j        ||z  ¦  «        t          j        |¦  «        z  S rK   r	  r
  s      r3   rr   zbradford_gen._cdfA  s!   € ÝŒx˜˜!™‰}Œ}�rœx¨™{œ{Ñ*Ð*r5   c                 óZ   — t          j        |t          j        |¦  «        z  ¦  «        |z  S rK   ©rt   Úexpm1r£  ©rB   rz   r  s      r3   r{   zbradford_gen._ppfD  s#   € ÝŒx˜�BœH Q™KœK™Ñ(Ô(¨1Ñ,Ð,r5   Úmvc                 ód  — t          j        d|z   ¦  «        }||z
  ||z  z  }|dz   |z  d|z  z
  d|z  |z  |z  z  }d }d }d|v ryt          j        d¦  «        d|z  |z  d|z  |z  |dz   z  z
  d|z  |z  ||dz   z  dz   z  z   z  }|t          j        |||dz
  z  d|z  z   z  ¦  «        d|z  |dz
  z  d|z  z   z  z  }d	|v rj|dz  |dz
  z  |d|z  d
z
  z  dz   z  d|z  |z  |z  |dz
  z  |dz
  z  z   d|z  |z  |z  d|z  dz
  z  z   d|dz  z  z   }|d|z  ||dz
  z  d|z  z   dz  z  z  }||||fS )Nr†   r³   rR   Úsr½  é	   rƒ  r‚  Úkr(  é   r   é   )rM   rí   rü   )rB   r  Úmomentsr  r@  rA  rB  rC  s           r3   r   zbradford_gen._statsG  s£  € ÝŒF�3�q‘5‰MŒMˆØ�‰c�A�a‘C‰[ˆØ�#‘�q‰y˜˜Q™‰  1¡ Q¡ q¡Ñ)ˆØˆØˆØ�'ˆ>ˆ>Ý”˜‘”˜R ™T !™V A a¡C¨¡E¨1¨Q©3¡KÑ/°°!±°A±°q¸!¸A¹#±w¸q±yÑ0AÑAÑBˆBØ•"”'˜!˜Q  !¡™W Q q¡S™[™/Ñ*Ô*¨A¨a©C°°1±©I°a¸±c©MÑ:Ñ:ˆBØ�'ˆ>ˆ>Ø�Q‘$˜˜!™‘*˜a  1¡ R¡™j¨™mÑ,¨R°©T°!©V°A©X°q¸±s©^¸Q¸q¹SÑ-AÑAØ�A‘#�a‘%˜‘'˜1˜Q™3˜r™6Ñ"ñ#Ø%'¨¨1©¡Wñ-ˆBà�!�A‘#�q˜!˜A™#‘w˜q ™s‘{ QÑ&Ñ&Ñ&ˆBØ�3˜˜BˆÐr5   c                 ój   — t          j        d|z   ¦  «        }|dz  t          j        ||z  ¦  «        z
  S ©Nr   r³   r.  )rB   r  r  s      r3   rï   zbradford_gen._entropyV  s.   € ÝŒF�1�Q‘3‰KŒKˆØ�‰u•r”v˜a ™c‘{”{Ñ"Ð"r5   N©r  rE  r„   r5   r3   r  r  $  s€   € € € € € ðð ð*Eð Eð Eð-ð -ð -ð+ð +ð +ð-ð -ð -ðð ð ð ð#ð #ð #ð #ð #r5   r  Úbradfordc                   óT   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Zd„ Zd„ ZdS )Úburr_genaˆ  A Burr (Type III) continuous random variable.

    %(before_notes)s

    See Also
    --------
    fisk : a special case of either `burr` or `burr12` with ``d=1``
    burr12 : Burr Type XII distribution
    mielke : Mielke Beta-Kappa / Dagum distribution

    Notes
    -----
    The probability density function for `burr` is:

    .. math::

        f(x; c, d) = c d \frac{x^{-c - 1}}
                              {{(1 + x^{-c})}^{d + 1}}

    for :math:`x >= 0` and :math:`c, d > 0`.

    `burr` takes ``c`` and ``d`` as shape parameters for :math:`c` and
    :math:`d`.

    This is the PDF corresponding to the third CDF given in Burr's list;
    specifically, it is equation (11) in Burr's paper [1]_. The distribution
    is also commonly referred to as the Dagum distribution [2]_. If the
    parameter :math:`c < 1` then the mean of the distribution does not
    exist and if :math:`c < 2` the variance does not exist [2]_.
    The PDF is finite at the left endpoint :math:`x = 0` if :math:`c * d >= 1`.

    %(after_notes)s

    References
    ----------
    .. [1] Burr, I. W. "Cumulative frequency functions", Annals of
       Mathematical Statistics, 13(2), pp 215-232 (1942).
    .. [2] https://en.wikipedia.org/wiki/Dagum_distribution
    .. [3] Kleiber, Christian. "A guide to the Dagum distributions."
       Modeling Income Distributions and Lorenz Curves  pp 97-117 (2008).

    %(example)s

    c                 ó‚   — t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }||gS ©Nr  Fr   r  rÌ  re   ©rB   ÚicÚids      r3   rh   zburr_gen._shape_info�  rh  r5   c                 ód   — t          |dk    |||gd„ d„ ¬¦  «        }|j        dk    r|d         S |S )Nr   c                 ó6   — ||z  | ||z  dz
  z  z  d| |z  z   z  S r[   r„   ©râ  Úc_Úd_s      r3   rå  zburr_gen._pdf.<locals>.<lambda>˜  s(   € ˜r B™w¨"¨r°"©u°Q©w©-Ñ8¸AÀÀBÁ¹JÑG€ r5   c                 ó@   — ||z  | | dz
  z  z  d| | z  z   |dz   z  z  S ©Nr†   r   r„   r%  s      r3   rå  zburr_gen._pdf.<locals>.<lambda>™  s6   €  2¨¡7¨b°b°S¸3±YÑ.?Ñ#@Ø%&¨°°©¡_¸"¸s¹(Ñ$Cñ$E€ r5   rè  r„   ©r   Úndim©rB   rn   r  rÌ  Úoutputs        r3   ro   zburr_gen._pdf”  sX   € åØ�ŠF�Q˜˜1�IØGÐGðFð FðGñ Gô Gˆð
 Œ;˜!ÒÐØ˜"”:ÐØˆr5   c                 ód   — t          |dk    |||gd„ d„ ¬¦  «        }|j        dk    r|d         S |S )Nr   c                 óÈ   — t          j        |¦  «        t          j        |¦  «        z   t          j        ||z  dz
  | ¦  «        z   |dz   t          j        | |z  ¦  «        z  z
  S r[   )rM   rí   rt   ru  r£  r%  s      r3   rå  z"burr_gen._logpdf.<locals>.<lambda>¢  sS   € ¥¤ r¡
¤
­R¬V°B©Z¬ZÑ 7½"¼(À2ÀbÁ5È1Á9ÈbÑ:QÔ:QÑ QØ#% a¡4­2¬8°B¸±HÑ+=Ô+=Ñ"=ñ!>€ r5   c                 óÂ   — t          j        |¦  «        t          j        |¦  «        z   t          j        | dz
  | ¦  «        z   t          j        |dz   | | z  ¦  «        z
  S r[   ©rM   rí   rt   ru  rt  r%  s      r3   rå  z"burr_gen._logpdf.<locals>.<lambda>¤  sT   € ¥2¤6¨"¡:¤:µ´°r±
´
Ñ#:Ý%'¤X¨r¨c°A©g°rÑ%:Ô%:ñ$;å%'¤Z°°1±°b¸B¸3±iÑ%@Ô%@ñ$A€ r5   rè  r„   r*  r,  s        r3   rÛ   zburr_gen._logpdfŸ  s\   € ÝØ�ŠF�Q˜˜1�Ið?ð ?ðBð Bð	Cñ Cô Cˆð Œ;˜!ÒÐØ˜"”:ÐØˆr5   c                 ó   — d|| z  z   | z  S r[   r„   ©rB   rn   r  rÌ  s       r3   rr   zburr_gen._cdf«  s   € Ø�A˜˜‘G‘ ˜rÑ"Ð"r5   c                 ó:   — t          j        || z  ¦  «        | z  S rK   r	  r3  s       r3   rà   zburr_gen._logcdf®  s   € ÝŒx˜˜Q˜B™Ñ Ô  Q BÑ'Ð'r5   c                 óT   — t          j        |                      |||¦  «        ¦  «        S rK   ©rM   r´   rä   r3  s       r3   rv   zburr_gen._sf±  ó"   € ÝŒv�d—k’k ! Q¨Ñ*Ô*Ñ+Ô+Ð+r5   c                 óB   — t          j        d|| z  z   | z   ¦  «        S r[   ©rM   r£  r3  s       r3   rä   zburr_gen._logsf´  s&   € ÝŒx˜1˜q A 2™w™;¨1¨"Ñ-Ð-Ñ.Ô.Ð.r5   c                 ó$   — |d|z  z  dz
  d|z  z  S ©Nç      ð¿r   r„   ©rB   rz   r  rÌ  s       r3   r{   zburr_gen._ppf·  s   € Ø�D˜‘F‘˜a‘ 4¨¡6Ñ*Ð*r5   c                 óh   — t          j        d|z  | ¦  «        }t          j        |¦  «        d|z  z  S ©Nr<  ©rt   rt  r  )rB   rz   r  rÌ  Ú_qs        r3   r~   zburr_gen._isfº  s0   € ÝŒZ˜˜q™ 1 "Ñ%Ô%ˆÝŒx˜‰|Œ|  q¡Ñ)Ð)r5   c           	      ó¶  — t          j        dd¦  «                             dd¦  «        |z  }t          j        ||z   d|z
  ¦  «        |z  \  }}}}t          j        |dk    |t           j        ¦  «        }||dz  z
  }	t          j        |dk    |	t           j        ¦  «        }
t          |dk    |||||	fd„ t           j        ¬	¦  «        }t          |d
k    ||||||	fd„ t           j        ¬	¦  «        }t          j        |¦  «        dk    rN| 	                    ¦   «         |
 	                    ¦   «         | 	                    ¦   «         | 	                    ¦   «         fS ||
||fS )Nr   é   r   r†   rR   r³   ç      @c                 óZ   — |d|z  |z  z
  d|dz  z  z   t          j        |dz  ¦  «        z  S )Nrƒ  rR   r„  )r  Úe1Úe2Úe3Úmu2_if_cs        r3   rå  z!burr_gen._stats.<locals>.<lambda>È  s6   € ¨b°1°R±4¸±7©l¸Q¸rÀ1¹u¹WÑ.DÝ/1¬w¸À1±}Ñ/EÔ/Eñ.F€ r5   rÿ  ç      @c                 óT   — |d|z  |z  z
  d|z  |dz  z  z   d|dz  z  z
  |dz  z  dz
  S )Nr   r‚  rR   rƒ  r„   )r  rF  rG  rH  Úe4rI  s         r3   rå  z!burr_gen._stats.<locals>.<lambda>Î  sB   € Ø�q˜‘t˜B‘w‘,  2¡ b¨!¡e¡Ñ+¨a°°A±©gÑ5¸À1¹ÑDÈÑIð r5   r   )
rM   ÚarangeÚreshapert   rk  Úwherer  r   r+  Úitem)rB   r  rÌ  ÚncrF  rG  rH  rL  r@  rI  rA  rB  rC  s                r3   r   zburr_gen._stats¾  sS  € ÝŒY�q˜!‰_Œ_×$Ò$ Q qÑ)Ô)¨AÑ-ˆåœ  R¡¨¨b©Ñ1Ô1°AÑ5‰ˆˆB��BÝŒX�a˜#’g˜r¥2¤6Ñ*Ô*ˆØ˜˜A™‘:ˆÝŒh�q˜3’w ­"¬&Ñ1Ô1ˆÝØ�ŠGØ��B˜˜HÐ%ðGð Gå”fðñ ô ˆõ Ø�ŠGØ��B˜˜B Ð)ðKð Kå”fðñ ô ˆõ Œ7�1‰:Œ:˜Š?ˆ?Ø—7’7‘9”9˜cŸhšh™jœj¨"¯'ª'©)¬)°R·W²W±Y´YÐ>Ð>Ø�3˜˜BˆÐr5   c                 óê   ‡— d„ Št          j        |¦  «        t          j        |¦  «        t          j        |¦  «        }}}t          ||k    ||k    z  ||k    z  |||fˆfd„t           j        ¦  «        S )Nc                 óN   — d| z  |z  }|t          j        d|z
  ||z   ¦  «        z  S r  ©rt   rk  ©r_   r  rÌ  rQ  s       r3   Ú__munpzburr_gen._munp.<locals>.__munpÖ  ó.   € Ø�a‘˜!‘ˆBØ•r”w˜s R™x¨¨R©Ñ0Ô0Ñ0Ð0r5   c                 ó   •—  ‰|| |¦  «        S rK   r„   )r  rÌ  r_   Ú_burr_gen__munps      €r3   rå  z burr_gen._munp.<locals>.<lambda>Û  s   ø€ ¨&¨&°°A°q©/¬/€ r5   )rM   rø   r   r  )rB   r_   r  rÌ  rY  s       @r3   rÿ   zburr_gen._munpÕ  s|   ø€ ð	1ð 	1ð 	1õ ”*˜Q‘-”-¥¤¨A¡¤µ´
¸1±´ˆaˆ1ˆÝ˜1˜qš5 Q¨!¢VÑ,°°Q²Ñ7¸!¸QÀ¸Ø9Ð9Ð9Ð9Ýœ&ñ"ô "ð 	"r5   N)r€   r�   r‚   rƒ   rh   ro   rÛ   rr   rà   rv   rä   r{   r~   r   rÿ   r„   r5   r3   r  r  ^  sÄ   € € € € € ð+ð +ð`ð ð ð
	ð 	ð 	ð
ð 
ð 
ð#ð #ð #ð(ð (ð (ð,ð ,ð ,ð/ð /ð /ð+ð +ð +ð*ð *ð *ðð ð ð."ð "ð "ð "ð "r5   r  Úburrc                   óN   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Zd„ ZdS )Ú
burr12_gena}  A Burr (Type XII) continuous random variable.

    %(before_notes)s

    See Also
    --------
    fisk : a special case of either `burr` or `burr12` with ``d=1``
    burr : Burr Type III distribution

    Notes
    -----
    The probability density function for `burr12` is:

    .. math::

        f(x; c, d) = c d \frac{x^{c-1}}
                              {(1 + x^c)^{d + 1}}

    for :math:`x >= 0` and :math:`c, d > 0`.

    `burr12` takes ``c`` and ``d`` as shape parameters for :math:`c`
    and :math:`d`.

    This is the PDF corresponding to the twelfth CDF given in Burr's list;
    specifically, it is equation (20) in Burr's paper [1]_.

    %(after_notes)s

    The Burr type 12 distribution is also sometimes referred to as
    the Singh-Maddala distribution from NIST [2]_.

    References
    ----------
    .. [1] Burr, I. W. "Cumulative frequency functions", Annals of
       Mathematical Statistics, 13(2), pp 215-232 (1942).

    .. [2] https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/b12pdf.htm

    .. [3] "Burr distribution",
       https://en.wikipedia.org/wiki/Burr_distribution

    %(example)s

    c                 ó‚   — t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }||gS r  re   r   s      r3   rh   zburr12_gen._shape_info  rh  r5   c                 óT   — t          j        |                      |||¦  «        ¦  «        S rK   rÛ  r3  s       r3   ro   zburr12_gen._pdf  rÜ  r5   c                 óÀ   — t          j        |¦  «        t          j        |¦  «        z   t          j        |dz
  |¦  «        z   t          j        | dz
  ||z  ¦  «        z   S r[   r1  r3  s       r3   rÛ   zburr12_gen._logpdf  sN   € ÝŒv�a‰yŒy�2œ6 !™9œ9Ñ$¥r¤x°°A±°qÑ'9Ô'9Ñ9½B¼JÈÀrÈ!ÁtÈQÐPQÉTÑ<RÔ<RÑRÐRr5   c                 óV   — t          j        |                      |||¦  «        ¦  «         S rK   ©rt   r  rä   r3  s       r3   rr   zburr12_gen._cdf  ó%   € Ý”˜Ÿš Q¨¨1Ñ-Ô-Ñ.Ô.Ð.Ð.r5   c                 ó@   — t          j        d||z  z   | z   ¦  «        S r[   r	  r3  s       r3   rà   zburr12_gen._logcdf  s$   € ÝŒx˜!˜a ™d™( q bÑ)Ð)Ñ*Ô*Ð*r5   c                 óT   — t          j        |                      |||¦  «        ¦  «        S rK   r6  r3  s       r3   rv   zburr12_gen._sf!  r7  r5   c                 ó4   — t          j        | ||z  ¦  «        S rK   ©rt   rt  r3  s       r3   rä   zburr12_gen._logsf$  s   € ÝŒz˜1˜"˜a ™dÑ#Ô#Ð#r5   c                 óh   — t          j        d|z  t          j        | ¦  «        z  ¦  «        d|z  z  S ©Nr¼  r   r  r=  s       r3   r{   zburr12_gen._ppf'  s0   € õ Œx˜˜1™�rœx¨¨™|œ|Ñ+Ñ,Ô,¨q°©sÑ3Ð3r5   c                 óf   — t          j        d|z  t          j        |¦  «        z  ¦  «        d|z  z  S rh  )rt   r  rM   rí   )rB   rñ  r  rÌ  s       r3   r~   zburr12_gen._isf-  s,   € ÝŒx˜˜1™�rœv a™yœyÑ(Ñ)Ô)¨A¨a©CÑ0Ð0r5   c                 óV   — d„ }t          ||z  |k    |||f|t          j        ¬¦  «        S )Nc                 óN   — d| z  |z  }|t          j        d|z   ||z
  ¦  «        z  S r  rT  rU  s       r3   Úmoment_if_existsz*burr12_gen._munp.<locals>.moment_if_exists1  rW  r5   rÿ  )r   rM   r  )rB   r_   r  rÌ  rl  s        r3   rÿ   zburr12_gen._munp0  sD   € ð	1ð 	1ð 	1õ ˜!˜a™% !š) a¨¨A YÐ0@Ý$&¤Fð,ñ ,ô ,ð 	,r5   N)r€   r�   r‚   rƒ   rh   ro   rÛ   rr   rà   rv   rä   r{   r~   rÿ   r„   r5   r3   r\  r\  â  s¸   € € € € € ð+ð +ðXð ð ð
-ð -ð -ðSð Sð Sð/ð /ð /ð+ð +ð +ð,ð ,ð ,ð$ð $ð $ð4ð 4ð 4ð1ð 1ð 1ð,ð ,ð ,ð ,ð ,r5   r\  Úburr12c                   óZ   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Zd„ Zd„ Zd„ ZdS )Úfisk_genaº  A Fisk continuous random variable.

    The Fisk distribution is also known as the log-logistic distribution.

    %(before_notes)s

    See Also
    --------
    burr

    Notes
    -----
    The probability density function for `fisk` is:

    .. math::

        f(x, c) = \frac{c x^{c-1}}
                       {(1 + x^c)^2}

    for :math:`x >= 0` and :math:`c > 0`.

    Please note that the above expression can be transformed into the following
    one, which is also commonly used:

    .. math::

        f(x, c) = \frac{c x^{-c-1}}
                       {(1 + x^{-c})^2}

    `fisk` takes ``c`` as a shape parameter for :math:`c`.

    `fisk` is a special case of `burr` or `burr12` with ``d=1``.

    Suppose ``X`` is a logistic random variable with location ``l``
    and scale ``s``. Then ``Y = exp(X)`` is a Fisk (log-logistic)
    random variable with ``scale = exp(l)`` and shape ``c = 1/s``.

    %(after_notes)s

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r  re   rg   s    r3   rh   zfisk_gen._shape_infog  r  r5   c                 ó:   — t                                ||d¦  «        S r  )rZ  ro   r
  s      r3   ro   zfisk_gen._pdfj  s   € å�yŠy˜˜A˜sÑ#Ô#Ð#r5   c                 ó:   — t                                ||d¦  «        S r  )rZ  rr   r
  s      r3   rr   zfisk_gen._cdfn  ó   € Ý�yŠy˜˜A˜sÑ#Ô#Ð#r5   c                 ó:   — t                                ||d¦  «        S r  )rZ  rv   r
  s      r3   rv   zfisk_gen._sfq  s   € Ý�xŠx˜˜1˜cÑ"Ô"Ð"r5   c                 ó:   — t                                ||d¦  «        S r  )rZ  rÛ   r
  s      r3   rÛ   zfisk_gen._logpdft  s   € å�|Š|˜A˜q #Ñ&Ô&Ð&r5   c                 ó:   — t                                ||d¦  «        S r  )rZ  rà   r
  s      r3   rà   zfisk_gen._logcdfx  s   € Ý�|Š|˜A˜q #Ñ&Ô&Ð&r5   c                 ó:   — t                                ||d¦  «        S r  )rZ  rä   r
  s      r3   rä   zfisk_gen._logsf{  s   € Ý�{Š{˜1˜a Ñ%Ô%Ð%r5   c                 ó:   — t                                ||d¦  «        S r  )rZ  r{   r
  s      r3   r{   zfisk_gen._ppf~  rs  r5   c                 ó:   — t                                ||d¦  «        S r  )rZ  r~   r  s      r3   r~   zfisk_gen._isf�  rs  r5   c                 ó:   — t                                ||d¦  «        S r  )rZ  rÿ   ©rB   r_   r  s      r3   rÿ   zfisk_gen._munp„  s   € Ý�zŠz˜!˜Q Ñ$Ô$Ð$r5   c                 ó8   — t                                |d¦  «        S r  )rZ  r   ©rB   r  s     r3   r   zfisk_gen._stats‡  s   € Ý�{Š{˜1˜cÑ"Ô"Ð"r5   c                 ó0   — dt          j        |¦  «        z
  S r  r.  r}  s     r3   rï   zfisk_gen._entropyŠ  ó   € Ø•2”6˜!‘9”9‰}Ðr5   N)r€   r�   r‚   rƒ   rh   ro   rr   rv   rÛ   rà   rä   r{   r~   rÿ   r   rï   r„   r5   r3   ro  ro  <  sÖ   € € € € € ð)ð )ðTEð Eð Eð$ð $ð $ð$ð $ð $ð#ð #ð #ð'ð 'ð 'ð'ð 'ð 'ð&ð &ð &ð$ð $ð $ð$ð $ð $ð%ð %ð %ð#ð #ð #ðð ð ð ð r5   ro  Úfiskc                   óJ   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zdd„Zd
S )Ú
cauchy_gena	  A Cauchy continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `cauchy` is

    .. math::

        f(x) = \frac{1}{\pi (1 + x^2)}

    for a real number :math:`x`.

    %(after_notes)s

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   zcauchy_gen._shape_info¥  r£   r5   c                 ó2   — dt           j        z  d||z  z   z  S r  r+  r¦   s     r3   ro   zcauchy_gen._pdf¨  ó   € à•2”5‰y˜#˜a ™c™'Ñ"Ð"r5   c                 óP   — ddt           j        z  t          j        |¦  «        z  z   S r�   ©rM   rî   Úarctanr¦   s     r3   rr   zcauchy_gen._cdf¬  ó    € Ø�S�œ‘Y�rœy¨™|œ|Ñ+Ñ+Ð+r5   c                 ód   — t          j        t           j        |z  t           j        dz  z
  ¦  «        S r;  ©rM   Útanrî   r­   s     r3   r{   zcauchy_gen._ppf¯  s#   € ÝŒv•b”e˜A‘g�bœe C™iÑ'Ñ(Ô(Ð(r5   c                 óP   — ddt           j        z  t          j        |¦  «        z  z
  S r�   r‡  r¦   s     r3   rv   zcauchy_gen._sf²  r‰  r5   c                 ód   — t          j        t           j        dz  t           j        |z  z
  ¦  «        S r;  r‹  r­   s     r3   r~   zcauchy_gen._isfµ  s#   € ÝŒv•b”e˜C‘i¥¤ a¡Ñ'Ñ(Ô(Ð(r5   c                 ó^   — t           j        t           j        t           j        t           j        fS rK   ©rM   r  rg   s    r3   r   zcauchy_gen._stats¸  ó   € ÝŒv•r”v�rœv¥r¤vÐ-Ð-r5   c                 óD   — t          j        dt           j        z  ¦  «        S r%  rì   rg   s    r3   rï   zcauchy_gen._entropy»  ó   € ÝŒv�a�œ‘g‰ŒÐr5   Nc                 óž   — t          |t          ¦  «        r|                     ¦   «         }t          j        |g d¢¦  «        \  }}}|||z
  dz  fS )N©é   é2   éK   rR   ©r<   r(   r�  rM   Ú
percentile)rB   rC   rD   Úp25Úp50Úp75s         r3   r’  zcauchy_gen._fitstart¾  sQ   € å�d�LÑ)Ô)ð 	$Ø—>’>Ñ#Ô#ˆDÝœ d¨L¨L¨LÑ9Ô9‰ˆˆS�#Ø�S˜3‘Y ‘MÐ!Ð!r5   rK   )r€   r�   r‚   rƒ   rh   ro   rr   r{   rv   r~   r   rï   r’  r„   r5   r3   r‚  r‚  ‘  sª   € € € € € ðð ð&ð ð ð#ð #ð #ð,ð ,ð ,ð)ð )ð )ð,ð ,ð ,ð)ð )ð )ð.ð .ð .ðð ð ð"ð "ð "ð "ð "ð "r5   r‚  Úcauchyc                   óP   — e Zd ZdZd„ Zdd„Zd„ Zd„ Zd„ Zd„ Z	d	„ Z
d
„ Zd„ Zd„ ZdS )Úchi_genaß  A chi continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `chi` is:

    .. math::

        f(x, k) = \frac{1}{2^{k/2-1} \Gamma \left( k/2 \right)}
                   x^{k-1} \exp \left( -x^2/2 \right)

    for :math:`x >= 0` and :math:`k > 0` (degrees of freedom, denoted ``df``
    in the implementation). :math:`\Gamma` is the gamma function
    (`scipy.special.gamma`).

    Special cases of `chi` are:

        - ``chi(1, loc, scale)`` is equivalent to `halfnorm`
        - ``chi(2, 0, scale)`` is equivalent to `rayleigh`
        - ``chi(3, 0, scale)`` is equivalent to `maxwell`

    `chi` takes ``df`` as a shape parameter.

    %(after_notes)s

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS ©NÚdfFr   r  re   rg   s    r3   rh   zchi_gen._shape_infoè  ó   € Ý˜4 ¨­B¬F¨°^ÑDÔDÐEÐEr5   Nc                 ó`   — t          j        t                               |||¬¦  «        ¦  «        S rÔ  )rM   rü   Úchi2r×  ©rB   r£  rÔ   rÕ   s       r3   rÖ   zchi_gen._rvsë  s$   € ÝŒw•t—x’x ¨¸L�xÑIÔIÑJÔJÐJr5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   rÛ  ©rB   rn   r£  s      r3   ro   zchi_gen._pdfî  s"   € õ Œv�d—l’l 1 bÑ)Ô)Ñ*Ô*Ð*r5   c                 óØ   — t          j        d¦  «        dt          j        d¦  «        z  |z  z
  t          j        d|z  ¦  «        z
  }|t          j        |dz
  |¦  «        z   d|dz  z  z
  S )NrR   r‘   r†   )rM   rí   rt   rÃ  ru  )rB   rn   r£  Úls       r3   rÛ   zchi_gen._logpdfô  s_   € ÝŒF�1‰IŒI˜�2œ6 !™9œ9™ R™Ñ'­"¬*°R¸±UÑ*;Ô*;Ñ;ˆØ•2”8˜B ™G QÑ'Ô'Ñ'¨"¨Q°©T©'Ñ1Ð1r5   c                 ó>   — t          j        d|z  d|dz  z  ¦  «        S ©Nr‘   rR   ©rt   Úgammaincr©  s      r3   rr   zchi_gen._cdfø  s    € ÝŒ{˜2˜b™5 " Q¨¡T¡'Ñ*Ô*Ð*r5   c                 ó>   — t          j        d|z  d|dz  z  ¦  «        S r­  ©rt   Ú	gammainccr©  s      r3   rv   zchi_gen._sfû  s    € ÝŒ|˜B˜r™E 2 a¨¡d¡7Ñ+Ô+Ð+r5   c                 ó\   — t          j        dt          j        d|z  |¦  «        z  ¦  «        S ©NrR   r‘   ©rM   rü   rt   Úgammaincinv©rB   rz   r£  s      r3   r{   zchi_gen._ppfþ  s'   € ÝŒw�q�œ¨¨2©¨qÑ1Ô1Ñ1Ñ2Ô2Ð2r5   c                 ó\   — t          j        dt          j        d|z  |¦  «        z  ¦  «        S r´  ©rM   rü   rt   Úgammainccinvr·  s      r3   r~   zchi_gen._isf  s'   € ÝŒw�q�œ¨¨B©°Ñ2Ô2Ñ2Ñ3Ô3Ð3r5   c                 óp  — t          j        d¦  «        t          j        d|z  d¦  «        z  }|||z  z
  }d|dz  z  |dd|z  z
  z  z   t          j        t          j        |d¦  «        ¦  «        z  }d|z  d|z
  z  d|dz  z  z
  d|dz  z  d|z  dz
  z  z   }|t          j        |d	z  ¦  «        z  }||||fS )
NrR   r‘   rD  r   ç      ø?r†   r‚  r   r³   )rM   rü   rt   Úpochrø   Úpower©rB   r£  r@  rA  rB  rC  s         r3   r   zchi_gen._stats  sÈ   € åŒW�Q‰ZŒZ�"œ' #¨¡(¨CÑ0Ô0Ñ0ˆØ�2�b‘5‰jˆØ��C‘‰i˜"˜a  "¡™f™+Ñ%¥r¤zµ"´(¸3ÀÑ2DÔ2DÑ'EÔ'EÑEˆØˆr‰T�3�r‘6‰]˜1˜R ™U™7Ñ" Q r¨1¡u¡W°°"±°Q±Ñ%7Ñ7ˆØ
�bŒj˜˜c™Ñ"Ô"Ñ"ˆØ�3˜˜BˆÐr5   c                 ó>   — d„ }d„ }t          |dk     |f||¬¦  «        S )Nc                 ó¢   — t          j        d| z  ¦  «        d| t          j        d¦  «        z
  | dz
  t          j        d| z  ¦  «        z  z
  z  z   S rë   )rt   rÃ  rM   rí   Údigamma©r£  s    r3   Úregular_formulaz)chi_gen._entropy.<locals>.regular_formula  sO   € Ý”J˜r B™wÑ'Ô'Ø˜R¥"¤&¨¡)¤)™^¨r°A©v½¼ÀCÈ"ÁHÑ9MÔ9MÑ.MÑMÑNñOð Pr5   c                 ó’   — dt          j        t           j        ¦  «        dz  z   | dz  dz  z
  | dz  dz  z
  d| dz  z  z
  | dz  d	z  z   S )
Nr‘   rR   r¼  r‚  r  glÁlÁ¶?éýÿÿÿéüÿÿÿé   rì   rÃ  s    r3   Úasymptotic_formulaz,chi_gen._entropy.<locals>.asymptotic_formula  sW   € Ø�"œ&¥¤™-œ-¨™/Ñ)¨R°©V°Q©JÑ6¸"¸b¹&À!¹ÑCØ˜B ™F‘mñ$Ø')¨2¡v¨r¡kñ2ð 3r5   g     Àr@rè  rê  )rB   r£  rÄ  rÉ  s       r3   rï   zchi_gen._entropy  sK   € ð	Pð 	Pð 	Pð	3ð 	3ð 	3õ ˜"˜sš( R F¨OØ/ð1ñ 1ô 1ð 	1r5   r   ©r€   r�   r‚   rƒ   rh   rÖ   ro   rÛ   rr   rv   r{   r~   r   rï   r„   r5   r3   r   r   É  sÀ   € € € € € ðð ð<Fð Fð FðKð Kð Kð Kð+ð +ð +ð2ð 2ð 2ð+ð +ð +ð,ð ,ð ,ð3ð 3ð 3ð4ð 4ð 4ðð ð ð1ð 1ð 1ð 1ð 1r5   r   Úchic                   óP   — e Zd ZdZd„ Zdd„Zd„ Zd„ Zd„ Zd„ Z	d	„ Z
d
„ Zd„ Zd„ ZdS )Úchi2_genaÌ  A chi-squared continuous random variable.

    For the noncentral chi-square distribution, see `ncx2`.

    %(before_notes)s

    See Also
    --------
    ncx2

    Notes
    -----
    The probability density function for `chi2` is:

    .. math::

        f(x, k) = \frac{1}{2^{k/2} \Gamma \left( k/2 \right)}
                   x^{k/2-1} \exp \left( -x/2 \right)

    for :math:`x > 0`  and :math:`k > 0` (degrees of freedom, denoted ``df``
    in the implementation).

    `chi2` takes ``df`` as a shape parameter.

    The chi-squared distribution is a special case of the gamma
    distribution, with gamma parameters ``a = df/2``, ``loc = 0`` and
    ``scale = 2``.

    %(after_notes)s

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r¢  re   rg   s    r3   rh   zchi2_gen._shape_info@  r¤  r5   Nc                 ó.   — |                      ||¦  «        S rK   )Ú	chisquarer§  s       r3   rÖ   zchi2_gen._rvsC  s   € Ø×%Ò% b¨$Ñ/Ô/Ð/r5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   rÛ  r©  s      r3   ro   zchi2_gen._pdfF  s    € åŒv�d—l’l 1 bÑ)Ô)Ñ*Ô*Ð*r5   c                 óª   — t          j        |dz  dz
  |¦  «        |dz  z
  t          j        |dz  ¦  «        z
  t          j        d¦  «        |z  dz  z
  S )Nr³   r   rR   )rt   ru  rÃ  rM   rí   r©  s      r3   rÛ   zchi2_gen._logpdfJ  sO   € ÝŒx˜˜2™˜a™ Ñ#Ô# a¨¡dÑ*­R¬Z¸¸2¹Ñ->Ô->Ñ>Å"Ä&ÈÁ)Ä)ÈBÁ,ÐPRÑARÑRÐRr5   c                 ó,   — t          j        ||¦  «        S rK   )rt   Úchdtrr©  s      r3   rr   zchi2_gen._cdfM  ó   € ÝŒx˜˜A‰ŒÐr5   c                 ó,   — t          j        ||¦  «        S rK   )rt   Úchdtrcr©  s      r3   rv   zchi2_gen._sfP  ó   € ÝŒy˜˜QÑÔÐr5   c                 ó,   — t          j        ||¦  «        S rK   )rt   Úchdtri©rB   rñ  r£  s      r3   r~   zchi2_gen._isfS  rØ  r5   c                 ó8   — dt          j        |dz  |¦  «        z  S r  ©rt   r¶  rÛ  s      r3   r{   zchi2_gen._ppfV  s   € Ø•”  1¡ aÑ(Ô(Ñ(Ð(r5   c                 óZ   — |}d|z  }dt          j        d|z  ¦  «        z  }d|z  }||||fS )NrR   r³   ç      (@r„  r¿  s         r3   r   zchi2_gen._statsY  s=   € ØˆØ�‰dˆØ�rŒw�s˜2‘v‰ŒÑˆØ�"‰WˆØ�3˜˜BˆÐr5   c                 óH   — d|z  }d„ }d„ }t          |dk     |f||¬¦  «        S )Nr‘   c                 ó�   — | t          j        d¦  «        z   t          j        | ¦  «        z   d| z
  t          j        | ¦  «        z  z   S ©NrR   r   )rM   rí   rt   rÃ  rX  )Úhalf_dfs    r3   rÄ  z*chi2_gen._entropy.<locals>.regular_formulac  s?   € Ø�bœf Q™iœiÑ'­"¬*°WÑ*=Ô*=Ñ=Ø˜‘[¥B¤F¨7¡O¤OÑ3ñ4ð 5r5   c                 óè   — t          j        d¦  «        ddt          j        dt           j        z  ¦  «        z   z  z   }d| z  }|d|d|d|dz  z   z  z   z  z   z  dt          j        | ¦  «        z  z   |z   S )NrR   r‘   r   gUUUUUUå¿çUUUUUUÕ¿glÁlÁ¶¿g      @rì   )rã  r  Úhs      r3   rÉ  z-chi2_gen._entropy.<locals>.asymptotic_formulag  s}   € õ ”�q‘	”	˜C ¥R¤V¨A­b¬e©G¡_¤_Ñ!4Ñ5Ñ5ˆAØ�G‘ˆAØ�t˜a ¨¨5°1°S±5©=Ñ(9Ñ!9Ñ:Ñ:Ñ;Ø�œ˜w™œÑ'ñ(Ø*+ñ,ð -r5   é}   rè  rê  )rB   r£  rã  rÄ  rÉ  s        r3   rï   zchi2_gen._entropy`  sR   € Ø˜‘(ˆð	5ð 	5ð 	5ð		-ð 		-ð 		-õ ˜' Cš-¨'¨Ø)Ø/ð1ñ 1ô 1ð 	1r5   r   )r€   r�   r‚   rƒ   rh   rÖ   ro   rÛ   rr   rv   r~   r{   r   rï   r„   r5   r3   rÍ  rÍ    sÀ   € € € € € ð ð  ðBFð Fð Fð0ð 0ð 0ð 0ð+ð +ð +ðSð Sð Sðð ð ð ð  ð  ð ð  ð  ð)ð )ð )ðð ð ð1ð 1ð 1ð 1ð 1r5   rÍ  r¦  c                   óH   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ ZdS )Ú
cosine_gena\  A cosine continuous random variable.

    %(before_notes)s

    Notes
    -----
    The cosine distribution is an approximation to the normal distribution.
    The probability density function for `cosine` is:

    .. math::

        f(x) = \frac{1}{2\pi} (1+\cos(x))

    for :math:`-\pi \le x \le \pi`.

    %(after_notes)s

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   zcosine_gen._shape_info�  r£   r5   c                 óP   — dt           j        z  dt          j        |¦  «        z   z  S ©Nr‘   r   ©rM   rî   r  r¦   s     r3   ro   zcosine_gen._pdf’  s   € à•R”U‰{˜A�bœf Q™iœi™KÑ(Ð(r5   c                 ór   — t          j        |¦  «        }t          |dk    |fd„ t           j         ¬¦  «        S )Nr¼  c                 ón   — t          j        | ¦  «        t          j        dt           j        z  ¦  «        z
  S r  )rM   r£  rí   rî   ©r  s    r3   rå  z$cosine_gen._logpdf.<locals>.<lambda>™  s!   € ¥B¤H¨Q¡K¤Kµ"´&¸½2¼5¹±/´/Ñ$A€ r5   rÿ  )rM   r  r   rf   r
  s      r3   rÛ   zcosine_gen._logpdf–  s=   € ÝŒF�1‰IŒIˆÝ˜!˜rš' A 4ØAÐAÝ%'¤V Gð-ñ -ô -ð 	-r5   c                 ó*   — t          j        |¦  «        S rK   ©rk   Ú_cosine_cdfr¦   s     r3   rr   zcosine_gen._cdfœ  s   € ÝŒ˜qÑ!Ô!Ð!r5   c                 ó,   — t          j        | ¦  «        S rK   rò  r¦   s     r3   rv   zcosine_gen._sfŸ  s   € ÝŒ ˜rÑ"Ô"Ð"r5   c                 ó*   — t          j        |¦  «        S rK   ©rk   Ú_cosine_invcdf©rB   rñ  s     r3   r{   zcosine_gen._ppf¢  s   € ÝÔ! !Ñ$Ô$Ð$r5   c                 ó,   — t          j        |¦  «         S rK   rö  rø  s     r3   r~   zcosine_gen._isf¥  s   € ÝÔ" 1Ñ%Ô%Ð%Ð%r5   c                 ó¼   — t           j        t           j        z  dz  dz
  }dt           j        dz  dz
  z  dt           j        t           j        z  dz
  dz  z  z  }d	|d	|fS )
NrD  r³   rÀ  r   éZ   ç      @r‚  rR   r…   r+  )rB   rÉ  r  s      r3   r   zcosine_gen._stats¨  sW   € ÝŒU•R”U‰]˜SÑ  CÑ'ˆØ•B”E˜1‘H˜r‘MÑ" c­R¬UµR´U©]¸QÑ->ÀÑ,BÑ&BÑCˆØ�A�s˜Aˆ~Ðr5   c                 óJ   — t          j        dt           j        z  ¦  «        dz
  S )Nr   r†   rì   rg   s    r3   rï   zcosine_gen._entropy­  s   € ÝŒv�a�œ‘g‰Œ˜sÑ"Ð"r5   N©r€   r�   r‚   rƒ   rh   ro   rÛ   rr   rv   r{   r~   r   rï   r„   r5   r3   ré  ré  z  s¥   € € € € € ðð ð(ð ð ð)ð )ð )ð-ð -ð -ð"ð "ð "ð#ð #ð #ð%ð %ð %ð&ð &ð &ðð ð ð
#ð #ð #ð #ð #r5   ré  Úcosinec                   óP   — e Zd ZdZd„ Zdd„Zd„ Zd„ Zd„ Zd„ Z	d	„ Z
d
„ Zd„ Zd„ ZdS )Ú
dgamma_genaÔ  A double gamma continuous random variable.

    The double gamma distribution is also known as the reflected gamma
    distribution [1]_.

    %(before_notes)s

    Notes
    -----
    The probability density function for `dgamma` is:

    .. math::

        f(x, a) = \frac{1}{2\Gamma(a)} |x|^{a-1} \exp(-|x|)

    for a real number :math:`x` and :math:`a > 0`. :math:`\Gamma` is the
    gamma function (`scipy.special.gamma`).

    `dgamma` takes ``a`` as a shape parameter for :math:`a`.

    %(after_notes)s

    References
    ----------
    .. [1] Johnson, Kotz, and Balakrishnan, "Continuous Univariate
           Distributions, Volume 1", Second Edition, John Wiley and Sons
           (1994).

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r  re   rg   s    r3   rh   zdgamma_gen._shape_infoÔ  r  r5   Nc                 ó¢   — |                      |¬¦  «        }t                               |||¬¦  «        }|t          j        |dk    dd¦  «        z  S ©N©rÔ   rÕ  r‘   r   r¼  )ÚuniformrÖ  r×  rM   rO  )rB   rˆ   rÔ   rÕ   ÚuÚgms         r3   rÖ   zdgamma_gen._rvs×  sL   € Ø× Ò  dÐ Ñ+Ô+ˆÝ�YŠY�q˜t°,ˆYÑ?Ô?ˆØ•B”H˜Q #šX q¨"Ñ-Ô-Ñ-Ð-r5   c                 ó’   — t          |¦  «        }ddt          j        |¦  «        z  z  ||dz
  z  z  t          j        | ¦  «        z  S r	  )Úabsrt   rÖ  rM   r´   ©rB   rn   rˆ   Úaxs       r3   ro   zdgamma_gen._pdfÜ  s@   € å�‰VŒVˆØ�A•b”h˜q‘k”k‘MÑ" 2¨¨#©¡;Ñ.µ´¸¸±´Ñ<Ð<r5   c                 óª   — t          |¦  «        }t          j        |dz
  |¦  «        |z
  t          j        d¦  «        z
  t          j        |¦  «        z
  S r	  )r
  rt   ru  rM   rí   rÃ  r  s       r3   rÛ   zdgamma_gen._logpdfá  sB   € Ý�‰VŒVˆÝŒx˜˜C™ Ñ$Ô$ rÑ)­B¬F°1©I¬IÑ5½¼
À1¹¼ÑEÐEr5   c           	      ó–   — t          j        |dk    ddt          j        ||¦  «        z  z   dt          j        || ¦  «        z  ¦  «        S ©Nr   r‘   )rM   rO  rt   r¯  r²  r
  s      r3   rr   zdgamma_gen._cdfå  sK   € ÝŒx˜˜AšØ˜c¥"¤+¨a°Ñ"3Ô"3Ñ3Ñ3Ø�BœL¨¨Q¨BÑ/Ô/Ñ/ñ1ô 1ð 	1r5   c           
      ó–   — t          j        |dk    dt          j        ||¦  «        z  ddt          j        || ¦  «        z  z   ¦  «        S r  )rM   rO  rt   r²  r¯  r
  s      r3   rv   zdgamma_gen._sfê  sK   € ÝŒx˜˜AšØ�BœL¨¨AÑ.Ô.Ñ.Ø˜c¥"¤+¨a°!°Ñ"4Ô"4Ñ4Ñ4ñ6ô 6ð 	6r5   c                 ój   — t           j                             |¦  «        t          j        d¦  «        z
  S ©Nr‘   )rð  rÖ  rï   rM   rí   r  s     r3   rï   zdgamma_gen._entropyï  s%   € ÝŒ{×#Ò# AÑ&Ô&­¬°©¬Ñ4Ð4r5   c           	      ó–   — t          j        |dk    t          j        |d|z  dz
  ¦  «        t          j        |d|z  ¦  «         ¦  «        S rë   ©rM   rO  rt   r¶  rº  r  s      r3   r{   zdgamma_gen._ppfò  sI   € ÝŒx˜˜CšÝœ q¨!¨A©#°©'Ñ2Ô2Ýœ¨¨A¨a©CÑ0Ô0Ð0ñ2ô 2ð 	2r5   c           	      ó–   — t          j        |dk    t          j        |d|z  dz
  ¦  «         t          j        |d|z  ¦  «        ¦  «        S rë   r  r  s      r3   r~   zdgamma_gen._isf÷  sI   € ÝŒx˜˜CšÝœ¨¨1¨Q©3°©7Ñ3Ô3Ð3Ýœ¨¨1¨Q©3Ñ/Ô/ñ1ô 1ð 	1r5   c                 ó<   — ||dz   z  }d|d|dz   |dz   z  |z  dz
  fS )Nr†   r…   r³   rD  r„   )rB   rˆ   rA  s      r3   r   zdgamma_gen._statsü  s4   € Ø��3‘‰iˆØ�C˜˜q ™u q¨¡u™o¨cÑ1°#Ñ5Ð5Ð5r5   r   )r€   r�   r‚   rƒ   rh   rÖ   ro   rÛ   rr   rv   rï   r{   r~   r   r„   r5   r3   r  r  ´  s¿   € € € € € ðð ð>Eð Eð Eð.ð .ð .ð .ð
=ð =ð =ð
Fð Fð Fð1ð 1ð 1ð
6ð 6ð 6ð
5ð 5ð 5ð2ð 2ð 2ð
1ð 1ð 1ð
6ð 6ð 6ð 6ð 6r5   r  Údgammac                   óV   — e Zd ZdZd„ Zdd„Zd„ Zd„ Zd„ Zd„ Z	d	„ Z
d
„ Zd„ Zd„ Zd„ ZdS )Údweibull_genav  A double Weibull continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `dweibull` is given by

    .. math::

        f(x, c) = c / 2 |x|^{c-1} \exp(-|x|^c)

    for a real number :math:`x` and :math:`c > 0`.

    `dweibull` takes ``c`` as a shape parameter for :math:`c`.

    %(after_notes)s

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r  re   rg   s    r3   rh   zdweibull_gen._shape_info  r  r5   Nc                 ó¢   — |                      |¬¦  «        }t                               |||¬¦  «        }|t          j        |dk    dd¦  «        z  S r  )r  Úweibull_minr×  rM   rO  )rB   r  rÔ   rÕ   r  Úws         r3   rÖ   zdweibull_gen._rvs  sL   € Ø× Ò  dÐ Ñ+Ô+ˆÝ�OŠO˜A D°|ˆOÑDÔDˆØ•B”H˜Q #šX q¨"Ñ-Ô-Ñ.Ð.r5   c                 ór   — t          |¦  «        }|dz  ||dz
  z  z  t          j        ||z   ¦  «        z  }|S ©Nr³   r†   )r
  rM   r´   )rB   rn   r  r  ÚPxs        r3   ro   zdweibull_gen._pdf"  s;   € å�‰VŒVˆØ�‰W�r˜A˜c™E‘{Ñ"¥R¤V¨R°©U¨F¡^¤^Ñ3ˆØˆ	r5   c                 ó°   — t          |¦  «        }t          j        |¦  «        t          j        d¦  «        z
  t          j        |dz
  |¦  «        z   ||z  z
  S r  )r
  rM   rí   rt   ru  )rB   rn   r  r  s       r3   rÛ   zdweibull_gen._logpdf(  sF   € Ý�‰VŒVˆÝŒv�a‰yŒy�2œ6 #™;œ;Ñ&­¬°!°c±'¸2Ñ)>Ô)>Ñ>ÀÀQÁÑFÐFr5   c                 óŒ   — dt          j        t          |¦  «        |z   ¦  «        z  }t          j        |dk    d|z
  |¦  «        S ©Nr‘   r   r   )rM   r´   r
  rO  )rB   rn   r  ÚCx1s       r3   rr   zdweibull_gen._cdf,  s>   € Ø•B”F�C ™FœF A™I˜:Ñ&Ô&Ñ&ˆÝŒx˜˜Aš˜q 3™w¨Ñ,Ô,Ð,r5   c                 óÎ   — dt          j        |dk    |d|z
  ¦  «        z  }t          j        t          j        |¦  «         d|z  ¦  «        }t          j        |dk    || ¦  «        S ©Nr³   r‘   r†   )rM   rO  r¾  rí   )rB   rz   r  r¨  s       r3   r{   zdweibull_gen._ppf0  s[   € Ø•2”8˜A šH a¨¨a©Ñ0Ô0Ñ0ˆÝŒh�œ˜s™œ�| S¨1¡WÑ-Ô-ˆÝŒx˜˜Cš  s dÑ+Ô+Ð+r5   c                 ó¦   — dt           j                             t          j        |¦  «        |¦  «        z  }t          j        |dk    |d|z
  ¦  «        S r#  )rð  r  rv   rM   r
  rO  )rB   rn   r  Úhalf_weibull_min_sfs       r3   rv   zdweibull_gen._sf5  sG   € Ø!¥EÔ$5×$9Ò$9½"¼&À¹)¼)ÀQÑ$GÔ$GÑGÐÝŒx˜˜AšÐ2°AÐ8KÑ4KÑLÔLÐLr5   c                 ó¸   — dt          j        |dk    |d|z
  ¦  «        z  }t          j                             ||¦  «        }t          j        |dk    | |¦  «        S r&  )rM   rO  rð  r  r~   )rB   rz   r  Údouble_qÚweibull_min_isfs        r3   r~   zdweibull_gen._isf9  sU   € Ø�œ  c¢¨1¨b°1©fÑ5Ô5Ñ5ˆÝÔ+×0Ò0°¸1Ñ=Ô=ˆÝŒx˜˜Cš /Ð!1°?ÑCÔCÐCr5   c                 óN   — d|dz  z
  t          j        dd|z  |z  z   ¦  «        z  S )Nr   rR   r†   ©rt   rÖ  r{  s      r3   rÿ   zdweibull_gen._munp>  s,   € Ø�Q˜‘U‘�rœx¨¨c°A©g¸©kÑ(9Ñ:Ô:Ñ:Ð:r5   c                 ó   — dS ©N)r   Nr   Nr„   r}  s     r3   r   zdweibull_gen._statsD  ó   € ØÐr5   c                 ón   — t           j                             |¦  «        t          j        d¦  «        z
  }|S r  )rð  r  rï   rM   rí   )rB   r  ræ  s      r3   rï   zdweibull_gen._entropyG  s*   € ÝÔ×&Ò& qÑ)Ô)­B¬F°3©K¬KÑ7ˆØˆr5   r   )r€   r�   r‚   rƒ   rh   rÖ   ro   rÛ   rr   r{   rv   r~   rÿ   r   rï   r„   r5   r3   r  r    sÔ   € € € € € ðð ð*Eð Eð Eð/ð /ð /ð /ð
ð ð ðGð Gð Gð-ð -ð -ð,ð ,ð ,ð
Mð Mð MðDð Dð Dð
;ð ;ð ;ð ð  ð  ðð ð ð ð r5   r  Údweibullc                   ó’   — e Zd ZdZd„ Zdd„Zd„ Zd„ Zd„ Zd„ Z	d	„ Z
d
„ Zd„ Zd„ Zd„ Ze eed¬¦  «        d„ ¦   «         ¦   «         ZdS )Ú	expon_genaE  An exponential continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `expon` is:

    .. math::

        f(x) = \exp(-x)

    for :math:`x \ge 0`.

    %(after_notes)s

    A common parameterization for `expon` is in terms of the rate parameter
    ``lambda``, such that ``pdf = lambda * exp(-lambda * x)``. This
    parameterization corresponds to using ``scale = 1 / lambda``.

    The exponential distribution is a special case of the gamma
    distributions, with gamma shape parameter ``a = 1``.

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   zexpon_gen._shape_infoj  r£   r5   Nc                 ó,   — |                      |¦  «        S rK   )Ústandard_exponentialrÓ   s      r3   rÖ   zexpon_gen._rvsm  s   € Ø×0Ò0°Ñ6Ô6Ð6r5   c                 ó,   — t          j        | ¦  «        S rK   ©rM   r´   r¦   s     r3   ro   zexpon_gen._pdfp  s   € åŒv�q�b‰zŒzÐr5   c                 ó   — | S rK   r„   r¦   s     r3   rÛ   zexpon_gen._logpdft  ó	   € Øˆrˆ	r5   c                 ó.   — t          j        | ¦  «         S rK   ©rt   r  r¦   s     r3   rr   zexpon_gen._cdfw  ó   € Ý”˜!˜‘”ˆ}Ðr5   c                 ó.   — t          j        | ¦  «         S rK   r	  r­   s     r3   r{   zexpon_gen._ppfz  r>  r5   c                 ó,   — t          j        | ¦  «        S rK   r9  r¦   s     r3   rv   zexpon_gen._sf}  s   € ÝŒv�q�b‰zŒzÐr5   c                 ó   — | S rK   r„   r¦   s     r3   rä   zexpon_gen._logsf€  r;  r5   c                 ó,   — t          j        |¦  «         S rK   r.  r­   s     r3   r~   zexpon_gen._isfƒ  ó   € Ý”�q‘	”	ˆzÐr5   c                 ó   — dS )N)r†   r†   r³   ç      @r„   rg   s    r3   r   zexpon_gen._stats†  ré   r5   c                 ó   — dS r  r„   rg   s    r3   rï   zexpon_gen._entropy‰  ó   € Øˆsr5   zú        When `method='MLE'`,
        this function uses explicit formulas for the maximum likelihood
        estimation of the exponential distribution parameters, so the
        `optimizer`, `loc` and `scale` keyword arguments are
        ignored.

rð   c                 ób  — t          |¦  «        dk    rt          d¦  «        ‚|                     dd ¦  «        }|                     dd ¦  «        }t          |¦  «         |�|�t	          d¦  «        ‚t          j        |¦  «        }t          j        |¦  «                             ¦   «         st	          d¦  «        ‚| 	                    ¦   «         }|€|}n$|}||k     rt          d|t
          j        ¬¦  «        ‚|€|                     ¦   «         |z
  }n|}t          |¦  «        t          |¦  «        fS )	Nr   úToo many arguments.ró   rô   rõ   rö   Úexponrœ  )r¡  r1   r0   r4   r÷   rM   rø   rù   rú   ÚminrH  rf   rû   Úfloat)	rB   rC   rD   r2   ró   rô   Údata_minr,   r-   s	            r3   r@   zexpon_gen.fitŒ  s,  € õ ˆt‰9Œ9�qŠ=ˆ=ÝÐ1Ñ2Ô2Ð2à�xŠx˜ Ñ%Ô%ˆØ—’˜( DÑ)Ô)ˆå$ TÑ*Ô*Ð*àÐ Ð 2åð )ñ *ô *ð *õ Œz˜$ÑÔˆåŒ{˜4Ñ Ô ×$Ò$Ñ&Ô&ð 	EÝÐCÑDÔDÐDà—8’8‘:”:ˆàˆ<àˆCˆCàˆCØ˜#Š~ˆ~å" 7°$½b¼fÐEÑEÔEÐEàˆ>à—I’I‘K”K #Ñ%ˆEˆEàˆEõ �S‰zŒz�5 ™<œ<Ð'Ð'r5   r   )r€   r�   r‚   rƒ   rh   rÖ   ro   rÛ   rr   r{   rv   rä   r~   r   rï   rH   r
   r   r@   r„   r5   r3   r4  r4  O  s	  € € € € € ðð ð4ð ð ð7ð 7ð 7ð 7ðð ð ðð ð ðð ð ðð ð ðð ð ðð ð ðð ð ð"ð "ð "ðð ð ð ØÐ ð 6ð ñ ô ð&(ð &(ñô ñ „_ð&(ð &(ð &(r5   r4  rJ  c                   ó>   — e Zd ZdZd„ Zd
d„Zd„ Zd„ Zd„ Zd„ Z	d	„ Z
dS )Úexponnorm_genaè  An exponentially modified Normal continuous random variable.

    Also known as the exponentially modified Gaussian distribution [1]_.

    %(before_notes)s

    Notes
    -----
    The probability density function for `exponnorm` is:

    .. math::

        f(x, K) = \frac{1}{2K} \exp\left(\frac{1}{2 K^2} - x / K \right)
                  \text{erfc}\left(-\frac{x - 1/K}{\sqrt{2}}\right)

    where :math:`x` is a real number and :math:`K > 0`.

    It can be thought of as the sum of a standard normal random variable
    and an independent exponentially distributed random variable with rate
    ``1/K``.

    %(after_notes)s

    An alternative parameterization of this distribution (for example, in
    the Wikipedia article [1]_) involves three parameters, :math:`\mu`,
    :math:`\lambda` and :math:`\sigma`.

    In the present parameterization this corresponds to having ``loc`` and
    ``scale`` equal to :math:`\mu` and :math:`\sigma`, respectively, and
    shape parameter :math:`K = 1/(\sigma\lambda)`.

    .. versionadded:: 0.16.0

    References
    ----------
    .. [1] Exponentially modified Gaussian distribution, Wikipedia,
           https://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS )NÚKFr   r  re   rg   s    r3   rh   zexponnorm_gen._shape_infoé  r  r5   Nc                 óf   — |                      |¦  «        |z  }|                     |¦  «        }||z   S rK   )r7  rÒ   )rB   rQ  rÔ   rÕ   ÚexpvalÚgvals         r3   rÖ   zexponnorm_gen._rvsì  s7   € Ø×2Ò2°4Ñ8Ô8¸1Ñ<ˆØ×+Ò+¨DÑ1Ô1ˆØ˜‰}Ðr5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   rÛ  )rB   rn   rQ  s      r3   ro   zexponnorm_gen._pdfñ  ó    € ÝŒv�d—l’l 1 aÑ(Ô(Ñ)Ô)Ð)r5   c                 óv   — d|z  }|d|z  |z
  z  }|t          ||z
  ¦  «        z   t          j        |¦  «        z
  S ©Nr†   r‘   ©rÀ   rM   rí   )rB   rn   rQ  ÚinvKÚexpargs        r3   rÛ   zexponnorm_gen._logpdfô  sA   € Ø�Q‰wˆØ˜˜t™ a™Ñ(ˆØ� Q¨¡XÑ.Ô.Ñ.µ´¸±´Ñ:Ð:r5   c                 ó”   — d|z  }|d|z  |z
  z  }|t          ||z
  ¦  «        z   }t          |¦  «        t          j        |¦  «        z
  S rX  ©rÀ   r½   rM   r´   ©rB   rn   rQ  rZ  rS  Úlogprods         r3   rr   zexponnorm_gen._cdfù  sL   € Ø�Q‰wˆØ˜˜t™ a™Ñ(ˆØ�<¨¨D©Ñ1Ô1Ñ1ˆÝ˜‰|Œ|�bœf W™oœoÑ-Ð-r5   c                 ó–   — d|z  }|d|z  |z
  z  }|t          ||z
  ¦  «        z   }t          | ¦  «        t          j        |¦  «        z   S rX  r]  r^  s         r3   rv   zexponnorm_gen._sfÿ  sN   € Ø�Q‰wˆØ˜˜t™ a™Ñ(ˆØ�<¨¨D©Ñ1Ô1Ñ1ˆÝ˜!˜‰}Œ}�rœv g™œÑ.Ð.r5   c                 óZ   — ||z  }d|z   }d|dz  z  |dz  z  }d|z  |z  |dz  z  }||||fS )Nr†   rR   rƒ  r>  rE  r  r„   )rB   rQ  ÚK2ÚopK2ÚskwÚkrts         r3   r   zexponnorm_gen._stats  sO   € Ø�‰UˆØ�R‰xˆØ�!�Q‘$‰h˜ ™Ñ%ˆØ�B‰h˜‰m˜d R™jÑ(ˆØ�$˜˜SÐ Ð r5   r   )r€   r�   r‚   rƒ   rh   rÖ   ro   rÛ   rr   rv   r   r„   r5   r3   rO  rO  ¿  s�   € € € € € ð(ð (ðREð Eð Eðð ð ð ð
*ð *ð *ð;ð ;ð ;ð
.ð .ð .ð/ð /ð /ð!ð !ð !ð !ð !r5   rO  Ú	exponnormc                 óP   — t          j        t          j        || ¦  «        ¦  «        S )a'  
    Compute (1 + x)**y - 1.

    Uses expm1 and xlog1py to avoid loss of precision when
    (1 + x)**y is close to 1.

    Note that the inverse of this function with respect to x is
    ``_pow1pm1(x, 1/y)``.  That is, if

        t = _pow1pm1(x, y)

    then

        x = _pow1pm1(t, 1/y)
    )rM   r  rt   rt  ©rn   Úys     r3   Ú_pow1pm1rj    s    € õ  Œ8•B”J˜q !Ñ$Ô$Ñ%Ô%Ð%r5   c                   ó<   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	S )
Úexponweib_gena   An exponentiated Weibull continuous random variable.

    %(before_notes)s

    See Also
    --------
    weibull_min, numpy.random.Generator.weibull

    Notes
    -----
    The probability density function for `exponweib` is:

    .. math::

        f(x, a, c) = a c [1-\exp(-x^c)]^{a-1} \exp(-x^c) x^{c-1}

    and its cumulative distribution function is:

    .. math::

        F(x, a, c) = [1-\exp(-x^c)]^a

    for :math:`x > 0`, :math:`a > 0`, :math:`c > 0`.

    `exponweib` takes :math:`a` and :math:`c` as shape parameters:

    * :math:`a` is the exponentiation parameter,
      with the special case :math:`a=1` corresponding to the
      (non-exponentiated) Weibull distribution `weibull_min`.
    * :math:`c` is the shape parameter of the non-exponentiated Weibull law.

    %(after_notes)s

    References
    ----------
    https://en.wikipedia.org/wiki/Exponentiated_Weibull_distribution

    %(example)s

    c                 ó‚   — t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }||gS ©Nrˆ   Fr   r  r  re   ©rB   rf  r!  s      r3   rh   zexponweib_gen._shape_infoL  rh  r5   c                 óT   — t          j        |                      |||¦  «        ¦  «        S rK   rÛ  ©rB   rn   rˆ   r  s       r3   ro   zexponweib_gen._pdfQ  ó$   € õ Œv�d—l’l 1 a¨Ñ+Ô+Ñ,Ô,Ð,r5   c                 óø   — ||z   }t          j        |¦  «         }t          j        |¦  «        t          j        |¦  «        z   t          j        |dz
  |¦  «        z   |z   t          j        |dz
  |¦  «        z   }|S r  )rt   r  rM   rí   ru  )rB   rn   rˆ   r  ÚnegxcÚexm1cÚlogps          r3   rÛ   zexponweib_gen._logpdfV  sq   € Ø�A‘�ˆÝ”˜%‘”Ð ˆÝ”�q‘	”	�BœF 1™IœIÑ%­¬°°S±¸%Ñ(@Ô(@Ñ@ØñÝœ  S¡¨!Ñ,Ô,ñ-ˆàˆr5   c                 ó>   — t          j        ||z   ¦  «         }||z  S rK   r=  )rB   rn   rˆ   r  ru  s        r3   rr   zexponweib_gen._cdf]  s!   € Ý”˜1˜a™4˜%‘”Ð ˆØ�a‰xˆr5   c                 ój   — t          j        |d|z  z   ¦  «         t          j        d|z  ¦  «        z  S r  )rt   r£  rM   rø   )rB   rz   rˆ   r  s       r3   r{   zexponweib_gen._ppfa  s2   € Ý”˜1˜s 1™u™:˜+Ñ&Ô&Ð&­¬°C¸±EÑ):Ô):Ñ:Ð:r5   c                 óR   — t          t          j        ||z   ¦  «         |¦  «         S rK   )rj  rM   r´   rq  s       r3   rv   zexponweib_gen._sfd  s%   € Ý�"œ& ! Q¡$ ™-œ-˜¨Ñ+Ô+Ð+Ð+r5   c                 ó^   — t          j        t          | d|z  ¦  «         ¦  «         d|z  z  S r[   )rM   rí   rj  )rB   rñ  rˆ   r  s       r3   r~   zexponweib_gen._isfg  s1   € Ý”� 1 " a¨¡cÑ*Ô*Ð*Ñ+Ô+Ð+¨q°©sÑ3Ð3r5   N©r€   r�   r‚   rƒ   rh   ro   rÛ   rr   r{   rv   r~   r„   r5   r3   rl  rl  #  sˆ   € € € € € ð'ð 'ðPð ð ð
-ð -ð -ð
ð ð ðð ð ð;ð ;ð ;ð,ð ,ð ,ð4ð 4ð 4ð 4ð 4r5   rl  Ú	exponweibc                   ó<   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	S )
Úexponpow_genaƒ  An exponential power continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `exponpow` is:

    .. math::

        f(x, b) = b x^{b-1} \exp(1 + x^b - \exp(x^b))

    for :math:`x \ge 0`, :math:`b > 0`.  Note that this is a different
    distribution from the exponential power distribution that is also known
    under the names "generalized normal" or "generalized Gaussian".

    `exponpow` takes ``b`` as a shape parameter for :math:`b`.

    %(after_notes)s

    References
    ----------
    http://www.math.wm.edu/~leemis/chart/UDR/PDFs/Exponentialpower.pdf

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS ©Nr‰   Fr   r  re   rg   s    r3   rh   zexponpow_gen._shape_infoŠ  r  r5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   rÛ  ©rB   rn   r‰   s      r3   ro   zexponpow_gen._pdf�  ó    € åŒv�d—l’l 1 aÑ(Ô(Ñ)Ô)Ð)r5   c                 ó    — ||z  }dt          j        |¦  «        z   t          j        |dz
  |¦  «        z   |z   t          j        |¦  «        z
  }|S ©Nr   r†   )rM   rí   rt   ru  r´   )rB   rn   r‰   ÚxbÚfs        r3   rÛ   zexponpow_gen._logpdf‘  sH   € Ø�‰TˆØ•”�q‘	”	‰M�BœH Q¨¡W¨aÑ0Ô0Ñ0°2Ñ5½¼¸r¹
¼
ÑBˆØˆr5   c                 óX   — t          j        t          j        ||z  ¦  «         ¦  «         S rK   r=  r‚  s      r3   rr   zexponpow_gen._cdf–  s#   € Ý”�"œ( 1 a¡4™.œ.˜Ñ)Ô)Ð)Ð)r5   c                 óV   — t          j        t          j        ||z  ¦  «         ¦  «        S rK   ©rM   r´   rt   r  r‚  s      r3   rv   zexponpow_gen._sf™  s    € ÝŒv•r”x  1¡‘~”~�oÑ&Ô&Ð&r5   c                 ó\   — t          j        t          j        |¦  «         ¦  «        d|z  z  S r  ©rt   r£  rM   rí   r‚  s      r3   r~   zexponpow_gen._isfœ  s%   € Ý”�"œ& ™)œ)˜Ñ$Ô$¨¨1©Ñ-Ð-r5   c                 ót   — t          t          j        t          j        | ¦  «         ¦  «        d|z  ¦  «        S r  ©Úpowrt   r£  ©rB   rz   r‰   s      r3   r{   zexponpow_gen._ppfŸ  s,   € Ý•2”8�RœX q b™\œ\˜MÑ*Ô*¨C°©EÑ2Ô2Ð2r5   N)r€   r�   r‚   rƒ   rh   ro   rÛ   rr   rv   r~   r{   r„   r5   r3   r~  r~  n  sŠ   € € € € € ðð ð6Eð Eð Eð*ð *ð *ðð ð ð
*ð *ð *ð'ð 'ð 'ð.ð .ð .ð3ð 3ð 3ð 3ð 3r5   r~  Úexponpowc                   óX   — e Zd ZdZej        Zd„ Zdd„Zd„ Z	d„ Z
d„ Zd„ Zd	„ Zd
„ Zd„ ZdS )Úfatiguelife_gena0  A fatigue-life (Birnbaum-Saunders) continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `fatiguelife` is:

    .. math::

        f(x, c) = \frac{x+1}{2c\sqrt{2\pi x^3}} \exp(-\frac{(x-1)^2}{2x c^2})

    for :math:`x >= 0` and :math:`c > 0`.

    `fatiguelife` takes ``c`` as a shape parameter for :math:`c`.

    %(after_notes)s

    References
    ----------
    .. [1] "Birnbaum-Saunders distribution",
           https://en.wikipedia.org/wiki/Birnbaum-Saunders_distribution

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r  re   rg   s    r3   rh   zfatiguelife_gen._shape_infoÃ  r  r5   Nc                 ó–   — |                      |¦  «        }d|z  |z  }||z  }dd|z  z   d|z  t          j        d|z   ¦  «        z  z   }|S )Nr‘   r†   rR   r   )rÒ   rM   rü   )rB   r  rÔ   rÕ   Úzrn   Úx2Úts           r3   rÖ   zfatiguelife_gen._rvsÆ  sW   € Ø×(Ò(¨Ñ.Ô.ˆØ�‰E�!‰GˆØˆq‰SˆØ�!�B‘$‰J˜˜1™�RœW Q¨¡V™_œ_Ñ,Ñ,ˆØˆr5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   rÛ  r
  s      r3   ro   zfatiguelife_gen._pdfÍ  s"   € õ Œv�d—l’l 1 aÑ(Ô(Ñ)Ô)Ð)r5   c                 ó  — t          j        |dz   ¦  «        |dz
  dz  d|z  |dz  z  z  z
  t          j        d|z  ¦  «        z
  dt          j        dt           j        z  ¦  «        dt          j        |¦  «        z  z   z  z
  S )Nr   rR   r³   r‘   rƒ  rì   r
  s      r3   rÛ   zfatiguelife_gen._logpdfÒ  sq   € Ý”�q˜‘s‘”˜q ™s Q™h¨#¨a©%°°1±©*Ñ5Ñ5½¼¸qÀ¹s¹¼ÑCØ•R”V˜A�bœe™G‘_”_ q­¬°©¬¡{Ñ2Ñ3ñ4ð 	5r5   c                 ó€   — t          d|z  t          j        |¦  «        dt          j        |¦  «        z  z
  z  ¦  «        S r  )r½   rM   rü   r
  s      r3   rr   zfatiguelife_gen._cdfÖ  s2   € Ý˜˜q™¥B¤G¨A¡J¤J°µR´W¸Q±Z´Z±Ñ$?Ñ@ÑAÔAÐAr5   c                 ól   — |t          |¦  «        z  }d|t          j        |dz  dz   ¦  «        z   dz  z  S ©Nç      Ð?rR   r   ©rÄ   rM   rü   ©rB   rz   r  Útmps       r3   r{   zfatiguelife_gen._ppfÙ  s9   € Ø•)˜A‘,”,ÑˆØ�s�RœW S¨!¡V¨a¡ZÑ0Ô0Ñ0°1Ñ4Ñ4Ð4r5   c                 ó€   — t          d|z  t          j        |¦  «        dt          j        |¦  «        z  z
  z  ¦  «        S r  )rÇ   rM   rü   r
  s      r3   rv   zfatiguelife_gen._sfÝ  s2   € Ý˜˜a™¥2¤7¨1¡:¤:°µB´G¸A±J´J±Ñ#>Ñ?Ñ@Ô@Ð@r5   c                 ón   — | t          |¦  «        z  }d|t          j        |dz  dz   ¦  «        z   dz  z  S r�  rŸ  r   s       r3   r~   zfatiguelife_gen._isfà  s;   € Øˆb•9˜Q‘<”<ÑˆØ�s�RœW S¨!¡V¨a¡ZÑ0Ô0Ñ0°1Ñ4Ñ4Ð4r5   c                 ó¸   — ||z  }|dz  dz   }d|z  dz   }||z  dz  }d|z  d|z  dz   z  t          j        |d¦  «        z  }d	|z  d
|z  dz   z  |dz  z  }||||fS )Nr³   r†   rü  rJ  r   é   rE  r¼  r‚  é]   g      D@©rM   r¾  )rB   r  Úc2r@  ÚdenrA  rB  rC  s           r3   r   zfatiguelife_gen._statsä  sˆ   € ð ˆq‰SˆØ�#‰X˜‰^ˆØ�B‰h˜‰nˆØ�‰f�s‰lˆØ�‰U�b˜‘e˜c‘kÑ"¥R¤X¨c°3Ñ%7Ô%7Ñ7ˆØ�‰V�r˜"‘u˜t‘|Ñ$ s¨C¡xÑ/ˆØ�3˜˜BˆÐr5   r   )r€   r�   r‚   rƒ   r   r  r  rh   rÖ   ro   rÛ   rr   r{   rv   r~   r   r„   r5   r3   r“  r“  ¦  s½   € € € € € ðð ð4 "Ô4€MðEð Eð Eðð ð ð ð*ð *ð *ð
5ð 5ð 5ðBð Bð Bð5ð 5ð 5ðAð Að Að5ð 5ð 5ðð ð ð ð r5   r“  Úfatiguelifec                   ó>   — e Zd ZdZd„ Zd„ Zd
d„Zd„ Zd„ Zd„ Z	d	„ Z
dS )Úfoldcauchy_genao  A folded Cauchy continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `foldcauchy` is:

    .. math::

        f(x, c) = \frac{1}{\pi (1+(x-c)^2)} + \frac{1}{\pi (1+(x+c)^2)}

    for :math:`x \ge 0` and :math:`c \ge 0`.

    `foldcauchy` takes ``c`` as a shape parameter for :math:`c`.

    %(example)s

    c                 ó   — |dk    S ©Nr   r„   r}  s     r3   r`   zfoldcauchy_gen._argcheck
	  ó   € Ø�AŠvˆr5   c                 ó@   — t          dddt          j        fd¦  «        gS ©Nr  Fr   rd   re   rg   s    r3   rh   zfoldcauchy_gen._shape_info	  ó   € Ý˜3 ¨­2¬6 {°MÑBÔBÐCÐCr5   Nc                 óV   — t          t                               |||¬¦  «        ¦  «        S )N©r,   rÔ   rÕ   )r
  rž  r×  ©rB   r  rÔ   rÕ   s       r3   rÖ   zfoldcauchy_gen._rvs	  s0   € Ý•6—:’: !¨$Ø+7ð ñ 9ô 9ñ :ô :ð 	:r5   c                 ó\   — dt           j        z  dd||z
  dz  z   z  dd||z   dz  z   z  z   z  S ©Nr†   r   rR   r+  r
  s      r3   ro   zfoldcauchy_gen._pdf	  s:   € à•2”5‰y˜#˜q ! A¡#¨¡™zÑ*¨S°!°Q°q±S¸1±H±*Ñ-=Ñ=Ñ>Ð>r5   c                 ó€   — dt           j        z  t          j        ||z
  ¦  «        t          j        ||z   ¦  «        z   z  S r  r‡  r
  s      r3   rr   zfoldcauchy_gen._cdf	  s0   € Ø•2”5‰y�"œ) A a¡C™.œ.­2¬9°Q°q±S©>¬>Ñ9Ñ:Ð:r5   c                 ó~   — t          j        d||z
  ¦  «        t          j        d||z   ¦  «        z   t           j        z  S r[   )rM   Úarctan2rî   r
  s      r3   rv   zfoldcauchy_gen._sf	  s6   € õ
 ”
˜1˜a !™eÑ$Ô$¥r¤z°!°Q¸±UÑ';Ô';Ñ;½R¼UÑBÐBr5   c                 ó^   — t           j        t           j        t           j        t           j        fS rK   r  r}  s     r3   r   zfoldcauchy_gen._stats"	  r‘  r5   r   ©r€   r�   r‚   rƒ   r`   rh   rÖ   ro   rr   rv   r   r„   r5   r3   r¬  r¬  ö  s’   € € € € € ðð ð&ð ð ðDð Dð Dð:ð :ð :ð :ð?ð ?ð ?ð;ð ;ð ;ðCð Cð Cð.ð .ð .ð .ð .r5   r¬  Ú
foldcauchyc                   óJ   — e Zd ZdZd„ Zdd„Zd„ Zd„ Zd„ Zd„ Z	d	„ Z
d
„ Zd„ ZdS )Úf_genaù  An F continuous random variable.

    For the noncentral F distribution, see `ncf`.

    %(before_notes)s

    See Also
    --------
    ncf

    Notes
    -----
    The F distribution with :math:`df_1 > 0` and :math:`df_2 > 0` degrees of freedom is
    the distribution of the ratio of two independent chi-squared distributions with
    :math:`df_1` and :math:`df_2` degrees of freedom, after rescaling by
    :math:`df_2 / df_1`.

    The probability density function for `f` is:

    .. math::

        f(x, df_1, df_2) = \frac{df_2^{df_2/2} df_1^{df_1/2} x^{df_1 / 2-1}}
                                {(df_2+df_1 x)^{(df_1+df_2)/2}
                                 B(df_1/2, df_2/2)}

    for :math:`x > 0`.

    `f` accepts shape parameters ``dfn`` and ``dfd`` for :math:`df_1`, the degrees of
    freedom of the chi-squared distribution in the numerator, and :math:`df_2`, the
    degrees of freedom of the chi-squared distribution in the denominator, respectively.

    %(after_notes)s

    %(example)s

    c                 ó‚   — t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }||gS )NÚdfnFr   r  Údfdre   )rB   ÚidfnÚidfds      r3   rh   zf_gen._shape_infoN	  s>   € Ý˜% ¨­B¬F¨°^ÑDÔDˆÝ˜% ¨­B¬F¨°^ÑDÔDˆØ�dˆ|Ðr5   Nc                 ó0   — |                      |||¦  «        S rK   )r‡  )rB   rÁ  rÂ  rÔ   rÕ   s        r3   rÖ   z
f_gen._rvsS	  s   € Ø�~Š~˜c 3¨Ñ-Ô-Ð-r5   c                 óT   — t          j        |                      |||¦  «        ¦  «        S rK   rÛ  ©rB   rn   rÁ  rÂ  s       r3   ro   z
f_gen._pdfV	  s$   € õ Œv�d—l’l 1 c¨3Ñ/Ô/Ñ0Ô0Ð0r5   c                 ó<  — d|z  }d|z  }|dz  t          j        |¦  «        z  |dz  t          j        |¦  «        z  z   t          j        |dz  dz
  |¦  «        z   ||z   dz  t          j        |||z  z   ¦  «        z  t          j        |dz  |dz  ¦  «        z   z
  }|S ©Nr†   rR   r   )rM   rí   rt   ru  rv  )rB   rn   rÁ  rÂ  r_   Úmrw  s          r3   rÛ   zf_gen._logpdf\	  s›   € Ø�#‰IˆØ�#‰IˆØ�‰s•R”V˜A‘Y”Y‰  1¡¥r¤v¨a¡y¤y¡Ñ0µ2´8¸A¸a¹CÀ!¹GÀQÑ3GÔ3GÑGØ�a‘C˜‘7�bœf Q¨¨1©¡W™oœoÑ-µ´	¸!¸A¹#¸qÀ¹sÑ0CÔ0CÑCñEˆàˆ
r5   c                 ó.   — t          j        |||¦  «        S rK   )rt   ÚfdtrrÇ  s       r3   rr   z
f_gen._cdfc	  s   € ÝŒw�s˜C Ñ#Ô#Ð#r5   c                 ó.   — t          j        |||¦  «        S rK   )rt   ÚfdtrcrÇ  s       r3   rv   z	f_gen._sff	  ó   € ÝŒx˜˜S !Ñ$Ô$Ð$r5   c                 ó.   — t          j        |||¦  «        S rK   )rt   Úfdtri)rB   rz   rÁ  rÂ  s       r3   r{   z
f_gen._ppfi	  rÏ  r5   c                 óª  — d|z  d|z  }}|dz
  |dz
  |dz
  |dz
  f\  }}}}t          |dk    ||fd„ t          j        ¦  «        }	t          |dk    ||||fd	„ t          j        ¦  «        }
t          |d
k    ||||fd„ t          j        ¦  «        }|t          j        d¦  «        z  }t          |dk    |||fd„ t          j        ¦  «        }|dz  }|	|
||fS )Nr†   r³   rJ  rE  ç       @rR   c                 ó   — | |z  S rK   r„   )Úv2Úv2_2s     r3   rå  zf_gen._stats.<locals>.<lambda>r	  s
   € ˜R $™Y€ r5   r   c                 ó6   — d|z  |z  | |z   z  | |dz  z  |z  z  S r  r„   )Úv1rÕ  rÖ  Úv2_4s       r3   rå  zf_gen._stats.<locals>.<lambda>w	  s-   € Ø�‰F�R‰K˜2 ™9Ñ%¨¨d°A©g©¸Ñ)<Ñ=ð r5   r‚  c                 óT   — d| z  |z   |z  t          j        || | |z   z  z  ¦  «        z  S r  r„  )rØ  rÖ  rÙ  Úv2_6s       r3   rå  zf_gen._stats.<locals>.<lambda>}	  s4   € Ø�‰V�d‰]˜dÑ"¥R¤W¨T°R¸2À¹9Ñ5EÑ-FÑ%GÔ%GÑGð r5   r*  c                 ó   — d| | z  |z  z   |z  S )Nr*  r„   )rB  rÛ  Úv2_8s      r3   rå  zf_gen._stats.<locals>.<lambda>„	  s   €  A¨¨R©°$©Ñ$6¸$Ñ#>€ r5   r¼  )r   rM   rf   r  rü   )rB   rÁ  rÂ  rØ  rÕ  rÖ  rÙ  rÛ  rÝ  r@  rA  rB  rC  s                r3   r   zf_gen._statsl	  s  € Ø�c‘˜2 ™8ˆBˆØ!# b¡¨"¨r©'°2¸±7¸BÀ¹GÐ!CÑˆˆd�D˜$åØ�ŠF�R˜�JØ&Ð&ÝŒFñô ˆõ
 Ø�ŠF�R˜˜T 4Ð(ð>ð >åŒFñ	ô ˆõ Ø�ŠF�R˜˜t TÐ*ðHð HåŒFñ	ô ˆð
 	�bŒg�b‰kŒkÑˆåØ�ŠF�R˜˜tÐ$Ø>Ð>ÝŒFñô ˆð 	ˆg‰ˆà�3˜˜BˆÐr5   c                 ó@  — d|z  }d|z  }d||z   z  }t          j        |¦  «        t          j        |¦  «        z
  t          j        ||¦  «        z   d|z
  t          j        |¦  «        z  z   d|z   t          j        |¦  «        z  z
  |t          j        |¦  «        z  z   S rì  )rM   rí   rt   rv  rX  )rB   rÁ  rÂ  Úhalf_dfnÚhalf_dfdÚhalf_sums         r3   rï   zf_gen._entropyŠ	  s£   € ð ˜‘9ˆØ˜‘9ˆØ˜# ™)Ñ$ˆå”�s‘”�bœf S™kœkÑ)­B¬I°hÀÑ,IÔ,IÑIØ�X‘¥¤¨Ñ!1Ô!1Ñ1ñ2Ø56¸±\Ý”�xÑ Ô ñ5!ñ!à#+­b¬f°XÑ.>Ô.>Ñ#>ñ?ð 	@r5   r   )r€   r�   r‚   rƒ   rh   rÖ   ro   rÛ   rr   rv   r{   r   rï   r„   r5   r3   r¿  r¿  )	  s°   € € € € € ð#ð #ðHð ð ð
.ð .ð .ð .ð1ð 1ð 1ðð ð ð$ð $ð $ð%ð %ð %ð%ð %ð %ðð ð ð<
@ð 
@ð 
@ð 
@ð 
@r5   r¿  r‡  c                   ó>   — e Zd ZdZd„ Zd„ Zd
d„Zd„ Zd„ Zd„ Z	d	„ Z
dS )Úfoldnorm_genaz  A folded normal continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `foldnorm` is:

    .. math::

        f(x, c) = \sqrt{2/\pi} cosh(c x) \exp(-\frac{x^2+c^2}{2})

    for :math:`x \ge 0` and :math:`c \ge 0`.

    `foldnorm` takes ``c`` as a shape parameter for :math:`c`.

    %(after_notes)s

    %(example)s

    c                 ó   — |dk    S r®  r„   r}  s     r3   r`   zfoldnorm_gen._argcheck¸	  r¯  r5   c                 ó@   — t          dddt          j        fd¦  «        gS r±  re   rg   s    r3   rh   zfoldnorm_gen._shape_info»	  r²  r5   Nc                 óL   — t          |                     |¦  «        |z   ¦  «        S rK   ©r
  rÒ   rµ  s       r3   rÖ   zfoldnorm_gen._rvs¾	  s#   € Ý�<×/Ò/°Ñ5Ô5¸Ñ9Ñ:Ô:Ð:r5   c                 óL   — t          ||z   ¦  «        t          ||z
  ¦  «        z   S rK   rØ   r
  s      r3   ro   zfoldnorm_gen._pdfÁ	  s#   € å˜˜Q™ÑÔ¥)¨A¨a©C¡.¤.Ñ0Ð0r5   c                 óš   — t          j        d¦  «        }dt          j        ||z
  |z  ¦  «        t          j        ||z   |z  ¦  «        z   z  S r´  )rM   rü   rt   Úerf)rB   rn   r  Úsqrt_twos       r3   rr   zfoldnorm_gen._cdfÅ	  sE   € Ý”7˜1‘:”:ˆØ•b”f˜a !™e XÑ-Ñ.Ô.µ´¸¸Q¹ÀÑ8HÑ1IÔ1IÑIÑJÐJr5   c                 óL   — t          ||z
  ¦  «        t          ||z   ¦  «        z   S rK   râ   r
  s      r3   rv   zfoldnorm_gen._sfÉ	  s!   € Ý˜˜A™‰Œ¥¨!¨a©%¡¤Ñ0Ð0r5   c                 óÎ  — ||z  }t          j        d|z  ¦  «        t          j        dt           j        z  ¦  «        z  }d|z  |t	          j        |t          j        d¦  «        z  ¦  «        z  z   }|dz   ||z  z
  }d||z  |z  ||z  z
  |z
  z  }|t          j        |d¦  «        z  }||dz   z  dz   d|z  |z  z   }|d|d	z
  z  d	|dz  z  z
  |dz  z  z  }||dz  z  d	z
  }||||fS )
Nç      à¿r³   rR   r   r¼  rE  rƒ  rÓ  rD  )rM   r´   rü   rî   rt   rê  r¾  )rB   r  r¨  Úexpfacr@  rA  rB  rC  s           r3   r   zfoldnorm_gen._statsÌ	  s
  € ð ˆq‰SˆÝ”˜˜R™‘”¥2¤7¨2­b¬e©8Ñ#4Ô#4Ñ4ˆà�‰Y˜�RœV A¥b¤g¨a¡j¤j¡LÑ1Ô1Ñ1Ñ1ˆØ�1‰f�r˜"‘u‰nˆà�2�b‘5˜‘8˜b ™eÑ# fÑ,Ñ-ˆØ
�bŒh�s˜CÑ Ô Ñ ˆà�2˜‘7‰^˜aÑ " V¡)¨B¡,Ñ.ˆØ
ˆr�R˜"‘W‰~  R¨¡U¡
Ñ*¨b°!©eÑ3Ñ3ˆØ�#�s‘(‰]˜RÑˆà�3˜˜BˆÐr5   r   r¼  r„   r5   r3   rã  rã  ¢	  s’   € € € € € ðð ð*ð ð ðDð Dð Dð;ð ;ð ;ð ;ð1ð 1ð 1ðKð Kð Kð1ð 1ð 1ðð ð ð ð r5   rã  Úfoldnormc                   ó„   ‡ — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Zd„ Z eed¬¦  «        ˆ fd„¦   «         Zˆ xZS )Úweibull_min_genaý  Weibull minimum continuous random variable.

    The Weibull Minimum Extreme Value distribution, from extreme value theory
    (Fisher-Gnedenko theorem), is also often simply called the Weibull
    distribution. It arises as the limiting distribution of the rescaled
    minimum of iid random variables.

    %(before_notes)s

    See Also
    --------
    weibull_max, numpy.random.Generator.weibull, exponweib

    Notes
    -----
    The probability density function for `weibull_min` is:

    .. math::

        f(x, c) = c x^{c-1} \exp(-x^c)

    for :math:`x > 0`, :math:`c > 0`.

    `weibull_min` takes ``c`` as a shape parameter for :math:`c`.
    (named :math:`k` in Wikipedia article and :math:`a` in
    ``numpy.random.weibull``).  Special shape values are :math:`c=1` and
    :math:`c=2` where Weibull distribution reduces to the `expon` and
    `rayleigh` distributions respectively.

    Suppose ``X`` is an exponentially distributed random variable with
    scale ``s``. Then ``Y = X**k`` is `weibull_min` distributed with shape
    ``c = 1/k`` and scale ``s**k``.

    %(after_notes)s

    References
    ----------
    https://en.wikipedia.org/wiki/Weibull_distribution

    https://en.wikipedia.org/wiki/Fisher-Tippett-Gnedenko_theorem

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r  re   rg   s    r3   rh   zweibull_min_gen._shape_info
  r  r5   c                 óv   — |t          ||dz
  ¦  «        z  t          j        t          ||¦  «         ¦  «        z  S r[   ©r�  rM   r´   r
  s      r3   ro   zweibull_min_gen._pdf
  s1   € à•�Q˜˜!™‘”‰}�RœV¥S¨¨A¡Y¤Y JÑ/Ô/Ñ/Ð/r5   c                 ó~   — t          j        |¦  «        t          j        |dz
  |¦  «        z   t	          ||¦  «        z
  S r[   ©rM   rí   rt   ru  r�  r
  s      r3   rÛ   zweibull_min_gen._logpdf
  s2   € ÝŒv�a‰yŒy�2œ8 A¨¡E¨1Ñ-Ô-Ñ-µ°A°q±	´	Ñ9Ð9r5   c                 óJ   — t          j        t          ||¦  «         ¦  «         S rK   ©rt   r  r�  r
  s      r3   rr   zweibull_min_gen._cdf
  s   € Ý”�#˜a ™)œ)˜Ñ$Ô$Ð$Ð$r5   c                 óP   — t          t          j        | ¦  «         d|z  ¦  «        S r  rŽ  r  s      r3   r{   zweibull_min_gen._ppf
  s"   € Ý•B”H˜a˜R‘L”L�= # a¡%Ñ(Ô(Ð(r5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   r6  r
  s      r3   rv   zweibull_min_gen._sf 
  ó    € ÝŒv�d—k’k ! QÑ'Ô'Ñ(Ô(Ð(r5   c                 ó$   — t          ||¦  «         S rK   ©r�  r
  s      r3   rä   zweibull_min_gen._logsf#
  s   € Ý�A�q‘	”	ˆzÐr5   c                 ó8   — t          j        |¦  «         d|z  z  S r[   r.  r  s      r3   r~   zweibull_min_gen._isf&
  s   € Ý”˜‘”�
˜a ™cÑ"Ð"r5   c                 ó<   — t          j        d|dz  |z  z   ¦  «        S r  r-  r{  s      r3   rÿ   zweibull_min_gen._munp)
  s   € ÝŒx˜˜A˜c™E !™G™Ñ$Ô$Ð$r5   c                 óX   — t            |z  t          j        |¦  «        z
  t           z   dz   S r[   ©r#   rM   rí   r}  s     r3   rï   zweibull_min_gen._entropy,
  ó%   € Ýˆw˜‰{�RœV A™YœYÑ&­Ñ/°!Ñ3Ð3r5   aÌ          If ``method='mm'``, parameters fixed by the user are respected, and the
        remaining parameters are used to match distribution and sample moments
        where possible. For example, if the user fixes the location with
        ``floc``, the parameters will only match the distribution skewness and
        variance to the sample skewness and variance; no attempt will be made
        to match the means or minimize a norm of the errors.
        

rð   c           	      óÜ  •‡‡— t          |t          ¦  «        rJ|                     ¦   «         dk    r|                     ¦   «         }n t	          ¦   «         j        |g|¢R i |¤ŽS |                     dd¦  «        r t	          ¦   «         j        |g|¢R i |¤ŽS t          | |||¦  «        \  }}}}|                     dd¦  «         	                    ¦   «         }d„ Št          j        |¦  «        Šd} ‰|¦  «        }	‰|	k     r'|dk    r!|€|s t	          ¦   «         j        |g|¢R i |¤ŽS |dk    rd	\  }
}}nEt          |¦  «        r|d         nd }
|                     d
d ¦  «        }|                     dd ¦  «        }|€ |
€t          ˆˆfd„d|gd¬¦  «        j        }
n|�|}
|€d|€bt          j        |¦  «        }t          j        |t%          j        dd|
z  z   ¦  «        t%          j        dd|
z  z   ¦  «        dz  z
  z  ¦  «        }n|�|}|€7|€5t          j        |¦  «        }||t%          j        dd|
z  z   ¦  «        z  z
  }n|�|}|dk    r|
||fS  t	          ¦   «         j        ||
f||dœ|¤ŽS )Nr   ÚsuperfitFr/   r8   c                 óæ   — t          j        dd| z  z   ¦  «        }t          j        dd| z  z   ¦  «        }t          j        dd| z  z   ¦  «        }d|dz  z  d|z  |z  z
  |z   }||dz  z
  dz  }||z  S )Nr   rR   rƒ  r¼  r-  )r  Úgamma1Úgamma2Úgamma3Únumr©  s         r3   Úskewz!weibull_min_gen.fit.<locals>.skewJ
  s|   € Ý”X˜a  !¡™e‘_”_ˆFÝ”X˜a  !¡™e‘_”_ˆFÝ”X˜a  !¡™e‘_”_ˆFØ�f˜a‘i‘- ! F¡(¨6¡/Ñ1°FÑ:ˆCØ˜F A™IÑ%¨Ñ-ˆCØ�s‘7ˆNr5   g     ˆÃ@r9   ©NNNr,   r-   c                 ó    •—  ‰| ¦  «        ‰z
  S rK   r„   )r  r  r  s    €€r3   rå  z%weibull_min_gen.fit.<locals>.<lambda>k
  s   ø€  d d¨1¡g¤g°¡k€ r5   g{®Gáz”?Úbisect)Úbracketr/   r   rR   ©r,   r-   )r<   r(   r=   r�  r>   r@   r0   Ú_check_fit_input_parametersr:   r;   rð  r  r¡  r)   ÚrootrM   r¤  rü   rt   rÖ  rû   )rB   rC   rD   r2   Úfcró   rô   r/   Úmax_cÚs_minr  r,   r-   rÉ  rÊ  r  r  r“  s                  @@€r3   r@   zweibull_min_gen.fit/
  sÚ  øøø€ õ �d�LÑ)Ô)ð 	8Ø× Ò Ñ"Ô" aÒ'Ð'Ø—~’~Ñ'Ô'��à"•u‘w”w”{ 4Ð7¨$Ð7Ð7Ð7°$Ð7Ð7Ð7à�8Š8�J Ñ&Ô&ð 	4Ø•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3õ "=¸TÀ4Ø=AÀ4ñ"Iô "IÑˆˆb�$˜à—’˜( EÑ*Ô*×0Ò0Ñ2Ô2ˆð	ð 	ð 	õ ŒJ�tÑÔˆØˆØ��U‘”ˆØˆuŠ9ˆ9˜ 4š˜¨B¨J¸t¨JØ•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3ð �TŠ>ˆ>Ø,‰MˆAˆs�E�Eå˜t™9œ9Ð.��Q”�¨$ˆAØ—(’(˜5 $Ñ'Ô'ˆCØ—H’H˜W dÑ+Ô+ˆEàˆ:˜!˜)õ Ð1Ð1Ð1Ð1Ð1¸DÀ%¸=Ø#+ð-ñ -ô -Ü-1ð ˆAàˆ^ØˆAàˆ>˜e˜mÝ”�t‘”ˆAÝ”G˜A¥¤¨!¨A¨a©C©%¡¤µ2´8¸A¸aÀ¹c¹E±?´?ÀAÑ3EÑ!EÑFÑGÔGˆEˆEØÐØˆEàˆ<˜C˜KÝ”˜‘”ˆAØ�e�BœH Q¨¨1©¡WÑ-Ô-Ñ-Ñ-ˆCˆCØÐØˆCà�TŠ>ˆ>Ø�c˜5�=Ð ð •5‘7”7”;˜t QÐE¨C°uÐEÐEÀÐEÐEÐEr5   )r€   r�   r‚   rƒ   rh   ro   rÛ   rr   r{   rv   rä   r~   rÿ   rï   r	   r   r@   rÎ  rÏ  s   @r3   rò  rò  ã	  s  ø€ € € € € ð+ð +ðXEð Eð Eð0ð 0ð 0ð:ð :ð :ð%ð %ð %ð)ð )ð )ð)ð )ð )ðð ð ð#ð #ð #ð%ð %ð %ð4ð 4ð 4ð Ð˜}ð 5ð ñ ô ðJFð JFð JFð JFñô ðJFð JFð JFð JFð JFr5   rò  r  c                   ój   ‡ — e Zd ZdZd„ Zd„ Zˆ fd„Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Zd„ Zd„ Zd„ Zd„ Zˆ xZS )Útruncweibull_min_gena9  A doubly truncated Weibull minimum continuous random variable.

    %(before_notes)s

    See Also
    --------
    weibull_min, truncexpon

    Notes
    -----
    The probability density function for `truncweibull_min` is:

    .. math::

        f(x, a, b, c) = \frac{c x^{c-1} \exp(-x^c)}{\exp(-a^c) - \exp(-b^c)}

    for :math:`a < x <= b`, :math:`0 \le a < b` and :math:`c > 0`.

    `truncweibull_min` takes :math:`a`, :math:`b`, and :math:`c` as shape
    parameters.

    Notice that the truncation values, :math:`a` and :math:`b`, are defined in
    standardized form:

    .. math::

        a = (u_l - loc)/scale
        b = (u_r - loc)/scale

    where :math:`u_l` and :math:`u_r` are the specific left and right
    truncation values, respectively. In other words, the support of the
    distribution becomes :math:`(a*scale + loc) < x <= (b*scale + loc)` when
    :math:`loc` and/or :math:`scale` are provided.

    %(after_notes)s

    References
    ----------

    .. [1] Rinne, H. "The Weibull Distribution: A Handbook". CRC Press (2009).

    %(example)s

    c                 ó*   — |dk    ||k    z  |dk    z  S ©Nr…   r„   ©rB   r  rˆ   r‰   s       r3   r`   ztruncweibull_min_gen._argcheck´
  s   € Ø�R’˜A šEÑ" a¨"¢fÑ-Ð-r5   c                 óÀ   — t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }|||gS )Nr  Fr   r  rˆ   rd   r‰   re   )rB   r!  rf  rg  s       r3   rh   z truncweibull_min_gen._shape_info·
  sY   € Ý˜˜U Q­¬ K°Ñ@Ô@ˆÝ˜˜U Q­¬ K°Ñ?Ô?ˆÝ˜˜U Q­¬ K°Ñ@Ô@ˆØ�B˜ˆ|Ðr5   c                 óJ   •— t          ¦   «                              |d¬¦  «        S )N)r   r   r   rJ  ©r>   r’  ©rB   rC   r“  s     €r3   r’  ztruncweibull_min_gen._fitstart½
  s    ø€ å‰wŒw× Ò  ¨IÐ Ñ6Ô6Ð6r5   c                 ó
   — ||fS rK   r„   r  s       r3   r“   z!truncweibull_min_gen._get_supportÁ
  ó   € Ø�!ˆtˆr5   c                 ó
  — t          j        t          ||¦  «         ¦  «        t          j        t          ||¦  «         ¦  «        z
  }|t          ||dz
  ¦  «        z  t          j        t          ||¦  «         ¦  «        z  |z  S r[   ©rM   r´   r�  )rB   rn   r  rˆ   r‰   Údenums         r3   ro   ztruncweibull_min_gen._pdfÄ
  sh   € Ý”�˜Q ™œ˜
Ñ#Ô#¥b¤f­c°!°Q©i¬i¨ZÑ&8Ô&8Ñ8ˆØ•C˜˜1˜Q™3‘K”K‘¥"¤&­#¨a°©)¬)¨Ñ"4Ô"4Ñ4¸Ñ=Ð=r5   c           	      ó6  — t          j        t          j        t          ||¦  «         ¦  «        t          j        t          ||¦  «         ¦  «        z
  ¦  «        }t          j        |¦  «        t	          j        |dz
  |¦  «        z   t          ||¦  «        z
  |z
  S r[   )rM   rí   r´   r�  rt   ru  )rB   rn   r  rˆ   r‰   Úlogdenums         r3   rÛ   ztruncweibull_min_gen._logpdfÈ
  ss   € Ý”6�"œ&¥# a¨¡)¤) Ñ,Ô,­r¬vµs¸1¸a±y´y°jÑ/AÔ/AÑAÑBÔBˆÝŒv�a‰yŒy�2œ8 A¨¡E¨1Ñ-Ô-Ñ-µ°A°q±	´	Ñ9¸HÑDÐDr5   c                 ó(  — t          j        t          ||¦  «         ¦  «        t          j        t          ||¦  «         ¦  «        z
  }t          j        t          ||¦  «         ¦  «        t          j        t          ||¦  «         ¦  «        z
  }||z  S rK   r"  ©rB   rn   r  rˆ   r‰   r
  r#  s          r3   rr   ztruncweibull_min_gen._cdfÌ
  óp   € ÝŒv•s˜1˜a‘y”y�jÑ!Ô!¥B¤F­C°°1©I¬I¨:Ñ$6Ô$6Ñ6ˆÝ”�˜Q ™œ˜
Ñ#Ô#¥b¤f­c°!°Q©i¬i¨ZÑ&8Ô&8Ñ8ˆØ�U‰{Ðr5   c           	      óp  — t          j        t          j        t          ||¦  «         ¦  «        t          j        t          ||¦  «         ¦  «        z
  ¦  «        }t          j        t          j        t          ||¦  «         ¦  «        t          j        t          ||¦  «         ¦  «        z
  ¦  «        }||z
  S rK   ©rM   rí   r´   r�  ©rB   rn   r  rˆ   r‰   Úlognumr%  s          r3   rà   ztruncweibull_min_gen._logcdfÑ
  ó…   € Ý”�œ¥ A q¡	¤	˜zÑ*Ô*­R¬VµS¸¸A±Y´Y°JÑ-?Ô-?Ñ?Ñ@Ô@ˆÝ”6�"œ&¥# a¨¡)¤) Ñ,Ô,­r¬vµs¸1¸a±y´y°jÑ/AÔ/AÑAÑBÔBˆØ˜Ñ Ð r5   c                 ó(  — t          j        t          ||¦  «         ¦  «        t          j        t          ||¦  «         ¦  «        z
  }t          j        t          ||¦  «         ¦  «        t          j        t          ||¦  «         ¦  «        z
  }||z  S rK   r"  r'  s          r3   rv   ztruncweibull_min_gen._sfÖ
  r(  r5   c           	      óp  — t          j        t          j        t          ||¦  «         ¦  «        t          j        t          ||¦  «         ¦  «        z
  ¦  «        }t          j        t          j        t          ||¦  «         ¦  «        t          j        t          ||¦  «         ¦  «        z
  ¦  «        }||z
  S rK   r*  r+  s          r3   rä   ztruncweibull_min_gen._logsfÛ
  r-  r5   c                 óê   — t          t          j        d|z
  t          j        t          ||¦  «         ¦  «        z  |t          j        t          ||¦  «         ¦  «        z  z   ¦  «         d|z  ¦  «        S r[   ©r�  rM   rí   r´   ©rB   rz   r  rˆ   r‰   s        r3   r~   ztruncweibull_min_gen._isfà
  óe   € ÝÝŒV�Q˜‘U�bœf¥c¨!¨Q¡i¤i ZÑ0Ô0Ñ0°1µr´v½sÀ1Àa¹y¼y¸jÑ7IÔ7IÑ3IÑIÑJÔJÐJÈAÈaÉCñô ð 	r5   c                 óê   — t          t          j        d|z
  t          j        t          ||¦  «         ¦  «        z  |t          j        t          ||¦  «         ¦  «        z  z   ¦  «         d|z  ¦  «        S r[   r1  r2  s        r3   r{   ztruncweibull_min_gen._ppfå
  r3  r5   c           	      óv  — t          j        ||z  dz   ¦  «        t          j        ||z  dz   t          ||¦  «        ¦  «        t          j        ||z  dz   t          ||¦  «        ¦  «        z
  z  }t	          j        t          ||¦  «         ¦  «        t	          j        t          ||¦  «         ¦  «        z
  }||z  S r  )rt   rÖ  r¯  r�  rM   r´   )rB   r_   r  rˆ   r‰   Ú	gamma_funr#  s          r3   rÿ   ztruncweibull_min_gen._munpê
  s�   € Ý”H˜Q˜q™S 2™XÑ&Ô&ÝŒK˜˜!™˜b™¥# a¨¡)¤)Ñ,Ô,­r¬{¸1¸Q¹3À¹8ÅSÈÈAÁYÄYÑ/OÔ/OÑOñˆ	õ ”�˜Q ™œ˜
Ñ#Ô#¥b¤f­c°!°Q©i¬i¨ZÑ&8Ô&8Ñ8ˆØ˜5Ñ Ð r5   )r€   r�   r‚   rƒ   r`   rh   r’  r“   ro   rÛ   rr   rà   rv   rä   r~   r{   rÿ   rÎ  rÏ  s   @r3   r  r  ‡
  sú   ø€ € € € € ð+ð +ðX.ð .ð .ðð ð ð7ð 7ð 7ð 7ð 7ðð ð ð>ð >ð >ðEð Eð Eðð ð ð
!ð !ð !ð
ð ð ð
!ð !ð !ð
ð ð ð
ð ð ð
!ð !ð !ð !ð !ð !ð !r5   r  Útruncweibull_minc                   óH   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ ZdS )Úweibull_max_gena0  Weibull maximum continuous random variable.

    The Weibull Maximum Extreme Value distribution, from extreme value theory
    (Fisher-Gnedenko theorem), is the limiting distribution of rescaled
    maximum of iid random variables. This is the distribution of -X
    if X is from the `weibull_min` function.

    %(before_notes)s

    See Also
    --------
    weibull_min

    Notes
    -----
    The probability density function for `weibull_max` is:

    .. math::

        f(x, c) = c (-x)^{c-1} \exp(-(-x)^c)

    for :math:`x < 0`, :math:`c > 0`.

    `weibull_max` takes ``c`` as a shape parameter for :math:`c`.

    %(after_notes)s

    References
    ----------
    https://en.wikipedia.org/wiki/Weibull_distribution

    https://en.wikipedia.org/wiki/Fisher-Tippett-Gnedenko_theorem

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r  re   rg   s    r3   rh   zweibull_max_gen._shape_info  r  r5   c                 óz   — |t          | |dz
  ¦  «        z  t          j        t          | |¦  «         ¦  «        z  S r[   rõ  r
  s      r3   ro   zweibull_max_gen._pdf  s5   € à•�a�R˜˜1™‘”‰~�bœf¥c¨1¨"¨a¡j¤j [Ñ1Ô1Ñ1Ð1r5   c                 ó‚   — t          j        |¦  «        t          j        |dz
  | ¦  «        z   t	          | |¦  «        z
  S r[   r÷  r
  s      r3   rÛ   zweibull_max_gen._logpdf!  s6   € ÝŒv�a‰yŒy�2œ8 A a¡C¨!¨Ñ,Ô,Ñ,­s°A°2°q©z¬zÑ9Ð9r5   c                 óJ   — t          j        t          | |¦  «         ¦  «        S rK   r"  r
  s      r3   rr   zweibull_max_gen._cdf$  s   € ÝŒv•s˜A˜2˜q‘z”z�kÑ"Ô"Ð"r5   c                 ó&   — t          | |¦  «         S rK   rþ  r
  s      r3   rà   zweibull_max_gen._logcdf'  s   € Ý�Q�B˜‘
”
ˆ{Ðr5   c                 óL   — t          j        t          | |¦  «         ¦  «         S rK   rù  r
  s      r3   rv   zweibull_max_gen._sf*  s!   € Ý”�#˜q˜b !™*œ*˜Ñ%Ô%Ð%Ð%r5   c                 óP   — t          t          j        |¦  «         d|z  ¦  «         S r  )r�  rM   rí   r  s      r3   r{   zweibull_max_gen._ppf-  s#   € Ý•R”V˜A‘Y”Y�J  A¡Ñ&Ô&Ð&Ð&r5   c                 ót   — t          j        d|dz  |z  z   ¦  «        }t          |¦  «        dz  rd}nd}||z  S )Nr†   rR   r¼  r   )rt   rÖ  rÈ  )rB   r_   r  ÚvalÚsgns        r3   rÿ   zweibull_max_gen._munp0  sE   € ÝŒh�s˜1˜S™5 ™7‘{Ñ#Ô#ˆÝˆq‰6Œ6�A‰:ð 	ØˆCˆCàˆCØ�S‰yÐr5   c                 óX   — t            |z  t          j        |¦  «        z
  t           z   dz   S r[   r  r}  s     r3   rï   zweibull_max_gen._entropy8  r  r5   N)r€   r�   r‚   rƒ   rh   ro   rÛ   rr   rà   rv   r{   rÿ   rï   r„   r5   r3   r9  r9  õ
  s©   € € € € € ð#ð #ðHEð Eð Eð2ð 2ð 2ð:ð :ð :ð#ð #ð #ðð ð ð&ð &ð &ð'ð 'ð 'ðð ð ð4ð 4ð 4ð 4ð 4r5   r9  Úweibull_max)r‰   rŠ   c                   óN   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Zd„ ZdS )Úgenlogistic_gena…  A generalized logistic continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `genlogistic` is:

    .. math::

        f(x, c) = c \frac{\exp(-x)}
                         {(1 + \exp(-x))^{c+1}}

    for real :math:`x` and :math:`c > 0`. In literature, different
    generalizations of the logistic distribution can be found. This is the type 1
    generalized logistic distribution according to [1]_. It is also referred to
    as the skew-logistic distribution [2]_.

    `genlogistic` takes ``c`` as a shape parameter for :math:`c`.

    %(after_notes)s

    References
    ----------
    .. [1] Johnson et al. "Continuous Univariate Distributions", Volume 2,
           Wiley. 1995.
    .. [2] "Generalized Logistic Distribution", Wikipedia,
           https://en.wikipedia.org/wiki/Generalized_logistic_distribution

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r  re   rg   s    r3   rh   zgenlogistic_gen._shape_info`  r  r5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   rÛ  r
  s      r3   ro   zgenlogistic_gen._pdfc  rƒ  r5   c                 óÚ   — |dz
   |dk     z  dz
  }t          j        |¦  «        }t          j        |¦  «        ||z  z   |dz   t          j        t          j        | ¦  «        ¦  «        z  z
  S ©Nr   r   )rM   r
  rí   rt   r£  r´   )rB   rn   r  ÚmultÚabsxs        r3   rÛ   zgenlogistic_gen._logpdfg  sc   € ð �Q‘ˆx˜1˜qš5Ñ! AÑ%ˆÝŒv�a‰yŒyˆÝŒv�a‰yŒy˜4 ™9Ñ$¨¨!©­r¬x½¼À¸u¹¼Ñ/FÔ/FÑ'FÑFÐFr5   c                 ó>   — dt          j        | ¦  «        z   | z  }|S r[   r9  )rB   rn   r  ÚCxs       r3   rr   zgenlogistic_gen._cdfo  s!   € Ø•”˜�r‘
”
‰l˜q˜bÑ!ˆØˆ	r5   c                 óX   — | t          j        t          j        | ¦  «        ¦  «        z  S rK   )rM   r£  r´   r
  s      r3   rà   zgenlogistic_gen._logcdfs  s#   € Øˆr•B”H�RœV Q B™ZœZÑ(Ô(Ñ(Ð(r5   c                 óX   — t          j        t          j        |d|z  ¦  «        ¦  «         S r?  )rM   rí   rt   Úpowm1r  s      r3   r{   zgenlogistic_gen._ppfv  s%   € Ý”•r”x  4¨¡6Ñ*Ô*Ñ+Ô+Ð+Ð+r5   c                 óT   — t          j        |                      ||¦  «        ¦  «         S rK   ©rt   r  rà   r
  s      r3   rv   zgenlogistic_gen._sfy  ó#   € Ý”˜Ÿš a¨Ñ+Ô+Ñ,Ô,Ð,Ð,r5   c                 ó4   — |                       d|z
  |¦  «        S r[   ©r{   r  s      r3   r~   zgenlogistic_gen._isf|  s   € Ø�yŠy˜˜Q™ Ñ"Ô"Ð"r5   c                 ó†  — t           t          j        |¦  «        z   }t          j        t          j        z  dz  t          j        d|¦  «        z   }dt          j        d|¦  «        z  dt          z  z   }|t          j        |d¦  «        z  }t          j        dz  dz  dt          j        d|¦  «        z  z   }||d	z  z  }||||fS )
NrE  rR   r  rƒ  r¼  r   ç      .@r‚  r³   )r#   rt   rX  rM   rî   Úzetar$   r¾  ©rB   r  r@  rA  rB  rC  s         r3   r   zgenlogistic_gen._stats  s¤   € Ý•b”f˜Q‘i”iÑˆÝŒe•B”E‰k˜#‰o¥¤¨¨1¡¤Ñ-ˆØ•”˜˜1‘”Ñ ¥&¡Ñ(ˆØ
�bŒh�s˜CÑ Ô Ñ ˆÝŒU�A‰X�d‰]˜Q�rœw q¨!™}œ}™_Ñ,ˆØ
ˆc�3‰h‰ˆØ�3˜˜BˆÐr5   c                 ó6   — t          |dk     |fd„ d„ ¬¦  «        S )Ng    €„^Ac                 ór   — t          j        | ¦  «         t          j        | dz   ¦  «        z   t          z   dz   S r[   )rM   rí   rt   rX  r#   rð  s    r3   rå  z*genlogistic_gen._entropy.<locals>.<lambda>Š  s+   € ¥R¤V¨A¡Y¤Y Jµ´¸¸A¹±´Ñ$>ÅÑ$GÈ!Ñ$K€ r5   c                 ó(   — dd| z  z  t           z   dz   S r-  ©r#   rð  s    r3   rå  z*genlogistic_gen._entropy.<locals>.<lambda>�  s   €  q¨!¨a©%¡yµ6Ñ'9¸AÑ'=€ r5   rè  rê  r}  s     r3   rï   zgenlogistic_gen._entropyˆ  s1   € Ý˜!˜cš' A 5ØKÐKð >Ð=ð?ñ ?ô ?ð 	?r5   N)r€   r�   r‚   rƒ   rh   ro   rÛ   rr   rà   r{   rv   r~   r   rï   r„   r5   r3   rG  rG  ?  s»   € € € € € ðð ð@Eð Eð Eð*ð *ð *ðGð Gð Gðð ð ð)ð )ð )ð,ð ,ð ,ð-ð -ð -ð#ð #ð #ðð ð ð?ð ?ð ?ð ?ð ?r5   rG  Úgenlogisticc                   ób   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Zd„ Zdd„Zd„ Zd„ ZdS )Úgenpareto_gena‰  A generalized Pareto continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `genpareto` is:

    .. math::

        f(x, c) = (1 + c x)^{-1 - 1/c}

    defined for :math:`x \ge 0` if :math:`c \ge 0`, and for
    :math:`0 \le x \le -1/c` if :math:`c < 0`.

    `genpareto` takes ``c`` as a shape parameter for :math:`c`.

    For :math:`c=0`, `genpareto` reduces to the exponential
    distribution, `expon`:

    .. math::

        f(x, 0) = \exp(-x)

    For :math:`c=-1`, `genpareto` is uniform on ``[0, 1]``:

    .. math::

        f(x, -1) = 1

    %(after_notes)s

    %(example)s

    c                 ó*   — t          j        |¦  «        S rK   ©rM   rù   r}  s     r3   r`   zgenpareto_gen._argcheckº  ó   € ÝŒ{˜1‰~Œ~Ðr5   c                 óV   — t          ddt          j         t          j        fd¦  «        gS ©Nr  Fr  re   rg   s    r3   rh   zgenpareto_gen._shape_info½  ó$   € Ý˜3 ­¬¨µ´Ð'8¸.ÑIÔIÐJÐJr5   c                 ó¾   — t          j        |¦  «        }t          |dk     |fd„ t           j        ¦  «        }t          j        |dk    | j        | j        ¦  «        }||fS )Nr   c                 ó   — d| z  S r?  r„   rð  s    r3   rå  z,genpareto_gen._get_support.<locals>.<lambda>Ã  s
   €   q¡€ r5   )rM   rø   r   rf   rO  rˆ   )rB   r  r‰   rˆ   s       r3   r“   zgenpareto_gen._get_supportÀ  sY   € ÝŒJ�q‰MŒMˆÝ�q˜1’u˜q˜dØ(Ð(Ý”vñô ˆõ ŒH�Q˜!’V˜TœV T¤VÑ,Ô,ˆØ�!ˆtˆr5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   rÛ  r
  s      r3   ro   zgenpareto_gen._pdfÈ  rƒ  r5   c                 óD   — t          ||k    |dk    z  ||fd„ | ¦  «        S )Nr   c                 ó@   — t          j        |dz   || z  ¦  «         |z  S r  rf  ©rn   r  s     r3   rå  z'genpareto_gen._logpdf.<locals>.<lambda>Î  s"   € ­¬
°1°r±6¸1¸Q¹3Ñ(?Ô(?Ð'?À!Ñ'C€ r5   rê  r
  s      r3   rÛ   zgenpareto_gen._logpdfÌ  s4   € Ý˜1 š6 a¨1¢fÑ-°°1¨vØCÐCØ˜"ñô ð 	r5   c                 ó2   — t          j        | | ¦  «         S rK   )rt   Úinv_boxcox1pr
  s      r3   rr   zgenpareto_gen._cdfÑ  s   € Ý”   Q BÑ'Ô'Ð'Ð'r5   c                 ó0   — t          j        | | ¦  «        S rK   )rt   Ú
inv_boxcoxr
  s      r3   rv   zgenpareto_gen._sfÔ  s   € ÝŒ}˜a˜R ! Ñ$Ô$Ð$r5   c                 óD   — t          ||k    |dk    z  ||fd„ | ¦  «        S )Nr   c                 ó8   — t          j        || z  ¦  «         |z  S rK   r	  rn  s     r3   rå  z&genpareto_gen._logsf.<locals>.<lambda>Ù  s   € ­¬°°1±©¬ ~¸Ñ'9€ r5   rê  r
  s      r3   rä   zgenpareto_gen._logsf×  s4   € Ý˜1 š6 a¨1¢fÑ-°°1¨vØ9Ð9Ø˜"ñô ð 	r5   c                 ó2   — t          j        | | ¦  «         S rK   )rt   Úboxcox1pr  s      r3   r{   zgenpareto_gen._ppfÜ  s   € Ý”˜Q˜B  Ñ#Ô#Ð#Ð#r5   c                 ó0   — t          j        || ¦  «         S rK   )rt   Úboxcoxr  s      r3   r~   zgenpareto_gen._isfß  s   € Ý”	˜!˜a˜RÑ Ô Ð Ð r5   r  c                 óV  — d|vrd }n"t          |dk     |fd„ t          j        ¦  «        }d|vrd }n"t          |dk     |fd„ t          j        ¦  «        }d|vrd }n"t          |dk     |fd	„ t          j        ¦  «        }d
|vrd }n"t          |dk     |fd„ t          j        ¦  «        }||||fS )NrÊ  r   c                 ó   — dd| z
  z  S r[   r„   ©Úxis    r3   rå  z&genpareto_gen._stats.<locals>.<lambda>ç  s   €  a¨¨R©¡j€ r5   rÉ  r‘   c                 ó*   — dd| z
  dz  z  dd| z  z
  z  S r-  r„   r{  s    r3   rå  z&genpareto_gen._stats.<locals>.<lambda>í  s   €  a¨1¨r©6°A©+¡o¸¸Q¸r¹T¹Ñ&B€ r5   r  gUUUUUUÕ?c                 óZ   — dd| z   z  t          j        dd| z  z
  ¦  «        z  dd| z  z
  z  S )NrR   r   rƒ  r„  r{  s    r3   rå  z&genpareto_gen._stats.<locals>.<lambda>ó  s5   €  q¨A°©F¡|µb´g¸aÀ!ÀBÁ$¹hÑ6GÔ6GÑ'GØ()¨A¨b©D©ñ(2€ r5   r  rž  c                 ó`   — ddd| z  z
  z  d| dz  z  | z   dz   z  dd| z  z
  z  dd| z  z
  z  dz
  S )Nrƒ  r   rR   r   r„   r{  s    r3   rå  z&genpareto_gen._stats.<locals>.<lambda>ú  sQ   €  q¨A°°"±©H¡~¸¸2¸q¹5¹À2¹ÈÑ9IÑ'JØ()¨A¨b©D©ñ(2Ø56¸¸2¹±Xñ(?ØABñ(C€ r5   ©r   rM   rf   r  )rB   r  r  rÊ  rÉ  r  r  s          r3   r   zgenpareto_gen._statsâ  sú   € Ø�gÐÐØˆAˆAå˜1˜qš5 1 $Ø0Ð0Ýœ6ñ#ô #ˆAð �gÐÐØˆAˆAå˜1˜sš7 Q DØBÐBÝœ6ñ#ô #ˆAð �gÐÐØˆAˆAå˜1˜sš7 Q Dð3ð 3åœ6ñ#ô #ˆAð �gÐÐØˆAˆAå˜1˜sš7 Q DðDð Dåœ6ñ#ô #ˆAð �!�Q˜ˆzÐr5   c           	      ól   ‡‡— d„ Št          |dk    |fˆˆfd„t          j        ‰dz   ¦  «        ¦  «        S )Nc                 ó  — d}t          j        d| dz   ¦  «        }t          |t          j        | |¦  «        ¦  «        D ]\  }}||d|z  z  d||z  z
  z  z   }Œt          j        || z  dk     |d|z  | z  z  t           j        ¦  «        S )Nr…   r   r   r¼  r†   r<  )rM   rM  Úziprt   ÚcombrO  rf   )r_   r  rB  r  ÚkiÚcnks         r3   rV  z#genpareto_gen._munp.<locals>.__munp   s�   € ØˆCÝ”	˜!˜Q ™UÑ#Ô#ˆAÝ˜q¥"¤'¨!¨Q¡-¤-Ñ0Ô0ð >ð >‘��CØ˜C 2¨"¡*Ñ,°°a¸"±f±Ñ=Ñ=��Ý”8˜A ™E AšI s¨d°Q©h¸1©_Ñ'<½b¼fÑEÔEÐEr5   r   c                 ó   •—  ‰‰| ¦  «        S rK   r„   )r  Ú_genpareto_gen__munpr_   s    €€r3   rå  z%genpareto_gen._munp.<locals>.<lambda>  s   ø€  F F¨1¨a¡L¤L€ r5   r   )r   rt   rÖ  )rB   r_   r  rˆ  s    ` @r3   rÿ   zgenpareto_gen._munpÿ  sR   øø€ ð	Fð 	Fð 	Fõ ˜!˜qš& 1 $Ø0Ð0Ð0Ð0Ð0Ýœ( 1 q¡5™/œ/ñ+ô +ð 	+r5   c                 ó   — d|z   S r  r„   r}  s     r3   rï   zgenpareto_gen._entropy
  s   € Ø�A‰vˆr5   Nr  )r€   r�   r‚   rƒ   r`   rh   r“   ro   rÛ   rr   rv   rä   r{   r~   r   rÿ   rï   r„   r5   r3   rb  rb  –  sê   € € € € € ð"ð "ðFð ð ðKð Kð Kðð ð ð*ð *ð *ðð ð ð
(ð (ð (ð%ð %ð %ðð ð ð
$ð $ð $ð!ð !ð !ðð ð ð ð:	+ð 	+ð 	+ðð ð ð ð r5   rb  Ú	genparetoc                   ó<   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	S )
Úgenexpon_gena!  A generalized exponential continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `genexpon` is:

    .. math::

        f(x, a, b, c) = (a + b (1 - \exp(-c x)))
                        \exp(-a x - b x + \frac{b}{c}  (1-\exp(-c x)))

    for :math:`x \ge 0`, :math:`a, b, c > 0`.

    `genexpon` takes :math:`a`, :math:`b` and :math:`c` as shape parameters.

    %(after_notes)s

    References
    ----------
    H.K. Ryu, "An Extension of Marshall and Olkin's Bivariate Exponential
    Distribution", Journal of the American Statistical Association, 1993.

    N. Balakrishnan, Asit P. Basu (editors), *The Exponential Distribution:
    Theory, Methods and Applications*, Gordon and Breach, 1995.
    ISBN 10: 2884491929

    %(example)s

    c                 óÀ   — t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }|||gS )Nrˆ   Fr   r  r‰   r  re   )rB   rf  rg  r!  s       r3   rh   zgenexpon_gen._shape_info1  sY   € Ý˜˜U Q­¬ K°Ñ@Ô@ˆÝ˜˜U Q­¬ K°Ñ@Ô@ˆÝ˜˜U Q­¬ K°Ñ@Ô@ˆØ�B˜ˆ|Ðr5   c           	      ó¸   — ||t          j        | |z  ¦  «         z  z   t          j        | |z
  |z  |t          j        | |z  ¦  «         z  |z  z   ¦  «        z  S rK   ©rt   r  rM   r´   ©rB   rn   rˆ   r‰   r  s        r3   ro   zgenexpon_gen._pdf7  sl   € ð �A�œ !  A¡™œ�Ñ'Ñ'­¬°!°°A±°q±Ø01µB´H¸a¸RÀ¹T±N´N°?Ñ0CÀAÑ0Eñ1Fñ *Gô *Gñ Gð 	Gr5   c                 ó¸   — t          j        ||t          j        | |z  ¦  «         z  z   ¦  «        | |z
  |z  z   |t          j        | |z  ¦  «         z  |z  z   S rK   ©rM   rí   rt   r  r�  s        r3   rÛ   zgenexpon_gen._logpdf=  sZ   € ÝŒv�a˜�BœH a R¨¡T™NœN˜?Ñ+Ñ+Ñ,Ô,°°°1±°a©xÑ7¸½B¼HÀaÀRÈÁT¹N¼N¸?Ñ8KÈAÑ8MÑMÐMr5   c                 óz   — t          j        | |z
  |z  |t          j        | |z  ¦  «         z  |z  z   ¦  «         S rK   r=  r�  s        r3   rr   zgenexpon_gen._cdf@  s>   € Ý”˜1˜"˜Q™$ ™ A­¬°!°°A±©¬ Ñ$7¸Ñ$9Ñ9Ñ:Ô:Ð:Ð:r5   c                 óº   — ||z   }||t          j        | ¦  «        z  z
  |z  }|t          j        | |z  t          j        | ¦  «        z  ¦  «        j        z   |z  S rK   )rM   r£  rt   Úlambertwr´   Úreal©rB   rñ  rˆ   r‰   r  r  r˜  s          r3   r{   zgenexpon_gen._ppfC  sZ   € Ø�‰EˆØ�•2”8˜Q˜B‘<”<‘Ñ Ñ"ˆØ•B”K   1¡¥r¤v¨q¨b¡z¤zÑ 1Ñ2Ô2Ô7Ñ7¸Ñ:Ð:r5   c                 óx   — t          j        | |z
  |z  |t          j        | |z  ¦  «         z  |z  z   ¦  «        S rK   rŠ  r�  s        r3   rv   zgenexpon_gen._sfH  s;   € ÝŒv˜�r˜!‘t˜Q‘h ¥R¤X¨q¨b°©d¡^¤^ OÑ!4°QÑ!6Ñ6Ñ7Ô7Ð7r5   c                 ó¸   — ||z   }||t          j        |¦  «        z  z
  |z  }|t          j        | |z  t          j        | ¦  «        z  ¦  «        j        z   |z  S rK   )rM   rí   rt   r•  r´   r–  r—  s          r3   r~   zgenexpon_gen._isfK  sW   € Ø�‰EˆØ�•2”6˜!‘9”9‘‰_˜aÑˆØ•B”K   1¡¥r¤v¨q¨b¡z¤zÑ 1Ñ2Ô2Ô7Ñ7¸Ñ:Ð:r5   Nr{  r„   r5   r3   rŒ  rŒ    s�   € € € € € ðð ð>ð ð ðGð Gð GðNð Nð Nð;ð ;ð ;ð;ð ;ð ;ð
8ð 8ð 8ð;ð ;ð ;ð ;ð ;r5   rŒ  Úgenexponc                   óv   ‡ — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Zd„ Zd„ Zd„ Zˆ fd„Zd„ Zd„ Zˆ xZS )Úgenextreme_genaB  A generalized extreme value continuous random variable.

    %(before_notes)s

    See Also
    --------
    gumbel_r

    Notes
    -----
    For :math:`c=0`, `genextreme` is equal to `gumbel_r` with
    probability density function

    .. math::

        f(x) = \exp(-\exp(-x)) \exp(-x),

    where :math:`-\infty < x < \infty`.

    For :math:`c \ne 0`, the probability density function for `genextreme` is:

    .. math::

        f(x, c) = \exp(-(1-c x)^{1/c}) (1-c x)^{1/c-1},

    where :math:`-\infty < x \le 1/c` if :math:`c > 0` and
    :math:`1/c \le x < \infty` if :math:`c < 0`.

    Note that several sources and software packages use the opposite
    convention for the sign of the shape parameter :math:`c`.

    `genextreme` takes ``c`` as a shape parameter for :math:`c`.

    %(after_notes)s

    %(example)s

    c                 ó*   — t          j        |¦  «        S rK   rd  r}  s     r3   r`   zgenextreme_gen._argcheck{  re  r5   c                 óV   — t          ddt          j         t          j        fd¦  «        gS rg  re   rg   s    r3   rh   zgenextreme_gen._shape_info~  rh  r5   c                 ó
  — t          j        |dk    dt          j        |t          ¦  «        z  t           j        ¦  «        }t          j        |dk     dt          j        |t           ¦  «        z  t           j         ¦  «        }||fS ©Nr   r†   )rM   rO  Úmaximumr!   rf   Úminimum)rB   r  Ú_bÚ_as       r3   r“   zgenextreme_gen._get_support�  sc   € ÝŒX�a˜!’e˜S¥2¤:¨aµÑ#7Ô#7Ñ7½¼Ñ@Ô@ˆÝŒX�a˜!’e˜S¥2¤:¨aµ%°Ñ#8Ô#8Ñ8½2¼6¸'ÑBÔBˆØ�2ˆvˆr5   c                 óD   — t          ||k    |dk    z  ||fd„ | ¦  «        S )Nr   c                 ó8   — t          j        | | z  ¦  «        |z  S rK   r	  rn  s     r3   rå  z+genextreme_gen._loglogcdf.<locals>.<lambda>‰  s   € ¥r¤x°°°1±¡~¤~°aÑ'7€ r5   rê  r
  s      r3   Ú
_loglogcdfzgenextreme_gen._loglogcdf†  s3   € å˜1 š6 a¨1¢fÑ-°°1¨vØ7Ð7¸!¸ñ=ô =ð 	=r5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   rÛ  r
  s      r3   ro   zgenextreme_gen._pdf‹  s"   € õ Œv�d—l’l 1 aÑ(Ô(Ñ)Ô)Ð)r5   c                 óÐ  — t          ||k    |dk    z  ||fd„ d¦  «        }t          j        | ¦  «        }|                      ||¦  «        }t	          j        |¦  «        }t	          j        ||dk    |t          j         k    z  d¦  «         t          |dk    |t          j         k    z   |||fd„ t          j         ¬¦  «        }t	          j        ||dk    |dk    z  d¦  «         |S )Nr   c                 ó   — || z  S rK   r„   rn  s     r3   rå  z(genextreme_gen._logpdf.<locals>.<lambda>’  s
   € À!ÀAÁ#€ r5   r…   r   c                 ó   — |  |z   |z
  S rK   r„   )Úpex2Úlpex2Úlex2s      r3   rå  z(genextreme_gen._logpdf.<locals>.<lambda>š  s   € °t°e¸e±mÀdÑ6J€ r5   rÿ  )r   rt   r£  r§  rM   r´   Úputmaskrf   )rB   rn   r  ÚcxÚlogex2Úlogpex2r¬  Úlogpdfs           r3   rÛ   zgenextreme_gen._logpdf‘  sç   € Ý˜˜aš A¨¢FÑ+¨a°¨VÐ5EÐ5EÀsÑKÔKˆÝ”˜2˜#‘”ˆØ—/’/ ! QÑ'Ô'ˆÝŒv�g‰Œˆå
Œ
�7˜Q !šV¨­b¬f¨WªÑ5°sÑ;Ô;Ð;Ý˜r Qšw¨2µ"´&°ª=Ñ9Ð:Ø! 7¨FÐ3ØJÐJÝ')¤v gð/ñ /ô /ˆõ 	Œ
�6˜A šF q¨A¢vÑ.°Ñ4Ô4Ð4Øˆr5   c                 óT   — t          j        |                      ||¦  «        ¦  «         S rK   )rM   r´   r§  r
  s      r3   rà   zgenextreme_gen._logcdfŸ  s#   € Ý”�t—’ q¨!Ñ,Ô,Ñ-Ô-Ð-Ð-r5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   ©rM   r´   rà   r
  s      r3   rr   zgenextreme_gen._cdf¢  rV  r5   c                 óT   — t          j        |                      ||¦  «        ¦  «         S rK   rT  r
  s      r3   rv   zgenextreme_gen._sf¥  rU  r5   c                 ó’   — t          j        t          j        |¦  «         ¦  «         }t          ||k    |dk    z  ||fd„ |¦  «        S )Nr   c                 ó:   — t          j        | | z  ¦  «         |z  S rK   r=  rn  s     r3   rå  z%genextreme_gen._ppf.<locals>.<lambda>«  ó   € ­¬°!°°a±Ñ(8Ô(8Ð'8¸1Ñ'<€ r5   )rM   rí   r   ©rB   rz   r  rn   s       r3   r{   zgenextreme_gen._ppf¨  sP   € ÝŒV•R”V˜A‘Y”Y�JÑÔÐˆÝ˜1 š6 a¨1¢fÑ-°°1¨vØ<Ð<¸añAô Að 	Ar5   c                 ó”   — t          j        t          j        | ¦  «         ¦  «         }t	          ||k    |dk    z  ||fd„ |¦  «        S )Nr   c                 ó:   — t          j        | | z  ¦  «         |z  S rK   r=  rn  s     r3   rå  z%genextreme_gen._isf.<locals>.<lambda>°  rº  r5   )rM   rí   rt   r£  r   r»  s       r3   r~   zgenextreme_gen._isf­  sR   € ÝŒV•R”X˜q˜b‘\”\�MÑ"Ô"Ð"ˆÝ˜1 š6 a¨1¢fÑ-°°1¨vØ<Ð<¸añAô Að 	Ar5   c                 óê  ‡— ˆfd„} |d¦  «        } |d¦  «        } |d¦  «        } |d¦  «        }t          j        t          ‰¦  «        dk     ‰t           j        z  dz  dz  ||dz  z
  ¦  «        }t          j        t          ‰¦  «        dk     t           j        dz  dz  t	          j        t	          j        d‰z  d	z   ¦  «        dt	          j        ‰d	z   ¦  «        z  z
  ¦  «        ‰dz  z  ¦  «        }d
}	t          j        t          ‰¦  «        |	k     t           t	          j        t	          j        ‰dz   ¦  «        ¦  «        ‰z  ¦  «        }
t          j        ‰dk     t           j        |
 ¦  «        }t          j        ‰dk     t           j        |dz  |z  ¦  «        }t          ‰dk    ‰||||fd„ t           j        ¬¦  «        }t          j        t          ‰¦  «        |	dz  k    dt          j
        d¦  «        z  t          z  t           j        dz  z  |¦  «        }t          ‰dk    |||||fd„ t           j        ¬¦  «        }t          j        t          ‰¦  «        |	dz  k    d|dz
  ¦  «        }||||fS )Nc                 ó8   •— t          j        | ‰z  dz   ¦  «        S r[   r-  )r_   r  s    €r3   Úgz genextreme_gen._stats.<locals>.g³  s   ø€ Ý”8˜A ™E A™IÑ&Ô&Ð&r5   r   rR   rƒ  r   gH¯¼šò×z>r³   rE  r†   ç›+¡†›„=r<  rî  rå  c                 óV   — t          j        | ¦  «        | |d|z  z   |z  z   z  |dz  z  S ©NrR   r¼  rL   )r  rB  rC  Úg3Úg2mg12s        r3   rå  z'genextreme_gen._stats.<locals>.<lambda>Å  s4   € ÝœW Q™ZœZ¨"¨°°Q°v±X±¸rÑ/AÑ)AÑBÀ6È3Á;ÑNð r5   rÿ  g�Âõ(\�Ò?r½  r‚  g      Ð¿c                 ó<   — |d|z  d||z   z  | z  z   | z  z   |dz  z  S )NrÇ  rƒ  rR   r„   )rB  rC  rÄ  Úg4rÅ  s        r3   rå  z'genextreme_gen._stats.<locals>.<lambda>Í  s3   € Ø  B r¡E¨A¨r°F©{©O¸BÑ,>Ñ$>ÀÑ#BÑBÀFÈAÁIÑMð r5   gq=
×£pÍ?ç333333@rD  )rM   rO  r
  rî   rt   r  rÃ  r#   r  r   rü   r$   )rB   r  rÀ  rB  rC  rÄ  rÇ  rÅ  Úgam2kÚepsÚgamkrÊ  rÉ  Úsk1rŽ  Úku1r�  s    `               r3   r   zgenextreme_gen._stats²  sY  ø€ ð	'ð 	'ð 	'ð 	'ð 	'àˆQˆq‰TŒTˆØˆQˆq‰TŒTˆØˆQˆq‰TŒTˆØˆQˆq‰TŒTˆÝ”�#˜a™&œ& 4š-¨!­B¬E©'°C©¸Ñ);¸RÀÀCÁ¹ZÑHÔHˆÝ”�˜Q™œ $š­¬¨s©
°3©Ýœ¥"¤*¨S°©U°3©YÑ"7Ô"7¸½"¼*ÀQÈÁWÑ:MÔ:MÑ8MÑ"MÑNÔNÈqÐRUÉvÑUñWô WˆàˆÝŒx�˜A™œ š¥v g­r¬x½¼
À1ÀqÁ5Ñ8IÔ8IÑ/JÔ/JÈ1Ñ/LÑMÔMˆåŒH�Q˜’X�rœv¨ uÑ-Ô-ˆÝŒH�Q˜’X�rœv r¨3¡w¨u¡}Ñ5Ô5ˆõ ˜˜ešØ˜R  R¨Ð0ðOð Oå#%¤6ð	+ñ +ô +ˆõ
 ŒX•c˜!‘f”f  T¡	Ò)¨2­b¬g°a©j¬j©=½Ñ+?ÅÄÀqÁÑ+HÈ#ÑNÔNˆõ ˜˜ešØ˜b " b¨&Ð1ðNð Nå#%¤6ð	+ñ +ô +ˆõ
 ŒX•c˜!‘f”f  t¡Ò+¨X°s¸3±wÑ?Ô?ˆØ�!�R˜ˆ|Ðr5   c                 óÒ   •— t          |t          ¦  «        r|                     ¦   «         }t          |¦  «        }|dk     rd}nd}t	          ¦   «                              ||f¬¦  «        S )Nr   r‘   rî  rJ  ©r<   r(   r�  r   r>   r’  )rB   rC   rÀ  rˆ   r“  s       €r3   r’  zgenextreme_gen._fitstartÓ  sc   ø€ Ý�d�LÑ)Ô)ð 	$Ø—>’>Ñ#Ô#ˆDå�$‰KŒKˆØˆqŠ5ˆ5ØˆAˆAàˆAÝ‰wŒw× Ò  ¨Q¨DÐ Ñ1Ô1Ð1r5   c                 ó&  — t          j        d|dz   ¦  «        }d||z  z  t          j        t          j        ||¦  «        d|z  z  t          j        ||z  dz   ¦  «        z  d¬¦  «        z  }t          j        ||z  dk    |t           j        ¦  «        S )Nr   r   r†   r¼  rû  )rM   rM  r¢  rt   r„  rÖ  rO  rf   )rB   r_   r  r  Úvalss        r3   rÿ   zgenextreme_gen._munpÞ  sŒ   € ÝŒI�a˜˜1™ÑÔˆØ�1�a‘4‰x�"œ&ÝŒG�A�q‰MŒM˜R !™GÑ#¥b¤h¨q°©s°Q©wÑ&7Ô&7Ñ7Øðñ ô ñ ˆõ Œx˜˜!™˜bš $­¬Ñ/Ô/Ð/r5   c                 ó"   — t           d|z
  z  dz   S r[   r_  r}  s     r3   rï   zgenextreme_gen._entropyå  s   € Ý�q˜1‘u‰~ Ñ!Ð!r5   )r€   r�   r‚   rƒ   r`   rh   r“   r§  ro   rÛ   rà   rr   rv   r{   r~   r   r’  rÿ   rï   rÎ  rÏ  s   @r3   rœ  rœ  T  s  ø€ € € € € ð%ð %ðLð ð ðKð Kð Kðð ð ð
=ð =ð =ð
*ð *ð *ðð ð ð.ð .ð .ð*ð *ð *ð-ð -ð -ðAð Að Að
Að Að Að
ð ð ðB	2ð 	2ð 	2ð 	2ð 	2ð0ð 0ð 0ð"ð "ð "ð "ð "ð "ð "r5   rœ  Ú
genextremec                 óZ  ‡ — d}ˆ fd„}‰ dk    r7t          j        ‰ ¦  «        dz   }‰ dk     rt          j        ||d¬¦  «        }|S n*‰ dk    rt          j        ‰ d	z  ¦  «        d
z   }n	d‰  |z
  z  }t          j        ||dd¬¦  «        \  }}}}|dk    rt          d‰ z  ¦  «        ‚|d         S )af  Inverse of the digamma function (real positive arguments only).

    This function is used in the `fit` method of `gamma_gen`.
    The function uses either optimize.fsolve or optimize.newton
    to solve `sc.digamma(x) - y = 0`.  There is probably room for
    improvement, but currently it works over a wide range of y:

    >>> import numpy as np
    >>> rng = np.random.default_rng()
    >>> y = 64*rng.standard_normal(1000000)
    >>> y.min(), y.max()
    (-311.43592651416662, 351.77388222276869)
    >>> x = [_digammainv(t) for t in y]
    >>> np.abs(sc.digamma(x) - y).max()
    1.1368683772161603e-13

    g¶oüŒxâ?c                 ó2   •— t          j        | ¦  «        ‰z
  S rK   )rt   rÂ  rh  s    €r3   r[  z_digammainv.<locals>.func   s   ø€ ÝŒz˜!‰}Œ}˜qÑ Ð r5   g      À¿r‘   r³  ç»½×Ùß|Û=)ÚtolrÆ  g-²�ï§@gë­�­,¶?r†   ç•dyáý¥=T)Úxtolr�  r   z"_digammainv: fsolve failed, y = %rr   )rM   r´   r   Únewtonr‘  ÚRuntimeError)ri  Ú_emr[  Úx0Úvaluer¦  r§  rT  s   `       r3   Ú_digammainvrß  ì  së   ø€ ð$ &€Cð!ð !ð !ð !ð !ð 	ˆ6‚z€zÝŒV�A‰YŒY˜‰_ˆØˆrŠ6ˆ6õ ”O D¨"°%Ð8Ñ8Ô8ˆEØˆLð ð 
ˆRŠˆÝŒV�A�e‘G‰_Œ_˜wÑ&ˆˆà�Q�B˜‘HÑˆå%œ_¨T°2¸EØ9=ð?ñ ?ô ?Ñ€Eˆ4��dà
ˆa‚x€xÝÐ?À!ÑCÑDÔDÐDà�Œ8€Or5   c                   ó�   ‡ — e Zd ZdZd„ Zdd„Zd„ Zd„ Zd„ Zd„ Z	d	„ Z
d
„ Zd„ Zd„ Zˆ fd„Z eed¬¦  «        ˆ fd„¦   «         Zˆ xZS )Ú	gamma_gena“  A gamma continuous random variable.

    %(before_notes)s

    See Also
    --------
    erlang, expon

    Notes
    -----
    The probability density function for `gamma` is:

    .. math::

        f(x, a) = \frac{x^{a-1} e^{-x}}{\Gamma(a)}

    for :math:`x \ge 0`, :math:`a > 0`. Here :math:`\Gamma(a)` refers to the
    gamma function.

    `gamma` takes ``a`` as a shape parameter for :math:`a`.

    When :math:`a` is an integer, `gamma` reduces to the Erlang
    distribution, and when :math:`a=1` to the exponential distribution.

    Gamma distributions are sometimes parameterized with two variables,
    with a probability density function of:

    .. math::

        f(x, \alpha, \beta) =
        \frac{\beta^\alpha x^{\alpha - 1} e^{-\beta x }}{\Gamma(\alpha)}

    Note that this parameterization is equivalent to the above, with
    ``scale = 1 / beta``.

    %(after_notes)s

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r  re   rg   s    r3   rh   zgamma_gen._shape_infoG  r  r5   Nc                 ó.   — |                      ||¦  «        S rK   ©Ústandard_gamma)rB   rˆ   rÔ   rÕ   s       r3   rÖ   zgamma_gen._rvsJ  s   € Ø×*Ò*¨1¨dÑ3Ô3Ð3r5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   rÛ  r
  s      r3   ro   zgamma_gen._pdfM  rƒ  r5   c                 ób   — t          j        |dz
  |¦  «        |z
  t          j        |¦  «        z
  S r  )rt   ru  rÃ  r
  s      r3   rÛ   zgamma_gen._logpdfQ  s*   € ÝŒx˜˜#™˜qÑ!Ô! AÑ%­¬
°1©¬Ñ5Ð5r5   c                 ó,   — t          j        ||¦  «        S rK   r®  r
  s      r3   rr   zgamma_gen._cdfT  r   r5   c                 ó,   — t          j        ||¦  «        S rK   r±  r
  s      r3   rv   zgamma_gen._sfW  s   € ÝŒ|˜A˜qÑ!Ô!Ð!r5   c                 ó,   — t          j        ||¦  «        S rK   rÝ  r  s      r3   r{   zgamma_gen._ppfZ  s   € ÝŒ~˜a Ñ#Ô#Ð#r5   c                 ó,   — t          j        ||¦  «        S rK   ©rt   rº  r  s      r3   r~   zgamma_gen._isf]  s   € ÝŒ˜q !Ñ$Ô$Ð$r5   c                 ó>   — ||dt          j        |¦  «        z  d|z  fS )Nr³   rE  r„  r  s     r3   r   zgamma_gen._stats`  s!   € Ø�!�S�œ ™œ‘^ S¨¡UÐ*Ð*r5   c                 ó>   — d„ }d„ }t          |dk     |f||¬¦  «        S )Nc                 óf   — t          j        | ¦  «        d| z
  z  | z   t          j        | ¦  «        z   S r[   ©rt   rX  rÃ  ©rˆ   s    r3   rÄ  z+gamma_gen._entropy.<locals>.regular_formulae  s+   € Ý”6˜!‘9”9  !¡Ñ$ qÑ(­2¬:°a©=¬=Ñ8Ð8r5   c                 óÂ   — ddt          j        dt           j        z  ¦  «        z   t          j        | ¦  «        z   z  dd| z  z  z
  | dz  dz  z
  | dz  d	z  z
  | d
z  dz  z   S )Nr‘   r†   rR   r   rƒ  r°  r½  r±  rû  r²  r´  rì   rñ  s    r3   rÉ  z.gamma_gen._entropy.<locals>.asymptotic_formulah  so   € ð
 ˜2¥¤ q­¬¡w¡¤Ñ/µ"´&¸±)´)Ñ;Ñ<¸qÀ!ÀaÁ%¹yÑHØ˜#‘v˜r‘kñ"Ø%&¨¡V¨R¡Kñ0Ø34°c±6¸3±,ñ?ð @r5   éú   rè  rê  )rB   rˆ   rÄ  rÉ  s       r3   rï   zgamma_gen._entropyc  sK   € ð	9ð 	9ð 	9ð	@ð 	@ð 	@õ ˜!˜cš' A 5¨/Ø/ð1ñ 1ô 1ð 	1r5   c                 óÒ   •— t          |t          ¦  «        r|                     ¦   «         }t          |¦  «        }dd|dz  z   z  }t	          ¦   «                              ||f¬¦  «        S )Nr   ç:Œ0âŽyE>rR   rJ  rÏ  )rB   rC   rŽ  rˆ   r“  s       €r3   r’  zgamma_gen._fitstarts  sb   ø€ õ �d�LÑ)Ô)ð 	$Ø—>’>Ñ#Ô#ˆDÝ�4‰[Œ[ˆØ�˜˜A™‘ÑˆÝ‰wŒw× Ò  ¨Q¨DÐ Ñ1Ô1Ð1r5   a<          When the location is fixed by using the argument `floc`
        and `method='MLE'`, this
        function uses explicit formulas or solves a simpler numerical
        problem than the full ML optimization problem.  So in that case,
        the `optimizer`, `loc` and `scale` arguments are ignored.
        

rð   c                 óN  •‡— |                      dd ¦  «        }|                      dd¦  «        }t          |t          ¦  «        s|€5|                     ¦   «         dk    r t	          ¦   «         j        |g|¢R i |¤ŽS |                     dd ¦  «         t          |g d¢¦  «        }|                     dd ¦  «        }t          |¦  «         |�|�|�t          d¦  «        ‚t          j        |¦  «        }t          j        |¦  «                             ¦   «         st          d¦  «        ‚|                     ¦   «         dk    r¬t          j        |¦  «        }t          j        |¦  «        }	t          j        ||z
  d	z  ¦  «        }
|||}}}|€|€
|€|
d
|	z  z  }|€|€t          j        |	|z  ¦  «        }|€
|€|	||z
  z  }|€
|€|	|d
z  z  }|€||z
  |z  }|€|||z  z
  }|€||z
  |z  }|||fS t          j        ||k    ¦  «        rt%          d|t          j        ¬¦  «        ‚|dk    r||z
  }|                     ¦   «         }|€—|�|}nŒt          j        |¦  «        t          j        |¦  «                             ¦   «         z
  Šd	‰z
  t          j        ‰d	z
  d
z  d‰z  z   ¦  «        z   d‰z  z  }|dz  }|dz  }t+          j        ˆfd„||d¬¦  «        }||z  }nLt          j        |¦  «                             ¦   «         t          j        |¦  «        z
  }t/          |¦  «        }|}|||fS )Nró   r/   r8   r9   r•  rô   rõ   rö   rƒ  rR   rÖ  rœ  r   r  r½  g333333ã?gffffffö?c                 ó\   •— t          j        | ¦  «        t          j        | ¦  «        z
  ‰z
  S rK   )rM   rí   rt   rÂ  )rˆ   r  s    €r3   rå  zgamma_gen.fit.<locals>.<lambda>Ý  s!   ø€ ­b¬f°Q©i¬i½"¼*ÀQ¹-¼-Ñ.GÈ!Ñ.K€ r5   )Údisp)r:   r<   r(   r;   r>   r@   r0   r   r4   r÷   rM   rø   rù   rú   rû   r¤  rü   r   rH  rf   rí   r   Úbrentqrß  )rB   rC   rD   r2   ró   r/   r–  rô   Úm1Úm2Úm3rˆ   r,   r-   r¥  ÚaestÚxar†  r  r  r“  s                      @€r3   r@   zgamma_gen.fit  sr  øø€ ð �xŠx˜ Ñ%Ô%ˆØ—’˜( EÑ*Ô*ˆå�t�\Ñ*Ô*ð 	4Ø� §¢¡¤°4Ò!7Ð!7ð •5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3ð 	�Š�˜ÑÔÐå! $Ð(=Ð(=Ð(=Ñ>Ô>ˆØ—’˜( DÑ)Ô)ˆå$ TÑ*Ô*Ð*àˆ>˜dÐ.°6Ð3Eõ ð )ñ *ô *ð *õ Œz˜$ÑÔˆåŒ{˜4Ñ Ô ×$Ò$Ñ&Ô&ð 	EÝÐCÑDÔDÐDð �<Š<‰>Œ>˜TÒ!Ð!Ý”˜‘”ˆBÝ”˜‘”ˆBÝ”˜$ ™)¨Ñ)Ñ*Ô*ˆBØ  f�EˆsˆAàˆy˜S˜[¨U¨]Ø˜a "™f™�àˆ{˜u˜}Ýœ  Q¡™œ�Øˆy˜U˜]Ø˜b 3™h™�Øˆy˜S˜[Ø˜% 1™*Ñ%�àˆyØ˜#‘X Ñ&�Øˆ{Ø˜1˜u™9‘n�Øˆ}Ø˜c™ Q™�Ø�c˜5�=Ð õ
 Œ6�$˜$’,ÑÔð 	BÝ˜w¨d½"¼&ÐAÑAÔAÐAà�1Š9ˆ9ð ˜$‘;ˆDØ�yŠy‰{Œ{ˆð ˆ>àˆ~à��õ ”F˜4‘L”L¥2¤6¨$¡<¤<×#4Ò#4Ñ#6Ô#6Ñ6�Ø˜!™�bœg q¨¡s¨Q¡h°°A±¡oÑ6Ô6Ñ6¸2¸a¹4Ñ@�Ø˜5‘\�Ø˜5‘\�Ý”OÐ$KÐ$KÐ$KÐ$KØ$&¨°ð4ñ 4ô 4�ð
 ˜1‘HˆEˆEõ
 ”�t‘”×!Ò!Ñ#Ô#¥b¤f¨V¡n¤nÑ4ˆAÝ˜A‘”ˆAØˆEà�$˜ˆ~Ðr5   r   )r€   r�   r‚   rƒ   rh   rÖ   ro   rÛ   rr   rv   r{   r~   r   rï   r’  r	   r   r@   rÎ  rÏ  s   @r3   rá  rá    s+  ø€ € € € € ð'ð 'ðPEð Eð Eð4ð 4ð 4ð 4ð*ð *ð *ð6ð 6ð 6ð!ð !ð !ð"ð "ð "ð$ð $ð $ð%ð %ð %ð+ð +ð +ð1ð 1ð 1ð 
2ð 
2ð 
2ð 
2ð 
2ð Ð˜}ð 5ð ñ ô ðeð eð eð eñô ðeð eð eð eð er5   rá  rÖ  c                   ó^   ‡ — e Zd ZdZd„ Zd„ Zˆ fd„Z eed¬¦  «        ˆ fd„¦   «         Z	ˆ xZ
S )Ú
erlang_gena¿  An Erlang continuous random variable.

    %(before_notes)s

    See Also
    --------
    gamma

    Notes
    -----
    The Erlang distribution is a special case of the Gamma distribution, with
    the shape parameter `a` an integer.  Note that this restriction is not
    enforced by `erlang`. It will, however, generate a warning the first time
    a non-integer value is used for the shape parameter.

    Refer to `gamma` for examples.

    c                 óª   — t          j        t          j        |¦  «        |k    ¦  «        }|s"d|›d�}t          j        |t
          d¬¦  «         |dk    S )NzRThe shape parameter of the erlang distribution has been given a non-integer value ú.rƒ  ©Ú
stacklevelr   )rM   rú   ÚfloorÚwarningsÚwarnÚRuntimeWarning)rB   rˆ   ÚallintÚmessages       r3   r`   zerlang_gen._argcheck  sd   € Ý”�œ ™œ qÒ(Ñ)Ô)ˆØð 	AðDØ=>ðDð Dð DˆGåŒM˜'¥>¸aÐ@Ñ@Ô@Ð@Ø�1Šuˆr5   c                 ó@   — t          dddt          j        fd¦  «        gS )Nrˆ   Tr   rd   re   rg   s    r3   rh   zerlang_gen._shape_info  ri   r5   c                 óö   •— t          |t          ¦  «        r|                     ¦   «         }t          ddt	          |¦  «        dz  z   z  ¦  «        }t          t          | ¦  «                             ||f¬¦  «        S )NrJ  rõ  rR   rJ  )r<   r(   r�  rÈ  r   r>   rá  r’  )rB   rC   rˆ   r“  s      €r3   r’  zerlang_gen._fitstart  sl   ø€ õ �d�LÑ)Ô)ð 	$Ø—>’>Ñ#Ô#ˆDÝ��t�e D™kœk¨1™nÑ,Ñ-Ñ.Ô.ˆÝ•Y Ñ%Ô%×/Ò/°¸A¸4Ð/Ñ@Ô@Ð@r5   a¦          The Erlang distribution is generally defined to have integer values
        for the shape parameter.  This is not enforced by the `erlang` class.
        When fitting the distribution, it will generally return a non-integer
        value for the shape parameter.  By using the keyword argument
        `f0=<integer>`, the fit method can be constrained to fit the data to
        a specific integer shape parameter.rð   c                 ó>   •—  t          ¦   «         j        |g|¢R i |¤ŽS rK   )r>   r@   ©rB   rC   rD   r2   r“  s       €r3   r@   zerlang_gen.fit  s+   ø€ ð �u‰wŒwŒ{˜4Ð/ $Ð/Ð/Ð/¨$Ð/Ð/Ð/r5   )r€   r�   r‚   rƒ   r`   rh   r’  r	   r   r@   rÎ  rÏ  s   @r3   r   r   ñ  s©   ø€ € € € € ðð ð&ð ð ðCð Cð CðAð Að Að Að Að Ð˜}ð 5/ð 0ñ 0ô 0ð0ð 0ð 0ð 0ñ0ô 0ð0ð 0ð 0ð 0ð 0r5   r   Úerlangc                   óV   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zdd„Z	d	„ Z
d
„ Zd„ Zd„ Zd„ ZdS )Úgengamma_gena½  A generalized gamma continuous random variable.

    %(before_notes)s

    See Also
    --------
    gamma, invgamma, weibull_min

    Notes
    -----
    The probability density function for `gengamma` is ([1]_):

    .. math::

        f(x, a, c) = \frac{|c| x^{c a-1} \exp(-x^c)}{\Gamma(a)}

    for :math:`x \ge 0`, :math:`a > 0`, and :math:`c \ne 0`.
    :math:`\Gamma` is the gamma function (`scipy.special.gamma`).

    `gengamma` takes :math:`a` and :math:`c` as shape parameters.

    %(after_notes)s

    References
    ----------
    .. [1] E.W. Stacy, "A Generalization of the Gamma Distribution",
       Annals of Mathematical Statistics, Vol 33(3), pp. 1187--1192.

    %(example)s

    c                 ó   — |dk    |dk    z  S r®  r„   )rB   rˆ   r  s      r3   r`   zgengamma_gen._argcheckK  ó   € Ø�A’˜!˜qš&Ñ!Ð!r5   c                 ó˜   — t          dddt          j        fd¦  «        }t          ddt          j         t          j        fd¦  «        }||gS rn  re   ro  s      r3   rh   zgengamma_gen._shape_infoN  óB   € Ý˜˜U Q­¬ K°Ñ@Ô@ˆÝ˜˜U¥b¤f W­b¬fÐ$5°~ÑFÔFˆØ�Bˆxˆr5   c                 óT   — t          j        |                      |||¦  «        ¦  «        S rK   rÛ  rq  s       r3   ro   zgengamma_gen._pdfS  ó"   € ÝŒv�d—l’l 1 a¨Ñ+Ô+Ñ,Ô,Ð,r5   c                 ó`   ‡— t          |dk    |dk    z  ||fˆfd„t          j         ¬¦  «        S )Nr   c                 ó´   •— t          j        t          |¦  «        ¦  «        t          j        |‰z  dz
  | ¦  «        z   | |z  z
  t          j        ‰¦  «        z
  S r[   )rM   rí   r
  rt   ru  rÃ  )rn   r  rˆ   s     €r3   rå  z&gengamma_gen._logpdf.<locals>.<lambda>X  sJ   ø€ ­¬­s°1©v¬v©¬½¼À!ÀAÁ#ÈÁ'È1Ñ9MÔ9MÑ(MØ*+¨Q©$ñ)/Ý13´¸A±´ñ)?€ r5   rÿ  r  rq  s     ` r3   rÛ   zgengamma_gen._logpdfV  sN   ø€ Ý˜1 š6 a¨!¢eÑ,¨q°!¨fð@ð @ð @ð @å%'¤V Gð-ñ -ô -ð 	-r5   c                 ó”   — ||z  }t          j        ||¦  «        }t          j        ||¦  «        }t          j        |dk    ||¦  «        S r®  ©rt   r¯  r²  rM   rO  ©rB   rn   rˆ   r  ÚxcÚval1Úval2s          r3   rr   zgengamma_gen._cdf\  óE   € Ø�‰TˆÝŒ{˜1˜bÑ!Ô!ˆÝŒ|˜A˜rÑ"Ô"ˆÝŒx˜˜Aš˜t TÑ*Ô*Ð*r5   Nc                 ó@   — |                      ||¬¦  «        }|d|z  z  S )Nr  r†   rä  )rB   rˆ   r  rÔ   rÕ   rò  s         r3   rÖ   zgengamma_gen._rvsb  s(   € Ø×'Ò'¨°Ð'Ñ5Ô5ˆØ�2�a‘4‰yÐr5   c                 ó”   — ||z  }t          j        ||¦  «        }t          j        ||¦  «        }t          j        |dk    ||¦  «        S r®  r  r  s          r3   rv   zgengamma_gen._sff  r   r5   c                 ó–   — t          j        ||¦  «        }t          j        ||¦  «        }t          j        |dk    ||¦  «        d|z  z  S r   ©rt   r¶  rº  rM   rO  ©rB   rz   rˆ   r  r  r  s         r3   r{   zgengamma_gen._ppfl  óE   € ÝŒ~˜a Ñ#Ô#ˆÝŒ˜q !Ñ$Ô$ˆÝŒx˜˜Aš˜t TÑ*Ô*¨S°©UÑ3Ð3r5   c                 ó–   — t          j        ||¦  «        }t          j        ||¦  «        }t          j        |dk    ||¦  «        d|z  z  S r   r$  r%  s         r3   r~   zgengamma_gen._isfq  r&  r5   c                 ó8   — t          j        ||dz  |z  ¦  «        S r  )rt   r½  )rB   r_   rˆ   r  s       r3   rÿ   zgengamma_gen._munpv  s   € åŒw�q˜!˜C™% ™'Ñ"Ô"Ð"r5   c                 óD   — d„ }d„ }t          |dk    ||f||¬¦  «        }|S )Nc                 óÀ   — t          j        | ¦  «        }| d|z
  z  ||z  z   }t          j        | ¦  «        t          j        t          |¦  «        ¦  «        z
  }||z   }|S r[   )rt   rX  rÃ  rM   rí   r
  )rˆ   r  rB  ÚAÚBræ  s         r3   r¬  z&gengamma_gen._entropy.<locals>.regular{  sS   € Ý”&˜‘)”)ˆCØ�Q˜‘W‘  a¡Ñ'ˆAÝ”
˜1‘”¥¤¥s¨1¡v¤v¡¤Ñ.ˆAØ�A‘ˆAØˆHr5   c                 ó<  — t                                ¦   «         t          j        | ¦  «        dz  z
  t          j        t          j        |¦  «        ¦  «        z
  | dz  dz  z   | dz  dz  z
  t          j        | ¦  «        | dz  dz  z
  | dz  dz  z
  | dz  d	z  z   |z  z   S )
NrR   r<  r‚  r±  rû  r°  r½  r²  r´  )r  rï   rM   rí   r
  )rˆ   r  s     r3   Ú
asymptoticz)gengamma_gen._entropy.<locals>.asymptotic‚  sœ   € å—M’M‘O”O¥b¤f¨Q¡i¤i°¡kÑ1Ý”f�RœV A™YœYÑ'Ô'ñ(Ø+,¨c©6°1©*ñ5Ø89¸3¹À±{ñCå”v˜a‘y”y A s¡F¨A¡:Ñ-°°C±¸±Ñ;¸qÀ#¹vÀs¹lÑJÈAÑMñNð Or5   ç      i@©r‡  ré  rê  )rB   rˆ   r  r¬  r.  ræ  s         r3   rï   zgengamma_gen._entropyz  sH   € ð	ð 	ð 	ð	Oð 	Oð 	Oõ �q˜C’x ! Q ¨:¸'ÐBÑBÔBˆØˆr5   r   )r€   r�   r‚   rƒ   r`   rh   ro   rÛ   rr   rÖ   rv   r{   r~   rÿ   rï   r„   r5   r3   r  r  +  sÈ   € € € € € ðð ð>"ð "ð "ðð ð ð
-ð -ð -ð-ð -ð -ð+ð +ð +ðð ð ð ð+ð +ð +ð4ð 4ð 4ð
4ð 4ð 4ð
#ð #ð #ðð ð ð ð r5   r  Úgengammac                   ó6   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	dS )	Úgenhalflogistic_gena¡  A generalized half-logistic continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `genhalflogistic` is:

    .. math::

        f(x, c) = \frac{2 (1 - c x)^{1/(c-1)}}{[1 + (1 - c x)^{1/c}]^2}

    for :math:`0 \le x \le 1/c`, and :math:`c > 0`.

    `genhalflogistic` takes ``c`` as a shape parameter for :math:`c`.

    %(after_notes)s

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r  re   rg   s    r3   rh   zgenhalflogistic_gen._shape_info¥  r  r5   c                 ó   — | j         d|z  fS r  rñ  r}  s     r3   r“   z genhalflogistic_gen._get_support¨  s   € ØŒv�s˜1‘uˆ}Ðr5   c                 óv   — d|z  }t          j        d||z  z
  ¦  «        }||dz
  z  }||z  }d|z  d|z   dz  z  S r·  ©rM   rø   )rB   rn   r  Úlimitr¡  Útmp0Útmp2s          r3   ro   zgenhalflogistic_gen._pdf«  sQ   € ð �A‘ˆÝŒj˜˜1˜Q™3™ÑÔˆØ�U˜1‘W‰~ˆØ�C‰xˆØ�‰v˜˜4™ !™Ñ#Ð#r5   c                 ó`   — d|z  }t          j        d||z  z
  ¦  «        }||z  }d|z
  d|z   z  S r)  r7  )rB   rn   r  r8  r¡  r:  s         r3   rr   zgenhalflogistic_gen._cdf´  s>   € Ø�A‘ˆÝŒj˜˜1˜Q™3™ÑÔˆØ�U‰|ˆØ�D‘˜Q˜t™VÑ$Ð$r5   c                 ó0   — d|z  dd|z
  d|z   z  |z  z
  z  S r)  r„   r  s      r3   r{   zgenhalflogistic_gen._ppfº  s'   € Ø�1‰u�a˜#˜a™% # a¡%™¨1Ñ,Ñ,Ñ-Ð-r5   c                 óB   — dd|z  dz   t          j        d¦  «        z  z
  S râ  r.  r}  s     r3   rï   zgenhalflogistic_gen._entropy½  s"   € Ø�A�a‘C˜‘E�2œ6 !™9œ9Ñ$Ñ$Ð$r5   N)
r€   r�   r‚   rƒ   rh   r“   ro   rr   r{   rï   r„   r5   r3   r3  r3  �  s{   € € € € € ðð ð*Eð Eð Eðð ð ð$ð $ð $ð%ð %ð %ð.ð .ð .ð%ð %ð %ð %ð %r5   r3  Úgenhalflogisticc                   ó|   ‡ — e Zd ZdZd„ Zd„ Zˆ fd„Zd„ Zd„ Zd„ e	d„ ¦   «         ¦   «         Z
d	„ Zd
„ Zdd„Zd„ Zˆ xZS )Úgenhyperbolic_genu  A generalized hyperbolic continuous random variable.

    %(before_notes)s

    See Also
    --------
    t, norminvgauss, geninvgauss, laplace, cauchy

    Notes
    -----
    The probability density function for `genhyperbolic` is:

    .. math::

        f(x, p, a, b) =
            \frac{(a^2 - b^2)^{p/2}}
            {\sqrt{2\pi}a^{p-1/2}
            K_p\Big(\sqrt{a^2 - b^2}\Big)}
            e^{bx} \times \frac{K_{p - 1/2}
            (a \sqrt{1 + x^2})}
            {(\sqrt{1 + x^2})^{1/2 - p}}

    for :math:`x, p \in ( - \infty; \infty)`,
    :math:`|b| < a` if :math:`p \ge 0`,
    :math:`|b| \le a` if :math:`p < 0`.
    :math:`K_{p}(.)` denotes the modified Bessel function of the second
    kind and order :math:`p` (`scipy.special.kv`)

    `genhyperbolic` takes ``p`` as a tail parameter,
    ``a`` as a shape parameter,
    ``b`` as a skewness parameter.

    %(after_notes)s

    The original parameterization of the Generalized Hyperbolic Distribution
    is found in [1]_ as follows

    .. math::

        f(x, \lambda, \alpha, \beta, \delta, \mu) =
           \frac{(\gamma/\delta)^\lambda}{\sqrt{2\pi}K_\lambda(\delta \gamma)}
           e^{\beta (x - \mu)} \times \frac{K_{\lambda - 1/2}
           (\alpha \sqrt{\delta^2 + (x - \mu)^2})}
           {(\sqrt{\delta^2 + (x - \mu)^2} / \alpha)^{1/2 - \lambda}}

    for :math:`x \in ( - \infty; \infty)`,
    :math:`\gamma := \sqrt{\alpha^2 - \beta^2}`,
    :math:`\lambda, \mu \in ( - \infty; \infty)`,
    :math:`\delta \ge 0, |\beta| < \alpha` if :math:`\lambda \ge 0`,
    :math:`\delta > 0, |\beta| \le \alpha` if :math:`\lambda < 0`.

    The location-scale-based parameterization implemented in
    SciPy is based on [2]_, where :math:`a = \alpha\delta`,
    :math:`b = \beta\delta`, :math:`p = \lambda`,
    :math:`scale=\delta` and :math:`loc=\mu`

    Moments are implemented based on [3]_ and [4]_.

    For the distributions that are a special case such as Student's t,
    it is not recommended to rely on the implementation of genhyperbolic.
    To avoid potential numerical problems and for performance reasons,
    the methods of the specific distributions should be used.

    References
    ----------
    .. [1] O. Barndorff-Nielsen, "Hyperbolic Distributions and Distributions
       on Hyperbolae", Scandinavian Journal of Statistics, Vol. 5(3),
       pp. 151-157, 1978. https://www.jstor.org/stable/4615705

    .. [2] Eberlein E., Prause K. (2002) The Generalized Hyperbolic Model:
        Financial Derivatives and Risk Measures. In: Geman H., Madan D.,
        Pliska S.R., Vorst T. (eds) Mathematical Finance - Bachelier
        Congress 2000. Springer Finance. Springer, Berlin, Heidelberg.
        :doi:`10.1007/978-3-662-12429-1_12`

    .. [3] Scott, David J, WÃ¼rtz, Diethelm, Dong, Christine and Tran,
       Thanh Tam, (2009), Moments of the generalized hyperbolic
       distribution, MPRA Paper, University Library of Munich, Germany,
       https://EconPapers.repec.org/RePEc:pra:mprapa:19081.

    .. [4] E. Eberlein and E. A. von Hammerstein. Generalized hyperbolic
       and inverse Gaussian distributions: Limiting cases and approximation
       of processes. FDM Preprint 80, April 2003. University of Freiburg.
       https://freidok.uni-freiburg.de/fedora/objects/freidok:7974/datastreams/FILE1/content

    %(example)s

    c                 óÀ   — t          j        t          j        |¦  «        |k     |dk    ¦  «        t          j        t          j        |¦  «        |k    |dk     ¦  «        z  S r®  )rM   Úlogical_andr
  )rB   rñ  rˆ   r‰   s       r3   r`   zgenhyperbolic_gen._argcheck  sJ   € Ý”�rœv a™yœy¨1š}¨a°1ªfÑ5Ô5Ý”.¥¤¨¡¤¨a¢°°Q²Ñ7Ô7ñ8ð 	9r5   c                 óì   — t          ddt          j         t          j        fd¦  «        }t          dddt          j        fd¦  «        }t          ddt          j         t          j        fd¦  «        }|||gS )Nrñ  Fr  rˆ   r   rd   r‰   re   )rB   Úiprf  rg  s       r3   rh   zgenhyperbolic_gen._shape_info"  sc   € Ý˜˜U¥b¤f W­b¬fÐ$5°~ÑFÔFˆÝ˜˜U Q­¬ K°Ñ?Ô?ˆÝ˜˜U¥b¤f W­b¬fÐ$5°~ÑFÔFˆØ�B˜ˆ|Ðr5   c                 óJ   •— t          ¦   «                              |d¬¦  «        S )N)r   r   r‘   rJ  r  r  s     €r3   r’  zgenhyperbolic_gen._fitstart(  s"   ø€ õ ‰wŒw× Ò  ¨KÐ Ñ8Ô8Ð8r5   c                 óH   — t           j        d„ ¦   «         } |||||¦  «        S )Nc                 ó0   — t          j        | |||¦  «        S rK   )r   Úgenhyperbolic_logpdf©rn   rñ  rˆ   r‰   s       r3   Ú_logpdf_singlez1genhyperbolic_gen._logpdf.<locals>._logpdf_single0  s   € åÔ.¨q°!°Q¸Ñ:Ô:Ð:r5   ©rM   Ú	vectorize)rB   rn   rñ  rˆ   r‰   rJ  s         r3   rÛ   zgenhyperbolic_gen._logpdf-  s7   € õ 
Œð	;ð 	;ñ 
Œð	;ð ˆ~˜a  A qÑ)Ô)Ð)r5   c                 óH   — t           j        d„ ¦   «         } |||||¦  «        S )Nc                 ó0   — t          j        | |||¦  «        S rK   )r   Úgenhyperbolic_pdfrI  s       r3   Ú_pdf_singlez+genhyperbolic_gen._pdf.<locals>._pdf_single9  s   € åÔ+¨A¨q°!°QÑ7Ô7Ð7r5   rK  )rB   rn   rñ  rˆ   r‰   rP  s         r3   ro   zgenhyperbolic_gen._pdf6  s7   € õ 
Œð	8ð 	8ñ 
Œð	8ð ˆ{˜1˜a  AÑ&Ô&Ð&r5   c                 ót   — t          j        |                      t          ¦  «        t           j        g¬¦  «        S )N©Úotypes)rM   rL  Ú__get__ÚobjectÚfloat64)r[  s    r3   rå  zgenhyperbolic_gen.<lambda>E  s%   € •"”,˜tŸ|š|­FÑ3Ô3½R¼Z¸LÐIÑIÔI€ r5   c                 óÞ  — t          j        |||gt          ¦  «        j                             t          j        ¦  «        }t          j        t          d|¦  «        }t          j	        ||z   ||z
  z  ¦  «        }||z  t          j        |dz   |¦  «        z  t          j        ||¦  «        z  }d}	d}
| |cxk     r|k     rCn n@t          j        || ||	|
¬¦  «        d         t          j        ||||	|
¬¦  «        d         z   }nt          j        || ||	|
¬¦  «        d         }t          j        |¦  «        rd}t          j        |t"          d¬¦  «         t%          d	t'          d
|¦  «        ¦  «        S )zÈ
        Integrate the pdf of the genhyberbolic distribution from x0 to x1.
        This is a private function used by _cdf() and _sf() only; either x0
        will be -inf or x1 will be inf.
        Ú_genhyperbolic_pdfr   rÖ  r   )ÚepsrelÚepsabszdInfinite values encountered in scipy.special.kve. Values replaced by NaN to avoid incorrect results.rƒ  r  r…   r†   )rM   ÚarrayrL  ÚctypesÚdata_asÚc_void_pr   Úfrom_cythonr   rü   rt   Úkvr   ÚquadÚisnanr  r  r  ÚmaxrK  )rÝ  Úx1rñ  rˆ   r‰   Ú	user_dataÚllcrÌ  rû   rY  rZ  ÚintgrlrV   s                r3   Ú_integrate_pdfz genhyperbolic_gen._integrate_pdfE  s�  € õ ”H˜a  A˜Y­Ñ.Ô.Ô5×=Ò=½f¼oÑNÔNˆ	ÝÔ*­6Ð3GØ+4ñ6ô 6ˆåŒG�Q˜‘U˜Q ™U‘OÑ$Ô$ˆØ�‰s•R”U˜1˜q™5 !‘_”_Ñ$¥r¤u¨Q°¡{¤{Ñ2ˆØˆØˆØ�ˆ>ˆ>Š>ˆ>�rŠ>ˆ>ˆ>ˆ>ˆ>õ  ”n S¨"¨dØ,2¸6ðCñ Cô CØCDôFå!œ s¨D°"Ø.4¸VðEñ Eô EØEFôHñHˆFˆFõ
 ”^ C¨¨RØ+1¸&ðBñ Bô BØBCôEˆFåŒ8�FÑÔð 	=ðHˆCåŒM˜#�~¸!Ð<Ñ<Ô<Ð<Ý�3�˜C Ñ(Ô(Ñ)Ô)Ð)r5   c                 óJ   — |                       t          j         ||||¦  «        S rK   ©rh  rM   rf   ©rB   rn   rñ  rˆ   r‰   s        r3   rr   zgenhyperbolic_gen._cdfg  s"   € Ø×"Ò"¥B¤F 7¨A¨q°!°QÑ7Ô7Ð7r5   c                 óH   — |                       |t          j        |||¦  «        S rK   rj  rk  s        r3   rv   zgenhyperbolic_gen._sfj  s    € Ø×"Ò" 1¥b¤f¨a°°AÑ6Ô6Ð6r5   Nc                 ó\  — t          j        |d¦  «        t          j        |d¦  «        z
  }t          j        |d¦  «        }t          j        |d¦  «        }t                               |||||¬¦  «        }	t                               ||¬¦  «        }
||	z  t          j        |	¦  «        |
z  z   S )NrR   r‘   rî  )rñ  r‰   r-   rÔ   rÕ   rÕ  )rM   Úfloat_powerÚgeninvgaussr×  r  rü   )rB   rñ  rˆ   r‰   rÔ   rÕ   r·  r¸  r¹  ÚgigÚnormsts              r3   rÖ   zgenhyperbolic_gen._rvsm  s¢   € õ
 Œ^˜A˜qÑ!Ô!¥B¤N°1°aÑ$8Ô$8Ñ8ˆåŒ^˜B Ñ$Ô$ˆåŒ^˜B Ñ&Ô&ˆÝ�oŠoØØØØØ%ð ñ ô ˆõ —’˜t°,�Ñ?Ô?ˆà�3‰w�œ ™œ¨Ñ.Ñ.Ð.r5   c                 óv  ‡— t          j        |||¦  «        \  }}}t          j        |d¦  «        t          j        |d¦  «        z
  }t          j        |d¦  «        }t          j        dd¦  «        t          j        |d¦  «        z  }t          j        ddd¦  «        }|                     |j        d|j        z  z   ¦  «        }t          j        ||z   |¦  «        \  Š}}}	}
ˆfd	„|||	|
fD ¦   «         \  }}}}||z  |z  }||z  t          j        |d¦  «        t          j        |d¦  «        z  |t          j        |d¦  «        z
  z  z   }t          j        |d
¦  «        t          j        |d
¦  «        z  |d
|z  |z  t          j        ‰d¦  «        z  z
  dt          j        |d
¦  «        z  z   z  d
|z  t          j        |d¦  «        z  |t          j        |d¦  «        z
  z  z   }|t          j        |d¦  «        z  }t          j        |d¦  «        t          j        |d¦  «        z  |d|	z  |z  t          j        ‰d¦  «        z  z
  d|z  t          j        |d¦  «        z  t          j        ‰d¦  «        z  z   d
t          j        |d¦  «        z  z
  z  t          j        |d¦  «        t          j        |d
¦  «        z  d|z  d|z  |z  t          j        ‰d¦  «        z  z
  dt          j        |d
¦  «        z  z   z  z   d
t          j        |d¦  «        z  |z  z   }|t          j        |d¦  «        z  d
z
  }||||fS )NrR   r‘   r   r¼  r   r   rC  rø  c              3   ó"   •K  — | ]	}|‰z  V — Œ
d S rK   r„   )rù  r‰   Úb0s     €r3   ú	<genexpr>z+genhyperbolic_gen._stats.<locals>.<genexpr>Ž  s'   øè è € Ð;Ð; Q˜!˜b™&Ð;Ð;Ð;Ð;Ð;Ð;r5   rƒ  r  r>  r‚  rÆ  r½  )	rM   rï  rn  ÚlinspacerN  Úshaper+  rt   r`  )rB   rñ  rˆ   r‰   r·  r¸  ÚintegersÚb1Úb2Úb3Úb4Úr1Úr2Úr3Úr4rÊ  rÉ  Úm3er  Úm4er  rt  s                        @r3   r   zgenhyperbolic_gen._stats‚  sE  ø€ õ Ô% a¨¨AÑ.Ô.‰ˆˆ1ˆaÝŒ^˜A˜qÑ!Ô!¥B¤N°1°aÑ$8Ô$8Ñ8ˆÝŒ^˜B Ñ$Ô$ˆÝŒ^˜A˜qÑ!Ô!¥B¤N°2°sÑ$;Ô$;Ñ;ˆÝ”;˜q ! QÑ'Ô'ˆà×#Ò# H¤N°T¸A¼F±]Ñ$BÑCÔCˆÝœU 1 x¡<°Ñ4Ô4ÑˆˆB��B˜Ø;Ð;Ð;Ð;¨2¨r°2°rÐ*:Ð;Ñ;Ô;‰ˆˆB��Bà�‰F�R‰Kˆà�‰G•b”n Q¨Ñ*Ô*­R¬^¸BÀÑ-BÔ-BÑBØ•"”.  QÑ'Ô'Ñ'ñ)ñ )ð 	
õ
 ŒN˜1˜aÑ Ô ¥2¤>°"°aÑ#8Ô#8Ñ8Ø�!�b‘&˜2‘+¥¤¨r°2Ñ 6Ô 6Ñ6Ñ6Ø•”  AÑ&Ô&Ñ&ñ'ñ(ð �‰E•B”N 2 qÑ)Ô)Ñ)Ø•"”.  QÑ'Ô'Ñ'ñ)ñ)ð 	ð •"”.  GÑ,Ô,Ñ,ˆåŒN˜1˜aÑ Ô ¥2¤>°"°aÑ#8Ô#8Ñ8Ø�!�b‘&˜2‘+¥¤¨r°3Ñ 7Ô 7Ñ7Ñ7Ø�‰V•b”n R¨Ñ+Ô+Ñ+­b¬n¸RÀÑ.EÔ.EÑEñFà•”  AÑ&Ô&Ñ&ñ'ñ(õ ŒN˜1˜aÑ Ô ¥2¤>°"°aÑ#8Ô#8Ñ8Ø�‰V�b˜2‘g ‘l¥R¤^°B¸Ñ%<Ô%<Ñ<Ñ<Ø•”  AÑ&Ô&Ñ&ñ'ñ(ñ	(ð •”˜r 1Ñ%Ô%Ñ%¨Ñ*ñ+ð 	ð •"”.  BÑ'Ô'Ñ'¨!Ñ+ˆà�!�Q˜ˆzÐr5   r   )r€   r�   r‚   rƒ   r`   rh   r’  rÛ   ro   Ústaticmethodrh  rr   rv   rÖ   r   rÎ  rÏ  s   @r3   r@  r@  Ä  sî   ø€ € € € € ðWð Wðr9ð 9ð 9ðð ð ð9ð 9ð 9ð 9ð 9ð
*ð *ð *ð'ð 'ð 'ð JÐIØð*ð *ñ „\ñ JÔIð*ð@8ð 8ð 8ð7ð 7ð 7ð/ð /ð /ð /ð*'ð 'ð 'ð 'ð 'ð 'ð 'r5   r@  Úgenhyperbolicc                   óB   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
S )Úgompertz_genaq  A Gompertz (or truncated Gumbel) continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `gompertz` is:

    .. math::

        f(x, c) = c \exp(x) \exp(-c (e^x-1))

    for :math:`x \ge 0`, :math:`c > 0`.

    `gompertz` takes ``c`` as a shape parameter for :math:`c`.

    %(after_notes)s

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r  re   rg   s    r3   rh   zgompertz_gen._shape_infoÅ  r  r5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   rÛ  r
  s      r3   ro   zgompertz_gen._pdfÈ  rƒ  r5   c                 ó`   — t          j        |¦  «        |z   |t          j        |¦  «        z  z
  S rK   r’  r
  s      r3   rÛ   zgompertz_gen._logpdfÌ  s%   € ÝŒv�a‰yŒy˜1‰}˜q¥2¤8¨A¡;¤;™Ñ.Ð.r5   c                 óX   — t          j        | t          j        |¦  «        z  ¦  «         S rK   r=  r
  s      r3   rr   zgompertz_gen._cdfÏ  s$   € Ý”˜!˜�bœh q™kœkÑ)Ñ*Ô*Ð*Ð*r5   c                 ó\   — t          j        d|z  t          j        | ¦  «        z  ¦  «        S r?  r	  r  s      r3   r{   zgompertz_gen._ppfÒ  s%   € ÝŒx˜˜q™¥2¤8¨Q¨B¡<¤<Ñ/Ñ0Ô0Ð0r5   c                 óV   — t          j        | t          j        |¦  «        z  ¦  «        S rK   rŠ  r
  s      r3   rv   zgompertz_gen._sfÕ  s!   € ÝŒv�q�b�2œ8 A™;œ;Ñ&Ñ'Ô'Ð'r5   c                 óV   — t          j        t          j        |¦  «         |z  ¦  «        S rK   rŒ  ©rB   rñ  r  s      r3   r~   zgompertz_gen._isfØ  s    € ÝŒx�œ ™œ˜
 1™Ñ%Ô%Ð%r5   c                 óv   — dt          j        |¦  «        z
  t          j                             |¦  «        |z  z
  S r  )rM   rí   rt   Ú_ufuncsÚ_scaled_exp1r}  s     r3   rï   zgompertz_gen._entropyÛ  s.   € Ø•R”V˜A‘Y”Y‰¥¤×!8Ò!8¸Ñ!;Ô!;¸AÑ!=Ñ=Ð=r5   N©r€   r�   r‚   rƒ   rh   ro   rÛ   rr   r{   rv   r~   rï   r„   r5   r3   r†  r†  ¯  s™   € € € € € ðð ð*Eð Eð Eð*ð *ð *ð/ð /ð /ð+ð +ð +ð1ð 1ð 1ð(ð (ð (ð&ð &ð &ð>ð >ð >ð >ð >r5   r†  Úgompertzc                 óÔ   — t          j        | ¦  «        } t          j        |¦  «        }|                     ¦   «         }t          j        ||z
  ¦  «        }t          j        | |¬¦  «        S )N)Úweights)rM   rø   rc  r´   Úaverage)rn   Ú
logweightsÚmaxlogwr•  s       r3   Ú_average_with_log_weightsr™  â  sV   € Ý
Œ
�1‰Œ€AÝ”˜JÑ'Ô'€JØ�nŠnÑÔ€GÝŒf�Z 'Ñ)Ñ*Ô*€GÝŒ:�a Ð)Ñ)Ô)Ð)r5   c                   ó†   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Zd„ Ze ee¦  «        d„ ¦   «         ¦   «         ZdS )Úgumbel_r_gena÷  A right-skewed Gumbel continuous random variable.

    %(before_notes)s

    See Also
    --------
    gumbel_l, gompertz, genextreme

    Notes
    -----
    The probability density function for `gumbel_r` is:

    .. math::

        f(x) = \exp(-(x + e^{-x}))

    The Gumbel distribution is sometimes referred to as a type I Fisher-Tippett
    distribution.  It is also related to the extreme value distribution,
    log-Weibull and Gompertz distributions.

    %(after_notes)s

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   zgumbel_r_gen._shape_info  r£   r5   c                 óP   — t          j        |                      |¦  «        ¦  «        S rK   rÛ  r¦   s     r3   ro   zgumbel_r_gen._pdf  ó   € åŒv�d—l’l 1‘o”oÑ&Ô&Ð&r5   c                 ó4   — | t          j        | ¦  «        z
  S rK   r9  r¦   s     r3   rÛ   zgumbel_r_gen._logpdf  s   € Øˆr•B”F˜A˜2‘J”J‰Ðr5   c                 óR   — t          j        t          j        | ¦  «         ¦  «        S rK   r9  r¦   s     r3   rr   zgumbel_r_gen._cdf  s   € ÝŒv•r”v˜q˜b‘z”z�kÑ"Ô"Ð"r5   c                 ó.   — t          j        | ¦  «         S rK   r9  r¦   s     r3   rà   zgumbel_r_gen._logcdf  s   € Ý”˜�r‘
”
ˆ{Ðr5   c                 óR   — t          j        t          j        |¦  «         ¦  «         S rK   r.  r­   s     r3   r{   zgumbel_r_gen._ppf  s   € Ý”�œ˜q™	œ	�zÑ"Ô"Ð"Ð"r5   c                 óT   — t          j        t          j        | ¦  «         ¦  «         S rK   r�  r¦   s     r3   rv   zgumbel_r_gen._sf  s!   € Ý”�"œ& ! ™*œ*˜Ñ%Ô%Ð%Ð%r5   c                 óT   — t          j        t          j        | ¦  «         ¦  «         S rK   ©rM   rí   r£  rø  s     r3   r~   zgumbel_r_gen._isf  s!   € Ý”�œ ! ™œ�}Ñ%Ô%Ð%Ð%r5   c                 ó¦   — t           t          j        t          j        z  dz  dt          j        d¦  «        z  t          j        dz  z  t          z  dfS )NrE  r½  r‚  rƒ  rÈ  ©r#   rM   rî   rü   r$   rg   s    r3   r   zgumbel_r_gen._stats  s9   € Ý•r”u�RœU‘{ 3‘¨­2¬7°1©:¬:©µb´e¸Q±hÑ(>ÅÑ(GÈÐOÐOr5   c                 ó   — t           dz   S r  r_  rg   s    r3   rï   zgumbel_r_gen._entropy   s   € å˜‰{Ðr5   c                 óÌ  ‡‡‡— t          | ‰||¦  «        \  Š}}ˆfd„}|�|} ||¦  «        Šn³|�	|Šˆˆfd„Šnˆfd„Š|                     dd¦  «        }|dz  |dz  }
}	ˆfd„} ||	|
¦  «        sB|	dk    s|
t          j        k     r,|	dz  }	|
dz  }
 ||	|
¦  «        s|	dk    °|
t          j        k     °,t	          j        ‰|	|
fd	d	¬
¦  «        }|j        }|�|n
 ||¦  «        Š‰|fS )Nc                 ó€   •— |  t          j        ‰ | z  ¦  «        t          j        t	          ‰¦  «        ¦  «        z
  z  S rK   )rt   Ú	logsumexprM   rí   r¡  )r-   rC   s    €r3   Úget_loc_from_scalez,gumbel_r_gen.fit.<locals>.get_loc_from_scale1  s5   ø€ Ø�6�Rœ\¨4¨%°%©-Ñ8Ô8½2¼6Å#ÀdÁ)Ä)Ñ;LÔ;LÑLÑMÐMr5   c                 ó¢   •— ‰‰z
  t          j        ‰‰z
  | z  ¦  «        z  ‰z   }t          ‰¦  «        ‰| z   z  }|                     ¦   «         |z
  S rK   )rM   r´   r¡  r¢  )r-   Úterm1Úterm2rC   r,   s      €€r3   r[  zgumbel_r_gen.fit.<locals>.funcD  sP   ø€ Ø  4™Z­2¬6°3¸±:ÀÑ2FÑ+GÔ+GÑGÈ$ÑN�EÝ ™IœI¨¨u©Ñ5�EØ Ÿ9š9™;œ;¨Ñ.Ð.r5   c                 óf   •— ‰ | z  }t          ‰|¬¦  «        }‰                     ¦   «         |z
  | z
  S )N)r—  )r™  rû   )r-   ÚsdataÚwavgrC   s      €r3   r[  zgumbel_r_gen.fit.<locals>.funcK  s8   ø€ Ø!˜E E™M�EÝ4°TÀeÐLÑLÔL�DØŸ9š9™;œ;¨Ñ-°Ñ5Ð5r5   r-   r   rR   c                 ó|   •— t          j         ‰| ¦  «        ¦  «        t          j         ‰|¦  «        ¦  «        k    S rK   rL   )rO   rP   r[  s     €r3   rQ   z0gumbel_r_gen.fit.<locals>.interval_contains_rootY  s7   ø€ åœ   V¡¤Ñ-Ô-Ýœ   V¡¤Ñ-Ô-ò.ð /r5   r   rÁ  )r  ÚrtolrÙ  )r  r:   rM   rf   r   r)   r  )rB   rC   rD   r2   ró   rô   r¬  r-   Úbrack_startrO   rP   rQ   Úresr[  r,   s    `           @@r3   r@   zgumbel_r_gen.fit$  s§  øøø€ õ 9¸¸tØ9=¸tñEô EÑˆˆd�Fð	Nð 	Nð 	Nð 	Nð 	Nð Ðð ˆEØ$Ð$ UÑ+Ô+ˆCˆCð ÐØ�ð/ð /ð /ð /ð /ð /ð /ð6ð 6ð 6ð 6ð 6ð Ÿ(š( 7¨AÑ.Ô.ˆKØ(¨1™_¨k¸A©o�FˆFð
/ð /ð /ð /ð /ð .Ð-¨f°fÑ=Ô=ð Ø š
˜
 f­r¬v¢o oØ˜!‘�Ø˜!‘�ð .Ð-¨f°fÑ=Ô=ð Ø š
˜
 f­r¬v¢o oõ Ô& t°f¸fÐ5EØ,1¸ð?ñ ?ô ?ˆCà”HˆEØÐ*�$�$Ð0BÐ0BÀ5Ñ0IÔ0IˆCØ�EˆzÐr5   N)r€   r�   r‚   rƒ   rh   ro   rÛ   rr   rà   r{   rv   r~   r   rï   rH   r   r   r@   r„   r5   r3   r›  r›  ê  sí   € € € € € ðð ð2ð ð ð'ð 'ð 'ðð ð ð#ð #ð #ðð ð ð#ð #ð #ð&ð &ð &ð&ð &ð &ðPð Pð Pðð ð ð ØÐ˜MÑ*Ô*ð@ð @ñ +Ô*ñ „_ð@ð @ð @r5   r›  Úgumbel_rc                   ó†   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Zd„ Ze ee¦  «        d„ ¦   «         ¦   «         ZdS )Úgumbel_l_genað  A left-skewed Gumbel continuous random variable.

    %(before_notes)s

    See Also
    --------
    gumbel_r, gompertz, genextreme

    Notes
    -----
    The probability density function for `gumbel_l` is:

    .. math::

        f(x) = \exp(x - e^x)

    The Gumbel distribution is sometimes referred to as a type I Fisher-Tippett
    distribution.  It is also related to the extreme value distribution,
    log-Weibull and Gompertz distributions.

    %(after_notes)s

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   zgumbel_l_gen._shape_info‡  r£   r5   c                 óP   — t          j        |                      |¦  «        ¦  «        S rK   rÛ  r¦   s     r3   ro   zgumbel_l_gen._pdfŠ  rž  r5   c                 ó0   — |t          j        |¦  «        z
  S rK   r9  r¦   s     r3   rÛ   zgumbel_l_gen._logpdfŽ  r  r5   c                 óR   — t          j        t          j        |¦  «         ¦  «         S rK   r�  r¦   s     r3   rr   zgumbel_l_gen._cdf‘  s   € Ý”�"œ& ™)œ)˜Ñ$Ô$Ð$Ð$r5   c                 óR   — t          j        t          j        | ¦  «         ¦  «        S rK   ©rM   rí   rt   r£  r­   s     r3   r{   zgumbel_l_gen._ppf”  s   € ÝŒv•r”x  ‘|”|�mÑ$Ô$Ð$r5   c                 ó,   — t          j        |¦  «         S rK   r9  r¦   s     r3   rä   zgumbel_l_gen._logsf—  rC  r5   c                 óP   — t          j        t          j        |¦  «         ¦  «        S rK   r9  r¦   s     r3   rv   zgumbel_l_gen._sfš  ó   € ÝŒv•r”v˜a‘y”y�jÑ!Ô!Ð!r5   c                 óP   — t          j        t          j        |¦  «         ¦  «        S rK   r.  r¦   s     r3   r~   zgumbel_l_gen._isf�  rÂ  r5   c                 ó¨   — t            t          j        t          j        z  dz  dt          j        d¦  «        z  t          j        dz  z  t          z  dfS )NrE  éôÿÿÿr‚  rƒ  rÈ  r§  rg   s    r3   r   zgumbel_l_gen._stats   s@   € Ýˆw�œ�bœe™ C™Ø•2”7˜1‘:”:‰~�bœe Q™hÑ&­Ñ/°ð8ð 	8r5   c                 ó   — t           dz   S r  r_  rg   s    r3   rï   zgumbel_l_gen._entropy¤  s   € Ý˜‰{Ðr5   c                 ó¤   — |                      d¦  «        �|d          |d<   t          j        t          j        |¦  «         g|¢R i |¤Ž\  }}| |fS )Nró   )r:   r·  r@   rM   rø   )rB   rC   rD   r2   Úloc_rÚscale_rs         r3   r@   zgumbel_l_gen.fit§  sa   € ð �8Š8�FÑÔÐ'Ø  œL˜=ˆD�‰LÝ"œ,­¬
°4Ñ(8Ô(8Ð'8ÐH¸4ÐHÐHÐHÀ4ÐHÐH‰ˆˆwØˆv�wˆÐr5   N)r€   r�   r‚   rƒ   rh   ro   rÛ   rr   r{   rä   rv   r~   r   rï   rH   r   r   r@   r„   r5   r3   r¹  r¹  l  så   € € € € € ðð ð4ð ð ð'ð 'ð 'ðð ð ð%ð %ð %ð%ð %ð %ðð ð ð"ð "ð "ð"ð "ð "ð8ð 8ð 8ðð ð ð ØÐ˜MÑ*Ô*ðð ñ +Ô*ñ „_ðð ð r5   r¹  Úgumbel_lc                   óŠ   ‡ — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Ze ee¦  «        ˆ fd„¦   «         ¦   «         Zˆ xZS )Úhalfcauchy_gena  A Half-Cauchy continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `halfcauchy` is:

    .. math::

        f(x) = \frac{2}{\pi (1 + x^2)}

    for :math:`x \ge 0`.

    %(after_notes)s

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   zhalfcauchy_gen._shape_infoÏ  r£   r5   c                 ó2   — dt           j        z  d||z  z   z  S r  r+  r¦   s     r3   ro   zhalfcauchy_gen._pdfÒ  r…  r5   c                 ót   — t          j        dt           j        z  ¦  «        t          j        ||z  ¦  «        z
  S r;  ©rM   rí   rî   rt   r£  r¦   s     r3   rÛ   zhalfcauchy_gen._logpdfÖ  s)   € ÝŒv�c�"œ%‘iÑ Ô ¥2¤8¨A¨a©C¡=¤=Ñ0Ð0r5   c                 óJ   — dt           j        z  t          j        |¦  «        z  S r;  r‡  r¦   s     r3   rr   zhalfcauchy_gen._cdfÙ  s   € Ø•2”5‰y�œ 1™œÑ%Ð%r5   c                 óJ   — t          j        t           j        dz  |z  ¦  «        S r  r‹  r­   s     r3   r{   zhalfcauchy_gen._ppfÜ  s   € ÝŒv•b”e˜A‘g˜a‘iÑ Ô Ð r5   c                 óL   — dt           j        z  t          j        d|¦  «        z  S ©Nr³   r   )rM   rî   rº  r¦   s     r3   rv   zhalfcauchy_gen._sfß  s   € Ø•2”5‰y�2œ: a¨Ñ+Ô+Ñ+Ð+r5   c                 óP   — dt          j        t           j        |z  dz  ¦  «        z  S r	  r‹  rø  s     r3   r~   zhalfcauchy_gen._isfâ  s!   € Ø•2”6�"œ% ™' !™)Ñ$Ô$Ñ$Ð$r5   c                 ó^   — t           j        t           j        t           j        t           j        fS rK   r  rg   s    r3   r   zhalfcauchy_gen._statså  r‘  r5   c                 óD   — t          j        dt           j        z  ¦  «        S r  rì   rg   s    r3   rï   zhalfcauchy_gen._entropyè  r“  r5   c                 ó@  •— |                      dd¦  «        r t          ¦   «         j        |g|¢R i |¤ŽS t          | |||¦  «        \  }}}t	          j        |¦  «        }|�%||k     rt          d|t          j        ¬¦  «        ‚|}n|}d„ }|�|}	n |||¦  «        }	||	fS )Nr  FÚ
halfcauchyrœ  c                 óâ   ‡‡— || z
  }|j         Št          j        |¦  «        Šˆˆfd„}t          j        d¦  «        j        dz  }t          ||t          j        |¦  «        f¬¦  «        }|j        S )Nc                 óN   •— | dz  ‰z   }dt          j        ‰|z  ¦  «        z  ‰z
  S r  ©rM   r¢  )r-   Údenominatorr_   Úshifted_data_squareds     €€r3   Úfun_to_solvez<halfcauchy_gen.fit.<locals>.find_scale.<locals>.fun_to_solve  s2   ø€ Ø# Q™hÐ)=Ñ=�Ø�2œ6Ð"6°{Ñ"BÑCÔCÑCÀaÑGÐGr5   r†   r‘   ©r  )rÔ   rM   ÚsquareÚfinfoÚtinyr)   rc  r  )r,   rC   Úshifted_datarß  Úsmallr¶  r_   rÞ  s         @@r3   Ú
find_scalez&halfcauchy_gen.fit.<locals>.find_scale   s‡   øø€ Ø #™:ˆLØ”	ˆAÝ#%¤9¨\Ñ#:Ô#:Ð ðHð Hð Hð Hð Hð Hõ ”H˜S‘M”MÔ&¨Ñ+ˆEÝ˜l°U½B¼FÀ<Ñ<PÔ<PÐ4QÐRÑRÔRˆCØ”8ˆOr5   ©r0   r>   r@   r  rM   rK  rH  rf   )rB   rC   rD   r2   ró   rô   rM  r,   ræ  r-   r“  s             €r3   r@   zhalfcauchy_gen.fitë  sÞ   ø€ ð �8Š8�J Ñ&Ô&ð 	4Ø•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3å8¸¸tØ9=¸tñEô EÑˆˆd�Fõ ”6˜$‘<”<ˆØÐØ˜$Šˆå" <°tÅ2Ä6ÐJÑJÔJÐJØˆCˆCð ˆCð	ð 	ð 	ð ÐØˆEˆEà�J˜s DÑ)Ô)ˆEà�EˆzÐr5   )r€   r�   r‚   rƒ   rh   ro   rÛ   rr   r{   rv   r~   r   rï   rH   r   r   r@   rÎ  rÏ  s   @r3   rÌ  rÌ  »  së   ø€ € € € € ðð ð&ð ð ð#ð #ð #ð1ð 1ð 1ð&ð &ð &ð!ð !ð !ð,ð ,ð ,ð%ð %ð %ð.ð .ð .ðð ð ð ØÐ˜MÑ*Ô*ð%ð %ð %ð %ñ +Ô*ñ „_ð%ð %ð %ð %ð %r5   rÌ  rÙ  c                   óŠ   ‡ — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Ze ee¦  «        ˆ fd„¦   «         ¦   «         Zˆ xZS )Úhalflogistic_genaÿ  A half-logistic continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `halflogistic` is:

    .. math::

        f(x) = \frac{ 2 e^{-x} }{ (1+e^{-x})^2 }
             = \frac{1}{2} \text{sech}(x/2)^2

    for :math:`x \ge 0`.

    %(after_notes)s

    References
    ----------
    .. [1] Asgharzadeh et al (2011). "Comparisons of Methods of Estimation for the
           Half-Logistic Distribution". Selcuk J. Appl. Math. 93-108.

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   zhalflogistic_gen._shape_info2  r£   r5   c                 óP   — t          j        |                      |¦  «        ¦  «        S rK   rÛ  r¦   s     r3   ro   zhalflogistic_gen._pdf5  s   € õ Œv�d—l’l 1‘o”oÑ&Ô&Ð&r5   c                 ó†   — t          j        d¦  «        |z
  dt          j        t          j        | ¦  «        ¦  «        z  z
  S r²   )rM   rí   rt   r£  r´   r¦   s     r3   rÛ   zhalflogistic_gen._logpdf:  s2   € ÝŒv�a‰yŒy˜1‰}˜r¥B¤H­R¬V°Q°B©Z¬ZÑ$8Ô$8Ñ8Ñ8Ð8r5   c                 ó0   — t          j        |dz  ¦  «        S r;  )rM   Útanhr¦   s     r3   rr   zhalflogistic_gen._cdf=  s   € ÝŒw�q˜‘u‰~Œ~Ðr5   c                 ó0   — dt          j        |¦  «        z  S r  ©rM   Úarctanhr­   s     r3   r{   zhalflogistic_gen._ppf@  s   € Ø•”˜A‘”‰Ðr5   c                 ó2   — dt          j        | ¦  «        z  S r  ©rt   Úexpitr¦   s     r3   rv   zhalflogistic_gen._sfC  s   € Ø•2”8˜Q˜B‘<”<ÑÐr5   c                 ó6   — t          |dk     |fd„ d„ ¬¦  «        S )Nr‘   c                 ó2   — t          j        d| z  ¦  «         S r  ©rt   ÚlogitrÃ   s    r3   rå  z'halflogistic_gen._isf.<locals>.<lambda>H  s   € ¥R¤X¨c°A©gÑ%6Ô%6Ð$6€ r5   c                 ó6   — dt          j        d| z
  ¦  «        z  S râ  rð  rÃ   s    r3   rå  z'halflogistic_gen._isf.<locals>.<lambda>I  s   €  q­¬°A¸±EÑ):Ô):Ñ':€ r5   rè  rê  r­   s     r3   r~   zhalflogistic_gen._isfF  s/   € Ý˜!˜cš' A 5Ø6Ð6Ø:Ð:ð<ñ <ô <ð 	<r5   c                 ód  — |dk    rdt          j        d¦  «        z  S |dk    rt           j        t           j        z  dz  S |dk    r
dt          z  S |dk    rdt           j        dz  z  dz  S ddt	          d	d|z
  ¦  «        z
  z  t          j        |dz   ¦  «        z  t          j        |d¦  «        z  S )
Nr   rR   rD  rƒ  r  r   rÆ  rY  r³   )rM   rí   rî   r$   r�  rt   rÖ  rZ  r^   s     r3   rÿ   zhalflogistic_gen._munpK  s£   € Ø�Š6ˆ6Ø•R”V˜A‘Y”Y‘;ÐØ�Š6ˆ6Ý”5�œ‘;˜s‘?Ð"Ø�Š6ˆ6Ø•V‘8ˆOØ�Š6ˆ6Ø•R”U˜A‘X‘: Ñ$Ð$Ø�!•C˜˜Q˜q™S‘M”M‘/Ñ"¥2¤8¨A¨a©C¡=¤=Ñ0µ´¸¸A±´Ñ>Ð>r5   c                 ó0   — dt          j        d¦  «        z
  S r  r.  rg   s    r3   rï   zhalflogistic_gen._entropyV  r/  r5   c                 ó>  •— |                      dd¦  «        r t          ¦   «         j        |g|¢R i |¤ŽS t          | |||¦  «        \  }}}d„ }t	          j        |¦  «        }|�%||k     rt          d|t          j        ¬¦  «        ‚|}n|}|�|n |||¦  «        }	||	fS )Nr  Fc                 óâ  — | j         d         }t          j        | d¬¦  «        }t          j        d|dz   ¦  «        |dz   z  }d|z
  }d|z   }|d|z  |z  t          j        ||z  ¦  «        z  z
  }d|z  |z  }||z
  }dt          j        |dd …         |dd …         z  ¦  «        z  }	dt          j        |dd …         |dd …         dz  z  ¦  «        z  }
|	t          j        |	dz  d|z  |
z  z   ¦  «        z   d|z  z  }d}d}|                     ¦   «         }||k    rU|t          j	        | |z  ¦  «        z  }|d|z  |                     ¦   «         z  z
  }t          ||z
  |z  ¦  «        }|}||k    °U|S )	Nr   rû  r   r‘   rR   r*  r   rõ  )rw  rM   ÚsortrM  rí   r¢  rü   rû   rt   rô  r
  )rC   r,   Ún_observationsÚsorted_datarñ  rz   Úpp1r  rk  r,  ÚCr-   r´  Úrelative_residualÚshifted_meanÚsum_termÚ	scale_news                    r3   ræ  z(halflogistic_gen.fit.<locals>.find_scaleb  s­  € ð "œZ¨œ]ˆNÝœ' $¨QÐ/Ñ/Ô/ˆKÝ”	˜!˜^¨aÑ/Ñ0Ô0°.À1Ñ2DÑEˆAØ�A‘ˆAØ�a‘%ˆCØ˜˜a™ #™­¬¨s°Q©w©¬Ñ7Ñ7ˆEØ˜‘7˜S‘=ˆDØ%¨Ñ+ˆKØ•B”F˜5   œ9 {°1°2°2¤Ñ6Ñ7Ô7Ñ7ˆAØ•B”F˜4   œ8 k°!°"°"¤o°qÑ&8Ñ8Ñ9Ô9Ñ9ˆAà�"œ' ! Q¡$¨¨^Ñ);¸aÑ)?Ñ"?Ñ@Ô@Ñ@Ø˜.Ñ(ñ*ˆEð ˆDØ !ÐØ&×+Ò+Ñ-Ô-ˆLð $ dÒ*Ð*Ø&­¬°;°,¸uÑ2DÑ)EÔ)EÑE�Ø(¨1¨^Ñ+;¸h¿lºl¹n¼nÑ+LÑL�	Ý$'¨°Ñ):¸EÑ(AÑ$BÔ$BÐ!Ø!�ð	 $ dÒ*Ð*ð
 ˆLr5   Úhalflogisticrœ  rç  )rB   rC   rD   r2   ró   rô   ræ  rM  r,   r-   r“  s             €r3   r@   zhalflogistic_gen.fitY  sÛ   ø€ ð �8Š8�J Ñ&Ô&ð 	4Ø•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3å8¸¸tØ9=¸tñEô EÑˆˆd�Fð	ð 	ð 	õD ”6˜$‘<”<ˆØÐØ˜$Šˆå" >¸ÅRÄVÐLÑLÔLÐLØˆCˆCð ˆCð !Ð,��°*°*¸TÀ3Ñ2GÔ2Gˆà�EˆzÐr5   )r€   r�   r‚   rƒ   rh   ro   rÛ   rr   r{   rv   r~   rÿ   rï   rH   r   r   r@   rÎ  rÏ  s   @r3   ré  ré    së   ø€ € € € € ðð ð2ð ð ð'ð 'ð 'ð
9ð 9ð 9ðð ð ðð ð ð ð  ð  ð<ð <ð <ð
	?ð 	?ð 	?ðð ð ð ØÐ˜MÑ*Ô*ð6ð 6ð 6ð 6ñ +Ô*ñ „_ð6ð 6ð 6ð 6ð 6r5   ré  r  c                   ó’   ‡ — e Zd ZdZd„ Zdd„Zd„ Zd„ Zd„ Zd„ Z	d	„ Z
d
„ Zd„ Zd„ Ze ee¦  «        ˆ fd„¦   «         ¦   «         Zˆ xZS )Úhalfnorm_genaF  A half-normal continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `halfnorm` is:

    .. math::

        f(x) = \sqrt{2/\pi} \exp(-x^2 / 2)

    for :math:`x >= 0`.

    `halfnorm` is a special case of `chi` with ``df=1``.

    %(after_notes)s

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   zhalfnorm_gen._shape_info­  r£   r5   Nc                 óH   — t          |                     |¬¦  «        ¦  «        S ©Nr  rç  rÓ   s      r3   rÖ   zhalfnorm_gen._rvs°  s!   € Ý�<×/Ò/°TÐ/Ñ:Ô:Ñ;Ô;Ð;r5   c                 ó|   — t          j        dt           j        z  ¦  «        t          j        | |z  dz  ¦  «        z  S r;  ©rM   rü   rî   r´   r¦   s     r3   ro   zhalfnorm_gen._pdf³  s1   € åŒw�s�2œ5‘yÑ!Ô!¥"¤&¨!¨¨A©¨c©Ñ"2Ô"2Ñ2Ð2r5   c                 ó\   — dt          j        dt           j        z  ¦  «        z  ||z  dz  z
  S ©Nr‘   r³   rì   r¦   s     r3   rÛ   zhalfnorm_gen._logpdf·  s*   € Ø•R”V˜C¥¤™IÑ&Ô&Ñ&¨¨1©¨S©Ñ0Ð0r5   c                 óT   — t          j        |t          j        d¦  «        z  ¦  «        S r  ©rt   rê  rM   rü   r¦   s     r3   rr   zhalfnorm_gen._cdfº  s   € ÝŒv�a�"œ' !™*œ*‘nÑ%Ô%Ð%r5   c                 ó,   — t          d|z   dz  ¦  «        S r  rÌ   r­   s     r3   r{   zhalfnorm_gen._ppf½  s   € Ý˜!˜A™#˜s™Ñ#Ô#Ð#r5   c                 ó&   — dt          |¦  «        z  S r  râ   r¦   s     r3   rv   zhalfnorm_gen._sfÀ  s   € Ø•8˜A‘;”;‰Ðr5   c                 ó&   — t          |dz  ¦  «        S r  rç   rø  s     r3   r~   zhalfnorm_gen._isfÃ  s   € Ý˜˜1™‰~Œ~Ðr5   c                 ó  — t          j        dt           j        z  ¦  «        ddt           j        z  z
  t          j        d¦  «        dt           j        z
  z  t           j        dz
  dz  z  dt           j        dz
  z  t           j        dz
  dz  z  fS )Nr³   r   rR   r   r¼  r*  rƒ  ©rM   rü   rî   rg   s    r3   r   zhalfnorm_gen._statsÆ  sm   € Ý”˜�BœE™	Ñ"Ô"Ø�#•b”e‘)‘Ý”˜‘
”
˜A�bœe™GÑ$¥b¤e¨A¡g°¡^Ñ3Ø•2”5˜‘7‘�RœU 1™W q™LÑ(ð*ð 	*r5   c                 óP   — dt          j        t           j        dz  ¦  «        z  dz   S r  rì   rg   s    r3   rï   zhalfnorm_gen._entropyÌ  s"   € Ø•2”6�"œ% ™)Ñ$Ô$Ñ$ SÑ(Ð(r5   c                 óV  •— |                      dd¦  «        r t          ¦   «         j        |g|¢R i |¤ŽS t          | |||¦  «        \  }}}t	          j        |¦  «        }|�%||k     rt          d|t          j        ¬¦  «        ‚|}n|}|�|}nt          j	        |d|¬¦  «        dz  }||fS )Nr  FÚhalfnormrœ  rR   )ÚorderÚcenterr‘   )
r0   r>   r@   r  rM   rK  rH  rf   rð  Úmoment)
rB   rC   rD   r2   ró   rô   rM  r,   r-   r“  s
            €r3   r@   zhalfnorm_gen.fitÏ  sÕ   ø€ ð �8Š8�J Ñ&Ô&ð 	4Ø•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3å8¸¸tØ9=¸tñEô EÑˆˆd�Fõ ”6˜$‘<”<ˆàÐØ˜$Šˆå" :°TÅÄÐHÑHÔHÐHØˆCˆCàˆCàÐØˆEˆEå”L ¨Q°sÐ;Ñ;Ô;¸SÑ@ˆEà�EˆzÐr5   r   )r€   r�   r‚   rƒ   rh   rÖ   ro   rÛ   rr   r{   rv   r~   r   rï   rH   r   r   r@   rÎ  rÏ  s   @r3   r	  r	  —  sÿ   ø€ € € € € ðð ð*ð ð ð<ð <ð <ð <ð3ð 3ð 3ð1ð 1ð 1ð&ð &ð &ð$ð $ð $ðð ð ðð ð ð*ð *ð *ð)ð )ð )ð ØÐ˜MÑ*Ô*ðð ð ð ñ +Ô*ñ „_ðð ð ð ð r5   r	  r  c                   óB   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
S )Úhypsecant_gena  A hyperbolic secant continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `hypsecant` is:

    .. math::

        f(x) = \frac{1}{\pi} \text{sech}(x)

    for a real number :math:`x`.

    %(after_notes)s

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   zhypsecant_gen._shape_info  r£   r5   c                 óJ   — dt           j        t          j        |¦  «        z  z  S r  )rM   rî   Úcoshr¦   s     r3   ro   zhypsecant_gen._pdf  s   € à•B”E�"œ' !™*œ*Ñ$Ñ%Ð%r5   c                 ón   — dt           j        z  t          j        t          j        |¦  «        ¦  «        z  S r;  ©rM   rî   rˆ  r´   r¦   s     r3   rr   zhypsecant_gen._cdf  s%   € Ø•2”5‰y�œ¥2¤6¨!¡9¤9Ñ-Ô-Ñ-Ð-r5   c                 ón   — t          j        t          j        t           j        |z  dz  ¦  «        ¦  «        S r;  ©rM   rí   rŒ  rî   r­   s     r3   r{   zhypsecant_gen._ppf  s&   € ÝŒv•b”f�RœU 1™W S™[Ñ)Ô)Ñ*Ô*Ð*r5   c                 óp   — dt           j        z  t          j        t          j        | ¦  «        ¦  «        z  S r;  r$  r¦   s     r3   rv   zhypsecant_gen._sf  s'   € Ø•2”5‰y�œ¥2¤6¨1¨"¡:¤:Ñ.Ô.Ñ.Ð.r5   c                 óp   — t          j        t          j        t           j        |z  dz  ¦  «        ¦  «         S r;  r&  r­   s     r3   r~   zhypsecant_gen._isf  s)   € Ý”•r”v�bœe A™g c™kÑ*Ô*Ñ+Ô+Ð+Ð+r5   c                 óB   — dt           j        t           j        z  dz  ddfS )Nr   r   rR   r+  rg   s    r3   r   zhypsecant_gen._stats  s   € Ø•"”%�œ‘+˜a‘-  AÐ%Ð%r5   c                 óD   — t          j        dt           j        z  ¦  «        S r  rì   rg   s    r3   rï   zhypsecant_gen._entropy  r“  r5   N)r€   r�   r‚   rƒ   rh   ro   rr   r{   rv   r~   r   rï   r„   r5   r3   r  r  í  s–   € € € € € ðð ð&ð ð ð&ð &ð &ð.ð .ð .ð+ð +ð +ð/ð /ð /ð,ð ,ð ,ð&ð &ð &ðð ð ð ð r5   r  Ú	hypsecantc                   ó*   — e Zd ZdZd„ Zd„ Zd„ Zd„ ZdS )Úgausshyper_gena_  A Gauss hypergeometric continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `gausshyper` is:

    .. math::

        f(x, a, b, c, z) = C x^{a-1} (1-x)^{b-1} (1+zx)^{-c}

    for :math:`0 \le x \le 1`, :math:`a,b > 0`, :math:`c` a real number,
    :math:`z > -1`, and :math:`C = \frac{1}{B(a, b) F[2, 1](c, a; a+b; -z)}`.
    :math:`F[2, 1]` is the Gauss hypergeometric function
    `scipy.special.hyp2f1`.

    `gausshyper` takes :math:`a`, :math:`b`, :math:`c` and :math:`z` as shape
    parameters.

    %(after_notes)s

    References
    ----------
    .. [1] Armero, C., and M. J. Bayarri. "Prior Assessments for Prediction in
           Queues." *Journal of the Royal Statistical Society*. Series D (The
           Statistician) 43, no. 1 (1994): 139-53. doi:10.2307/2348939

    %(example)s

    c                 ó8   — |dk    |dk    z  ||k    z  |dk    z  S )Nr   r¼  r„   )rB   rˆ   r‰   r  r–  s        r3   r`   zgausshyper_gen._argcheck?  s'   € à�A’˜!˜aš%Ñ  A¨¢FÑ+¨q°2ªvÑ6Ð6r5   c                 ó  — t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }t          ddt          j         t          j        fd¦  «        }t          dddt          j        fd¦  «        }||||gS )	Nrˆ   Fr   r  r‰   r  r–  r¼  re   )rB   rf  rg  r!  Úizs        r3   rh   zgausshyper_gen._shape_infoC  sz   € Ý˜˜U Q­¬ K°Ñ@Ô@ˆÝ˜˜U Q­¬ K°Ñ@Ô@ˆÝ˜˜U¥b¤f W­b¬fÐ$5°~ÑFÔFˆÝ˜˜U R­¬ L°.ÑAÔAˆØ�B˜˜BÐÐr5   c                 ó°   — t          j        ||¦  «        t          j        ||||z   | ¦  «        z  }d|z  ||dz
  z  z  d|z
  |dz
  z  z  d||z  z   |z  z  S r  ©rt   rk  Úhyp2f1)rB   rn   rˆ   r‰   r  r–  Únormalization_constants          r3   ro   zgausshyper_gen._pdfJ  sn   € Ý!#¤¨¨A¡¤µ´¸1¸aÀÀQÁÈÈÑ1KÔ1KÑ!KÐØÐ)Ñ)¨A°°B±©KÑ7¸2À¹6ÀQÈÁWÑ:MÑMØ˜˜1™‘9˜q‘.ñ!ð 	"r5   c                 óæ   — t          j        ||z   |¦  «        t          j        ||¦  «        z  }t          j        |||z   ||z   |z   | ¦  «        }t          j        ||||z   | ¦  «        }||z  |z  S rK   r2  )	rB   r_   rˆ   r‰   r  r–  r¨  r
  r©  s	            r3   rÿ   zgausshyper_gen._munpO  sp   € ÝŒg�a˜‘c˜1‰oŒo¥¤¨¨1¡¤Ñ-ˆÝŒi˜˜1˜Q™3  !¡ A¡¨ rÑ*Ô*ˆÝŒi˜˜1˜a ™c A 2Ñ&Ô&ˆØ�3‰w˜‰}Ðr5   N)r€   r�   r‚   rƒ   r`   rh   ro   rÿ   r„   r5   r3   r-  r-    s[   € € € € € ðð ð@7ð 7ð 7ð ð  ð  ð"ð "ð "ð
ð ð ð ð r5   r-  Ú
gausshyperc                   óX   — e Zd ZdZej        Zd„ Zd„ Zd„ Z	d„ Z
d„ Zd„ Zd„ Zdd
„Zd„ ZdS )Úinvgamma_gena_  An inverted gamma continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `invgamma` is:

    .. math::

        f(x, a) = \frac{x^{-a-1}}{\Gamma(a)} \exp(-\frac{1}{x})

    for :math:`x >= 0`, :math:`a > 0`. :math:`\Gamma` is the gamma function
    (`scipy.special.gamma`).

    `invgamma` takes ``a`` as a shape parameter for :math:`a`.

    `invgamma` is a special case of `gengamma` with ``c=-1``, and it is a
    different parameterization of the scaled inverse chi-squared distribution.
    Specifically, if the scaled inverse chi-squared distribution is
    parameterized with degrees of freedom :math:`\nu` and scaling parameter
    :math:`\tau^2`, then it can be modeled using `invgamma` with
    ``a=`` :math:`\nu/2` and ``scale=`` :math:`\nu \tau^2/2`.

    %(after_notes)s

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r  re   rg   s    r3   rh   zinvgamma_gen._shape_infoy  r  r5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   rÛ  r
  s      r3   ro   zinvgamma_gen._pdf|  rƒ  r5   c                 ón   — |dz    t          j        |¦  «        z  t          j        |¦  «        z
  d|z  z
  S r…  ©rM   rí   rt   rÃ  r
  s      r3   rÛ   zinvgamma_gen._logpdf€  s1   € Ø�1‘ˆv�œ˜q™	œ	Ñ!¥B¤J¨q¡M¤MÑ1°C¸±EÑ9Ð9r5   c                 ó2   — t          j        |d|z  ¦  «        S r  r±  r
  s      r3   rr   zinvgamma_gen._cdfƒ  s   € ÝŒ|˜A˜s Q™wÑ'Ô'Ð'r5   c                 ó2   — dt          j        ||¦  «        z  S r  rì  r  s      r3   r{   zinvgamma_gen._ppf†  s   € Ø•R”_ Q¨Ñ*Ô*Ñ*Ð*r5   c                 ó2   — t          j        |d|z  ¦  «        S r  r®  r
  s      r3   rv   zinvgamma_gen._sf‰  s   € ÝŒ{˜1˜c A™gÑ&Ô&Ð&r5   c                 ó2   — dt          j        ||¦  «        z  S r  rÝ  r  s      r3   r~   zinvgamma_gen._isfŒ  s   € Ø•R”^ A qÑ)Ô)Ñ)Ð)r5   Úmvskc                 ó8  — t          |dk    |fd„ t          j        ¦  «        }t          |dk    |fd„ t          j        ¦  «        }d\  }}d|v r"t          |dk    |fd„ t          j        ¦  «        }d	|v r"t          |d
k    |fd„ t          j        ¦  «        }||||fS )Nr   c                 ó   — d| dz
  z  S r  r„   r¶   s    r3   rå  z%invgamma_gen._stats.<locals>.<lambda>�  s   € ¨r°Q¸±V©}€ r5   rR   c                 ó$   — d| dz
  dz  z  | dz
  z  S )Nr†   rR   r³   r„   r¶   s    r3   rå  z%invgamma_gen._stats.<locals>.<lambda>‘  s   € ¨r°Q¸±V¸a±KÑ/?À1ÀrÁ6Ñ/J€ r5   r   r  rƒ  c                 óB   — dt          j        | dz
  ¦  «        z  | dz
  z  S )NrJ  r³   rD  r„  r¶   s    r3   rå  z%invgamma_gen._stats.<locals>.<lambda>˜  s    € ˜"�rœw q¨2¡v™œÑ.°!°b±&Ñ9€ r5   r  r   c                 ó0   — dd| z  dz
  z  | dz
  z  | dz
  z  S )NrE  rü  g      &@rD  rJ  r„   r¶   s    r3   rå  z%invgamma_gen._stats.<locals>.<lambda>œ  s%   € ˜"  Q¡¨¡Ñ-°°R±Ñ8¸AÀ¹FÑC€ r5   r€  )rB   rˆ   r  rú  rû  rB  rC  s          r3   r   zinvgamma_gen._stats�  sÀ   € Ý˜˜Aš ˜tÐ%<Ð%<½b¼fÑEÔEˆÝ˜˜Aš ˜tÐ%JÐ%JÝœñ ô  ˆð ‰ˆˆBØ�'ˆ>ˆ>ÝØ�A’˜�tØ9Ð9½2¼6ñCô CˆBð �'ˆ>ˆ>ÝØ�A’˜�tØCÐCÅRÄVñMô MˆBð �2�r˜2ˆ~Ðr5   c                 óB   — d„ }d„ }t          |dk    |f||¬¦  «        }|S )Nc                 ój   — | | dz   t          j        | ¦  «        z  z
  t          j        | ¦  «        z   }|S r  rð  ©rˆ   ræ  s     r3   r¬  z&invgamma_gen._entropy.<locals>.regular   s/   € Ø�Q˜‘W¥¤ q¡	¤	Ñ)Ñ)­B¬J°q©M¬MÑ9ˆAØˆHr5   c                 óð   — ddt          j        | ¦  «        z  z
  t          j        d¦  «        z   t          j        t           j        ¦  «        z   dz  d| dz  z  z   | dz  dz  z   | dz  d	z  z
  | d
z  dz  z
  }|S )Nr   rƒ  rR   çUUUUUUå?r<  r°  r½  r±  rû  r²  r´  rì   rI  s     r3   r.  z)invgamma_gen._entropy.<locals>.asymptotic¤  s€   € ð �a�œ˜q™	œ	‘k‘/¥B¤F¨1¡I¤IÑ-µ´µr´u±´Ñ=¸qÑ@Ø�q˜#‘v‘:ñØ ! 3¡ r¡	ñ*Ø,-¨s©F°2©Iñ6Ø89¸3¹¸s¹
ñCˆAàˆHr5   r/  r0  rê  )rB   rˆ   r¬  r.  ræ  s        r3   rï   zinvgamma_gen._entropyŸ  sC   € ð	ð 	ð 	ð	ð 	ð 	õ �q˜C’x ! ¨¸Ð@Ñ@Ô@ˆØˆr5   N©rA  )r€   r�   r‚   rƒ   r   r  r  rh   ro   rÛ   rr   r{   rv   r~   r   rï   r„   r5   r3   r8  r8  Y  s·   € € € € € ðð ð: "Ô4€MðEð Eð Eð*ð *ð *ð:ð :ð :ð(ð (ð (ð+ð +ð +ð'ð 'ð 'ð*ð *ð *ðð ð ð ð ð ð ð ð r5   r8  Úinvgammac                   ó¤   ‡ — e Zd ZdZej        Zd„ Zdd„Zd„ Z	d„ Z
d„ Zd„ Zd	„ Zd
„ Zˆ fd„Zˆ fd„Zd„ Z ee¦  «        ˆ fd„¦   «         Zd„ Zˆ xZS )Úinvgauss_gena`  An inverse Gaussian continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `invgauss` is:

    .. math::

        f(x; \mu) = \frac{1}{\sqrt{2 \pi x^3}}
                    \exp\left(-\frac{(x-\mu)^2}{2 \mu^2 x}\right)

    for :math:`x \ge 0` and :math:`\mu > 0`.

    `invgauss` takes ``mu`` as a shape parameter for :math:`\mu`.

    %(after_notes)s

    A common shape-scale parameterization of the inverse Gaussian distribution
    has density

    .. math::

        f(x; \nu, \lambda) = \sqrt{\frac{\lambda}{2 \pi x^3}}
                    \exp\left( -\frac{\lambda(x-\nu)^2}{2 \nu^2 x}\right)

    Using ``nu`` for :math:`\nu` and ``lam`` for :math:`\lambda`, this
    parameterization is equivalent to the one above with ``mu = nu/lam``,
    ``loc = 0``, and ``scale = lam``.

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS ©Nr@  Fr   r  re   rg   s    r3   rh   zinvgauss_gen._shape_info×  r¤  r5   Nc                 ó2   — |                      |d|¬¦  «        S ©Nr†   r  ©Úwald©rB   r@  rÔ   rÕ   s       r3   rÖ   zinvgauss_gen._rvsÚ  s   € Ø× Ò   S¨tÐ Ñ4Ô4Ð4r5   c                 ó¤   — dt          j        dt           j        z  |dz  z  ¦  «        z  t          j        dd|z  z  ||z
  |z  dz  z  ¦  «        z  S )Nr†   rR   rD  r<  r  ©rB   rn   r@  s      r3   ro   zinvgauss_gen._pdfÝ  sO   € ð •2”7˜1�RœU™7 1 c¡6™>Ñ*Ô*Ñ*­2¬6°$¸¸!¹±*¸qÀ¹tÀR¹iÈ!¹^Ñ2KÑ+LÔ+LÑLÐLr5   c                 óž   — dt          j        dt           j        z  ¦  «        z  dt          j        |¦  «        z  z
  ||z
  |z  dz  d|z  z  z
  S )Nrî  rR   r¼  rì   rX  s      r3   rÛ   zinvgauss_gen._logpdfâ  sF   € Ø•B”F˜1�RœU™7‘O”OÑ# c­"¬&°©)¬)¡mÑ3¸¸"¹¸b±yÀ1±nÀaÈÁcÑ6JÑJÐJr5   c                 óö   — dt          j        |¦  «        z  }t          |||z  dz
  z  ¦  «        }d|z  t          | ||z  dz   z  ¦  «        z   }|t          j        t          j        ||z
  ¦  «        ¦  «        z   S r-  )rM   rü   rÀ   r£  r´   ©rB   rn   r@  r¨  rˆ   r‰   s         r3   rà   zinvgauss_gen._logcdfé  ss   € Ø•"”'˜!‘*”*‰nˆÝ˜  R¡¨1¡Ñ-Ñ.Ô.ˆØ�‰F•\ 3 $¨1¨r©6°Q©,Ñ"7Ñ8Ô8Ñ8ˆØ•2”8�BœF 1 q¡5™MœMÑ*Ô*Ñ*Ð*r5   c                 óø   — dt          j        |¦  «        z  }t          |||z  dz
  z  ¦  «        }d|z  t          | ||z   z  |z  ¦  «        z   }|t          j        t          j        ||z
  ¦  «         ¦  «        z   S r-  )rM   rü   rÊ   rÀ   r£  r´   r[  s         r3   rä   zinvgauss_gen._logsfï  su   € Ø•"”'˜!‘*”*‰nˆÝ˜  B¡¨!™|Ñ,Ñ-Ô-ˆØ�‰F•\ 3 $¨!¨b©&¡/°BÑ"6Ñ7Ô7Ñ7ˆØ•2”8�RœV A¨¡E™]œ]˜NÑ+Ô+Ñ+Ð+r5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   r6  rX  s      r3   rv   zinvgauss_gen._sfõ  s    € ÝŒv�d—k’k ! RÑ(Ô(Ñ)Ô)Ð)r5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   r¶  rX  s      r3   rr   zinvgauss_gen._cdfø  ó    € ÝŒv�d—l’l 1 bÑ)Ô)Ñ*Ô*Ð*r5   c                 ó¨  •— t          j        ddd¬¦  «        5  t          j        ||¦  «        \  }}t          j        ||d¦  «        }|dk    }t          j        d||         z
  ||         d¦  «        ||<   t          j        |¦  «        }t          ¦   «                              ||         ||         ¦  «        ||<   d d d ¦  «         n# 1 swxY w Y   |S ©Nr5  )r7  ro  Úinvalidr   r‘   )	rM   r8  rï  rk   Ú_invgauss_ppfÚ_invgauss_isfrb  r>   r{   )rB   rn   r@  ÚppfÚi_wtÚi_nanr“  s         €r3   r{   zinvgauss_gen._ppfû  óý   ø€ ÝŒ[ ¨xÀÐJÑJÔJð 	;ð 	;ÝÔ'¨¨2Ñ.Ô.‰EˆAˆrÝÔ# A r¨1Ñ-Ô-ˆCØ�s’7ˆDÝÔ)¨!¨A¨d¬G©)°R¸´X¸qÑAÔAˆC�‰IÝ”H˜S‘M”MˆEÝ™œŸš a¨¤h°°5´	Ñ:Ô:ˆC�‰Jð	;ð 	;ð 	;ñ 	;ô 	;ð 	;ð 	;ð 	;ð 	;ð 	;ð 	;øøøð 	;ð 	;ð 	;ð 	;ð ˆ
ó   ™B"CÃCÃCc                 ó¨  •— t          j        ddd¬¦  «        5  t          j        ||¦  «        \  }}t          j        ||d¦  «        }|dk    }t          j        d||         z
  ||         d¦  «        ||<   t          j        |¦  «        }t          ¦   «                              ||         ||         ¦  «        ||<   d d d ¦  «         n# 1 swxY w Y   |S ra  )	rM   r8  rï  rk   rd  rc  rb  r>   r~   )rB   rn   r@  Úisfrf  rg  r“  s         €r3   r~   zinvgauss_gen._isf  rh  ri  c                 óD   — ||dz  dt          j        |¦  «        z  d|z  fS )NrD  rƒ  rÈ  r„  )rB   r@  s     r3   r   zinvgauss_gen._stats  s%   € Ø�2�s‘7˜A�bœg b™kœk™M¨2¨b©5Ð0Ð0r5   c                 óx  •— |                      dd¦  «        }t          |t          ¦  «        s0t          | ¦  «        t          k    s|                     ¦   «         dk    r t          ¦   «         j        |g|¢R i |¤ŽS t          | |||¦  «        \  }}}}	 |�|� t          ¦   «         j        |g|¢R i |¤ŽS t          j
        ||z
  dk     ¦  «        rt          ddt          j        ¬¦  «        ‚||z
  }t          j        |¦  «        }|€-t          |¦  «        t          j        |dz  |dz  z
  ¦  «        z  }||z  }|||fS )Nr/   r8   r9   r   Úinvgaussrœ  r¼  )r:   r<   r(   r?   Úwald_genr;   r>   r@   r  rM   r   rH  rf   rû   r¡  r¢  )
rB   rC   rD   r2   r/   Úfshape_sró   rô   Úfshape_nr“  s
            €r3   r@   zinvgauss_gen.fit  sU  ø€ à—’˜( EÑ*Ô*ˆå�t�\Ñ*Ô*ð 	4­d°4©j¬j½HÒ.DÐ.DØ—<’<‘>”> TÒ)Ð)Ø•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3å'BÀ4ÈØCGÈñ(Oô (OÑ$ˆˆh˜˜fð	ð ˆ<˜8Ð/Ø•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3ÝŒV�D˜4‘K !’OÑ$Ô$ð 	)Ý˜z°½"¼&ÐAÑAÔAÐAà˜$‘;ˆDÝ”w˜t‘}”}ˆHØˆ~Ý˜T™œ¥b¤f¨T°R©Z¸(Àb¹.Ñ-HÑ&IÔ&IÑJ�Ø &Ñ(ˆHØ˜˜vÐ%Ð%r5   c                 óÞ   — dt          j        dt           j        z  ¦  «        z   dt          j        |¦  «        z  z   }d|z  }t          j                             |¦  «        |z  }d|z  d|z  z
  S )zV
        Ref.: https://moser-isi.ethz.ch/docs/papers/smos-2012-10.pdf (eq. 9)
        r†   rR   rƒ  r‘   r¼  )rM   rí   rî   rt   r�  r‘  )rB   r@  rˆ   rò  r‰   s        r3   rï   zinvgauss_gen._entropy4  sg   € ð •”˜�BœE™	Ñ"Ô"Ñ" Q­¬°©¬¡^Ñ3ˆð ˆb‰DˆÝŒJ×#Ò# AÑ&Ô& qÑ(ˆØ�Q‰w˜˜q™Ñ Ð r5   r   )r€   r�   r‚   rƒ   r   r  r  rh   rÖ   ro   rÛ   rà   rä   rv   rr   r{   r~   r   r   r@   rï   rÎ  rÏ  s   @r3   rO  rO  ²  s<  ø€ € € € € ð!ð !ðD "Ô4€MðFð Fð Fð5ð 5ð 5ð 5ðMð Mð Mð
Kð Kð Kð+ð +ð +ð,ð ,ð ,ð*ð *ð *ð+ð +ð +ðð ð ð ð ðð ð ð ð ð1ð 1ð 1ð Ð˜MÑ*Ô*ð&ð &ð &ð &ñ +Ô*ð&ðB!ð !ð !ð !ð !ð !ð !r5   rO  rn  c                   óP   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	dd	„Z
d
„ Zd„ Zd„ ZdS )Úgeninvgauss_genaX  A Generalized Inverse Gaussian continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `geninvgauss` is:

    .. math::

        f(x, p, b) = x^{p-1} \exp(-b (x + 1/x) / 2) / (2 K_p(b))

    where `x > 0`, `p` is a real number and `b > 0`\([1]_).
    :math:`K_p` is the modified Bessel function of second kind of order `p`
    (`scipy.special.kv`).

    %(after_notes)s

    The inverse Gaussian distribution `stats.invgauss(mu)` is a special case of
    `geninvgauss` with `p = -1/2`, `b = 1 / mu` and `scale = mu`.

    Generating random variates is challenging for this distribution. The
    implementation is based on [2]_.

    References
    ----------
    .. [1] O. Barndorff-Nielsen, P. Blaesild, C. Halgreen, "First hitting time
       models for the generalized inverse gaussian distribution",
       Stochastic Processes and their Applications 7, pp. 49--54, 1978.

    .. [2] W. Hoermann and J. Leydold, "Generating generalized inverse Gaussian
       random variates", Statistics and Computing, 24(4), p. 547--557, 2014.

    %(example)s

    c                 ó   — ||k    |dk    z  S r®  r„   ©rB   rñ  r‰   s      r3   r`   zgeninvgauss_gen._argcheckj  s   € Ø�Q’˜1˜qš5Ñ!Ð!r5   c                 ó˜   — t          ddt          j         t          j        fd¦  «        }t          dddt          j        fd¦  «        }||gS )Nrñ  Fr  r‰   r   re   )rB   rD  rg  s      r3   rh   zgeninvgauss_gen._shape_infom  óB   € Ý˜˜U¥b¤f W­b¬fÐ$5°~ÑFÔFˆÝ˜˜U Q­¬ K°Ñ@Ô@ˆØ�Bˆxˆr5   c                 óð   — d„ }t          j        |t           j        g¬¦  «        } ||||¦  «        }t          j        |¦  «                             ¦   «         rd}t          j        |t          d¬¦  «         |S )Nc                 ó.   — t          j        | ||¦  «        S rK   )r   Úgeninvgauss_logpdf©rn   rñ  r‰   s      r3   Úlogpdf_singlez.geninvgauss_gen._logpdf.<locals>.logpdf_singlev  s   € ÝÔ,¨Q°°1Ñ5Ô5Ð5r5   rR  zjInfinite values encountered in scipy.special.kve(p, b). Values replaced by NaN to avoid incorrect results.rƒ  r  )rM   rL  rV  rb  r   r  r  r  )rB   rn   rñ  r‰   r}  r–  rV   s          r3   rÛ   zgeninvgauss_gen._logpdfr  s|   € ð	6ð 	6ð 	6õ œ ]½B¼J¸<ÐHÑHÔHˆàˆM˜!˜Q Ñ"Ô"ˆÝŒ8�A‰;Œ;�?Š?ÑÔð 	=ðHˆCåŒM˜#�~¸!Ð<Ñ<Ô<Ð<Øˆr5   c                 óT   — t          j        |                      |||¦  «        ¦  «        S rK   rÛ  ©rB   rn   rñ  r‰   s       r3   ro   zgeninvgauss_gen._pdf‚  rÜ  r5   c                 ó|   ‡—  | j         |Ž \  Š}ˆfd„}t          j        |t          j        g¬¦  «        } ||g|¢R Ž S )Nc                 óø   •— |\  }}t          j        ||gt          ¦  «        j                             t          j        ¦  «        }t          j        t          d|¦  «        }t          j
        |‰| ¦  «        d         S )NÚ_geninvgauss_pdfr   )rM   r[  rL  r\  r]  r^  r   r_  r   r   ra  )rn   rD   rñ  r‰   re  rf  r¤  s         €r3   Ú_cdf_singlez)geninvgauss_gen._cdf.<locals>._cdf_single‰  si   ø€ Ø‰DˆAˆqÝœ ! Q ­Ñ/Ô/Ô6×>Ò>½v¼ÑOÔOˆIÝ"Ô.­vÐ7IØ/8ñ:ô :ˆCõ ”> # r¨1Ñ-Ô-¨aÔ0Ð0r5   rR  )r“   rM   rL  rV  )rB   rn   rD   r£  rƒ  r¤  s        @r3   rr   zgeninvgauss_gen._cdf†  sa   ø€ Ø"�Ô" DÐ)‰ˆˆBð	1ð 	1ð 	1ð 	1ð 	1õ ”l ;½¼
°|ÐDÑDÔDˆàˆ{˜1Ð$˜tÐ$Ð$Ð$Ð$r5   c                 óL   — t          |dk    |||fd„ t          j         ¦  «        S )Nr   c                 óT   — |dz
  t          j        | ¦  «        z  || d| z  z   z  dz  z
  S r-  r.  r|  s      r3   rå  z.geninvgauss_gen._logquasipdf.<locals>.<lambda>˜  s,   € ¨1¨q©5µ"´&¸±)´)Ñ*;¸aÀÀQÀqÁSÁ¹kÈ!¹mÑ*K€ r5   r  r  s       r3   Ú_logquasipdfzgeninvgauss_gen._logquasipdf•  s/   € å˜!˜aš% ! Q¨ ØKÐKÝœ6˜'ñ#ô #ð 	#r5   Nc                 ó˜  ‡	‡
— t          j        |¦  «        r.t          j        |¦  «        r|                      ||||¦  «        }�nk|j        dk    rI|j        dk    r>|                      |                     ¦   «         |                     ¦   «         ||¦  «        }�nt          j        ||¦  «        \  }}t          |j        |¦  «        \  }Š	t          t          j	        |¦  «        ¦  «        }t          j
        |¦  «        }t          j        ||gdgdgdgg¬¦  «        Š
‰
j        s�t          ˆ	ˆ
fd„t          t          |¦  «         d¦  «        D ¦   «         ¦  «        }|                      ‰
d         ‰
d         ||¦  «                             |¦  «        ||<   ‰
                     ¦   «          ‰
j        ¯�|dk    r|                     ¦   «         }|S )Nr   Úmulti_indexÚreadonly©ÚflagsÚop_flagsc              3   ó`   •K  — | ](}‰|         s‰j         |         nt          d ¦  «        V — Œ)d S rK   ©rˆ  Úslice©rù  rÊ  ÚbcÚits     €€r3   ru  z'geninvgauss_gen._rvs.<locals>.<genexpr>È  óR   øè è € ð ;ð ;Ø !ð 79¸´eÐL˜Rœ^¨AÔ.Ð.ÅÀtÁÄð ;ð ;ð ;ð ;ð ;ð ;r5   r   r„   )rM   ÚisscalarÚ_rvs_scalarrÔ   rP  rï  r   rw  rÈ  rý  ÚemptyÚnditerÚfinishedÚtuplerþ  r¡  rN  Úiternext)rB   rñ  r‰   rÔ   rÕ   ró  ÚshpÚ
numsamplesÚidxr‘  r’  s            @@r3   rÖ   zgeninvgauss_gen._rvs›  sÍ  øø€ õ Œ;�q‰>Œ>ð .	�bœk¨!™nœnð .	Ø×"Ò" 1 a¨¨|Ñ<Ô<ˆC‰CØŒV�qŠ[ˆ[˜QœV qš[˜[Ø×"Ò" 1§6¢6¡8¤8¨Q¯VªV©X¬X°t¸\ÑJÔJˆC‰Cõ Ô& q¨!Ñ,Ô,‰DˆAˆqõ # 1¤7¨DÑ1Ô1‰GˆC�õ �RœW S™\œ\Ñ*Ô*ˆJõ ”(˜4‘.”.ˆCå”˜A˜q˜6Ø"/ Ø&0 \°J°<Ð$@ðBñ Bô BˆBð ”kð õ ð ;ð ;ð ;ð ;ð ;Ý%*­C°©I¬I¨:°qÑ%9Ô%9ð;ñ ;ô ;ñ ;ô ;�à×+Ò+¨B¨q¬E°2°a´5¸*Ø,8ñ:ô :ß:Aº'À#¹,¼,ð �C‘à—’‘”�ð ”kð ð  �2Š:ˆ:Ø—(’(‘*”*ˆCØˆ
r5   c           	      ó~  ‡ ‡‡‡3— d}|sd}‰dk     r‰ Šd}‰                       ‰‰¦  «        }d}‰dk    s‰dk    rd}n4‰t          ddt          j        d‰z
  ¦  «        z  dz  ¦  «        k    rd}nd}t	          t          j        |¦  «        ¦  «        }	t          j        |	¦  «        }
t          j        |
¦  «        }d}|�r|�rrd‰dz   z  ‰z  |z
  }d|z  ‰dz
  z  ‰z  dz
  }||dz  dz  z
  }d|dz  z  d	z  ||z  dz  z
  |z   }t          j        | t          j        d
|dz  z  ¦  «        z  dz  ¦  «        }t          j        d|z  dz  ¦  «         }|t          j	        |dz  t          j
        dz  z   ¦  «        z  |dz  z
  }| t          j	        |dz  ¦  «        z  |dz  z
  }‰                      |‰‰¦  «        Š3‰                      |‰‰¦  «        ‰3z
  }‰                      |‰‰¦  «        ‰3z
  }||z
  t          j        d|z  ¦  «        z  }||z
  t          j        d|z  ¦  «        z  }d}ˆˆ3ˆˆ fd„}|}n�t          j        d‰                      |‰‰¦  «        z  ¦  «        }d‰z   t          j        d‰z   dz  ‰dz  z   ¦  «        z   ‰z  }d}|t          j        d‰                      |‰‰¦  «        z  ¦  «        z  }d}ˆˆˆ fd„}||k    rt          d¦  «        ‚|dk    rt          d¦  «        ‚d}||
k     rÌ|
|z
  }||                     |¬¦  «        z  }|                     |¬¦  «        } |||z
  | z  z   } | |z  |z   }!dt          j        |¦  «        z   ||!¦  «        k    }"t          j        |"¦  «        }#|#dk    r|!|"         ||||#z   …<   ||#z  }|dk    r!||
z  dk    rd||
z  › d�}$t#          |$¦  «        ‚|dz  }||
k     °Ì�nÞ‰d‰z
  z  }%t          j        |%d‰z  f¦  «        }&t          j        ‰                      |‰‰¦  «        ¦  «        }'|'|%z  }(|%d‰z  k     rNt          j        ‰ ¦  «        })‰dk    r|)d‰z  ‰z  |%‰z  z
  z  ‰z  }*n#|)t          j        d‰dz  z  ¦  «        z  }*nd\  })}*|&‰dz
  z  }+d|+z  t          j        |& ‰z  dz  ¦  «        z  ‰z  },|(|*z   |,z   }-||
k     �rø|
|z
  }t          j        |¦  «        t          j        |¦  «        }!}.|                     |¬¦  «        }|-|                     |¬¦  «        z  } | |(k    }/t          j        |/¦  «        | |(|*z   k    z  }0t          j        |/|0z  ¦  «        }1|%| |/         z  |(z  |!|/<   |'|.|/<   ‰dk    r!|%‰z  | |0         |(z
  ‰z  |)z  z   d‰z  z  |!|0<   n8‰t          j        | |0         |(z
  t          j        ‰¦  «        z  ¦  «        z  |!|0<   |)|!|0         ‰dz
  z  z  |.|0<   t          j        |& ‰z  dz  ¦  «        ‰| |1         |(z
  |*z
  z  d|+z  z  z
  }2d‰z  t          j        |2¦  «        z  |!|1<   |+t          j        |!|1          ‰z  dz  ¦  «        z  |.|1<   t          j        ||.z  ¦  «        ‰                      |!‰‰¦  «        k    }"t!          |"¦  «        }#|#dk    r|!|"         ||||#z   …<   ||#z  }||
k     �°øt          j        ||	¦  «        }!|rd|!z  }!|!S )NFr   r   Tr‘   rR   rƒ  r  é   iåÿÿÿrÇ  c                 ó8   •— ‰                      | ‰‰¦  «        ‰z
  S rK   ©r†  )rn   r‰   Úlmrñ  rB   s    €€€€r3   Úlogqpdfz,geninvgauss_gen._rvs_scalar.<locals>.logqpdf  s    ø€ Ø×,Ò,¨Q°°1Ñ5Ô5¸Ñ:Ð:r5   c                 ó2   •— ‰                      | ‰‰¦  «        S rK   r¡  )rn   r‰   rñ  rB   s    €€€r3   r£  z,geninvgauss_gen._rvs_scalar.<locals>.logqpdf  s   ø€ Ø×,Ò,¨Q°°1Ñ5Ô5Ð5r5   zvmin must be smaller than vmax.zumax must be positive.r  iPÃ  z2Not a single random variate could be generated in zH attempts. Sampling does not appear to work for the provided parameters.)r   r   )Ú_moderK  rM   rü   r™  Ú
atleast_1drý  ÚzerosÚarccosr  rî   r†  r´   r÷   r  rí   r¢  rÛ  rc  Úlogical_notrN  )4rB   rñ  r‰   rœ  rÕ   Ú
invert_resrÊ  Ú
ratio_unifÚ
mode_shiftÚsize1dÚNrn   Ú	simulatedÚa2Úa1Úp1Úq1ÚphirY  Úroot1Úroot2Úd1Úd2ÚvminÚvmaxÚumaxr£  r  Úxplusrô  r  r  rÉ  r×  ÚacceptÚ
num_acceptrV   rÝ  ÚxsÚk1ÚA1Úk2ÚA2Úk3ÚA3r+  ræ  Úcond1Úcond2Úcond3r–  r¢  s4   ```                                                @r3   r•  zgeninvgauss_gen._rvs_scalarÒ  sÓ  øøøø€ ð ˆ
Øð 	ØˆJØˆqŠ5ˆ5à�ˆAØˆJØ�JŠJ�q˜!ÑÔˆð ˆ
Ø�Š6ˆ6�Q˜’U�UàˆJˆJØ•#�c˜1�rœw q¨1¡u™~œ~Ñ-°Ñ1Ñ2Ô2Ò2Ð2àˆJˆJð ˆJõ •r”} ZÑ0Ô0Ñ1Ô1ˆÝŒG�F‰OŒOˆÝŒH�Q‰KŒKˆØˆ	àñ t	,àñ (6Ø˜1˜q™5‘\ AÑ%¨Ñ)�Ø˜‘U˜a !™e‘_ qÑ(¨1Ñ,�à˜"˜a™% !™)‘^�Ø˜˜Q™‘Y ‘^ b¨2¡g°¡kÑ1°AÑ5�Ý”i  ¥b¤g¨c°B¸±E©kÑ&:Ô&:Ñ :¸QÑ >Ñ?Ô?�Ý”g˜b 2™g¨™kÑ*Ô*Ð*�Ø�RœV C¨!¡G­b¬e°a©iÑ$7Ñ8Ô8Ñ8¸2À¹6ÑA�Ø˜�bœf S¨1¡W™oœoÑ-°°Q±Ñ6�ð ×&Ò& q¨!¨QÑ/Ô/�Ø×&Ò& u¨a°Ñ3Ô3°bÑ8�Ø×&Ò& u¨a°Ñ3Ô3°bÑ8�ð  ™	¥R¤V¨C°"©HÑ%5Ô%5Ñ5�Ø ™	¥R¤V¨C°"©HÑ%5Ô%5Ñ5�Ø�ð;ð ;ð ;ð ;ð ;ð ;ð ;ð ;ð ��õ ”v˜c $×"3Ò"3°A°q¸!Ñ"<Ô"<Ñ<Ñ=Ô=�Ø˜a™%¥2¤7¨A°©E°A©:¸¸1¹Ñ+<Ñ#=Ô#=Ñ=¸qÑ@�Ø�à�rœv c¨D×,=Ò,=¸eÀQÈÑ,JÔ,JÑ&JÑKÔKÑK�Ø�ð6ð 6ð 6ð 6ð 6ð 6ð 6ð �tŠ|ˆ|Ý Ð!BÑCÔCÐCØ�qŠyˆyÝ Ð!9Ñ:Ô:Ð:àˆAØ˜a’-�-Ø˜	‘M�à˜<×/Ò/°QÐ/Ñ7Ô7Ñ7�Ø ×(Ò(¨aÐ(Ñ0Ô0�Ø˜D 4™K¨1Ñ,Ñ,�Ø˜!‘e˜a‘i�à�BœF 1™IœI™+¨¨°©¬Ò5�ÝœV F™^œ^�
Ø ’>�>Ø<?À¼K�A�i ¨ZÑ!7Ð8Ñ9Ø Ñ+�Ià ’N�N¨¨1©°ª¨ð?Ø!" 1¡ð?ð ?ð ?�Cõ ' sÑ+Ô+Ð+Ø�Q‘�ð' ˜a’-�-ùð, �a˜!‘e‘ˆBÝ”˜˜Q ™U˜Ñ$Ô$ˆBÝ”˜×)Ò)¨!¨Q°Ñ2Ô2Ñ3Ô3ˆBØ�b‘ˆBØ�A˜‘EŠzˆzÝ”V˜Q˜B‘Z”Z�Ø�q’5�5Ø  A¡¨™z¨B°©EÑ1Ñ2°QÑ6�B�Bà�bœf Q¨¨A©¡XÑ.Ô.Ñ.�B�Bà‘��BØ�a˜!‘e‘ˆBØ�R‘�"œ& "  q¡¨1¡Ñ-Ô-Ñ-°Ñ1ˆBØ�R‘˜"‘ˆAð ˜a’-‘-Ø˜	‘M�Ýœ !™œ¥b¤h¨q¡k¤k�3�à ×(Ò(¨aÐ(Ñ0Ô0�Ø˜×,Ò,°!Ð,Ñ4Ô4Ñ4�Ø˜Rš�Ýœ uÑ-Ô-°°b¸2±g²Ñ>�Ýœ u¨u¡}Ñ5Ô5�à ! E¤(™]¨RÑ/��E‘
Ø��%‘à�q’5�5Ø"$ a¡%¨1¨U¬8°b©=¸AÑ*=ÀÑ*BÑ"BÀaÈ!ÁeÑ!L�C˜‘J�Jà!"¥R¤V¨Q¨u¬X¸©]½b¼fÀQ¹i¼iÑ,GÑ%HÔ%HÑ!H�C˜‘JØ  E¤
¨Q°©UÑ 3Ñ3��%‘å”F˜B˜3 ™7 Q™;Ñ'Ô'¨!¨q°¬x¸"©}¸rÑ/AÑ*BÀaÈ"ÁfÑ*MÑM�Ø !™V¥b¤f¨Q¡i¤iÑ/��E‘
Ø¥¤¨¨E¬
 {°Q¡¸Ñ':Ñ ;Ô ;Ñ;��%‘åœ&  Q¡™-œ-¨4×+<Ò+<¸SÀ!ÀQÑ+GÔ+GÒG�Ý  ™[œ[�
Ø ’>�>Ø<?À¼K�A�i ¨ZÑ!7Ð8Ñ9Ø Ñ+�Ið7 ˜a’-‘-õ: Œj˜˜FÑ#Ô#ˆØð 	Ø�c‘'ˆCØˆ
r5   c                 ó²   — |dk     r)|t          j        |dz
  dz  |dz  z   ¦  «        dz   |z
  z  S t          j        d|z
  dz  |dz  z   ¦  «        d|z
  z
  |z  S r-  r„  rv  s      r3   r¥  zgeninvgauss_gen._modek  sj   € àˆqŠ5ˆ5Ø�œ  Q¡¨¡
¨Q°©TÑ 1Ñ2Ô2°QÑ6¸Ñ:Ñ;Ð;å”G˜Q ™U Q™J¨¨A©Ñ-Ñ.Ô.°!°a±%Ñ8¸AÑ=Ð=r5   c                 ó¦  — t          j        ||z   |¦  «        }t          j        ||¦  «        }t          j        |¦  «        t          j        |¦  «        z  }|                     ¦   «         rad}t          j        |t          d¬¦  «         t          j        |t          j	        t          j
        ¬¦  «        }||          ||          z  || <   n||z  }|S )Nz…Infinite values encountered in the moment calculation involving scipy.special.kve. Values replaced by NaN to avoid incorrect results.rƒ  r  ©Údtype)rt   ÚkverM   rS   r   r  r  r  Ú	full_liker  rV  )	rB   r_   rñ  r‰   r
  ÚdenomÚinf_valsrV   rÊ  s	            r3   rÿ   zgeninvgauss_gen._munpr  s·   € ÝŒf�Q˜‘U˜AÑÔˆÝ”�q˜!‘”ˆÝ”8˜C‘=”=¥2¤8¨E¡?¤?Ñ2ˆØ�<Š<‰>Œ>ð 	ð.ˆCõ ŒM˜#�~¸!Ð<Ñ<Ô<Ð<Ý”˜S¥"¤&µ´
Ð;Ñ;Ô;ˆAØ ˜yœ>¨E°8°)Ô,<Ñ<ˆAˆxˆi‰LˆLà�e‘ˆAØˆr5   r   )r€   r�   r‚   rƒ   r`   rh   rÛ   ro   rr   r†  rÖ   r•  r¥  rÿ   r„   r5   r3   rt  rt  E  s¿   € € € € € ð#ð #ðH"ð "ð "ðð ð ð
ð ð ð -ð -ð -ð%ð %ð %ð#ð #ð #ð5ð 5ð 5ð 5ðnWð Wð Wðr>ð >ð >ðð ð ð ð r5   rt  ro  c                   ó\   ‡ — e Zd ZdZej        Zd„ Zd„ Zˆ fd„Z	d„ Z
d„ Zd„ Zdd	„Zd
„ Zˆ xZS )Únorminvgauss_gena  A Normal Inverse Gaussian continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `norminvgauss` is:

    .. math::

        f(x, a, b) = \frac{a \, K_1(a \sqrt{1 + x^2})}{\pi \sqrt{1 + x^2}} \,
                     \exp(\sqrt{a^2 - b^2} + b x)

    where :math:`x` is a real number, the parameter :math:`a` is the tail
    heaviness and :math:`b` is the asymmetry parameter satisfying
    :math:`a > 0` and :math:`|b| <= a`.
    :math:`K_1` is the modified Bessel function of second kind
    (`scipy.special.k1`).

    %(after_notes)s

    A normal inverse Gaussian random variable `Y` with parameters `a` and `b`
    can be expressed as a normal mean-variance mixture:
    `Y = b * V + sqrt(V) * X` where `X` is `norm(0,1)` and `V` is
    `invgauss(mu=1/sqrt(a**2 - b**2))`. This representation is used
    to generate random variates.

    Another common parametrization of the distribution (see Equation 2.1 in
    [2]_) is given by the following expression of the pdf:

    .. math::

        g(x, \alpha, \beta, \delta, \mu) =
        \frac{\alpha\delta K_1\left(\alpha\sqrt{\delta^2 + (x - \mu)^2}\right)}
        {\pi \sqrt{\delta^2 + (x - \mu)^2}} \,
        e^{\delta \sqrt{\alpha^2 - \beta^2} + \beta (x - \mu)}

    In SciPy, this corresponds to
    `a = alpha * delta, b = beta * delta, loc = mu, scale=delta`.

    References
    ----------
    .. [1] O. Barndorff-Nielsen, "Hyperbolic Distributions and Distributions on
           Hyperbolae", Scandinavian Journal of Statistics, Vol. 5(3),
           pp. 151-157, 1978.

    .. [2] O. Barndorff-Nielsen, "Normal Inverse Gaussian Distributions and
           Stochastic Volatility Modelling", Scandinavian Journal of
           Statistics, Vol. 24, pp. 1-13, 1997.

    %(example)s

    c                 ó@   — |dk    t          j        |¦  «        |k     z  S r®  )rM   Úabsolute©rB   rˆ   r‰   s      r3   r`   znorminvgauss_gen._argcheck½  s   € Ø�A’�"œ+ a™.œ.¨1Ò,Ñ-Ð-r5   c                 ó˜   — t          dddt          j        fd¦  «        }t          ddt          j         t          j        fd¦  «        }||gS rd  re   re  s      r3   rh   znorminvgauss_gen._shape_infoÀ  r  r5   c                 óJ   •— t          ¦   «                              |d¬¦  «        S )N)r   r‘   rJ  r  r  s     €r3   r’  znorminvgauss_gen._fitstartÅ  s"   ø€ õ ‰wŒw× Ò  ¨HÐ Ñ5Ô5Ð5r5   c                 ó   — t          j        |dz  |dz  z
  ¦  «        }|t           j        z  }t          j        d|¦  «        }|t	          j        ||z  ¦  «        z  t          j        ||z  ||z  z
  |z   ¦  «        z  |z  S râ  )rM   rü   rî   Úhypotrt   Úk1er´   )rB   rn   rˆ   r‰   rÖ  Úfac1Úsqs          r3   ro   znorminvgauss_gen._pdfÊ  ss   € Ý”˜˜1™˜q !™t™Ñ$Ô$ˆØ•2”5‰yˆÝŒX�a˜‰^Œ^ˆØ•b”f˜Q ™V‘n”nÑ$¥r¤v¨a°©c°A°b±D©j¸5Ñ.@Ñ'AÔ'AÑAÀBÑFÐFr5   c           
      ó¸  — t          j        |¦  «        r/t          j        | j        |t           j        ||f¬¦  «        d         S t          j        |¦  «        }t          j        |¦  «        }g }t          |||¦  «        D ]H\  }}}|                     t          j        | j        |t           j        ||f¬¦  «        d         ¦  «         ŒIt          j	        |¦  «        S )NrJ  r   )
rM   r”  r   ra  ro   rf   r¦  rƒ  Úappendr[  )rB   rn   rˆ   r‰   ÚresultrÝ  Úa0rt  s           r3   rv   znorminvgauss_gen._sfÐ  s×   € ÝŒ;�q‰>Œ>ð 
	$å”> $¤)¨Qµ´¸aÀ¸VÐDÑDÔDÀQÔGÐGå”˜aÑ Ô ˆAÝ”˜aÑ Ô ˆAØˆFÝ # A q¨!¡¤ð @ð @‘��R˜Ø—’�iœn¨T¬Y¸½B¼FØ35°r°(ð<ñ <ô <Ø<=ô?ñ @ô @ð @ð @å”8˜FÑ#Ô#Ð#r5   c                 óì   ‡ — ˆ fd„}t          j        |¦  «        r ||||¦  «        S g }t          |||¦  «        D ]&\  }}}|                      ||||¦  «        ¦  «         Œ't          j        |¦  «        S )Nc                 ó–  •— ˆ
fd„}‰
                      ||¦  «        } ||||| ¦  «        }|dk    r|S |dk    r8d}|}||z   } ||||| ¦  «        dk    rd|z  }||z   } ||||| ¦  «        dk    °n7d}|}||z
  } ||||| ¦  «        dk     rd|z  }||z
  } ||||| ¦  «        dk     °t          j        |||||| f‰
j        ¬¦  «        }	|	S )Nc                 ó8   •— ‰                      | ||¦  «        |z
  S rK   ©rv   )rn   rˆ   r‰   rz   rB   s       €r3   Úeqz6norminvgauss_gen._isf.<locals>._isf_scalar.<locals>.eqà  s   ø€ à—x’x  1 aÑ(Ô(¨1Ñ,Ð,r5   r   r   rR   )rD   rÙ  )rû   r   rù  rÙ  )rz   rˆ   r‰   rå  ÚxmÚemÚdeltaÚleftÚrightrß  rB   s             €r3   Ú_isf_scalarz*norminvgauss_gen._isf.<locals>._isf_scalarÞ  sF  ø€ ð-ð -ð -ð -ð -ð —’˜1˜a‘”ˆBØ��B˜˜1˜a‘”ˆBØ�QŠwˆwà�	Ø�AŠvˆvØ�Ø�Ø˜U™
�Ø�b˜  1 aÑ(Ô(¨1Ò,Ð,Ø˜e™G�EØ ™J�Eð �b˜  1 aÑ(Ô(¨1Ò,Ð,øð
 �Ø�Ø˜E‘z�Ø�b˜˜q ! QÑ'Ô'¨!Ò+Ð+Ø˜e™G�EØ ™:�Dð �b˜˜q ! QÑ'Ô'¨!Ò+Ð+õ ”_ R¨¨u¸A¸qÀ!¸9Ø*.¬)ð5ñ 5ô 5ˆFàˆMr5   )rM   r”  rƒ  rÞ  r[  )	rB   rz   rˆ   r‰   rë  rß  Úq0rà  rt  s	   `        r3   r~   znorminvgauss_gen._isfÝ  sš   ø€ ð	ð 	ð 	ð 	ð 	õB Œ;�q‰>Œ>ð 	$Ø�;˜q ! QÑ'Ô'Ð'àˆFÝ # A q¨!¡¤ð 7ð 7‘��R˜Ø—’˜k˜k¨"¨b°"Ñ5Ô5Ñ6Ô6Ð6Ð6Ý”8˜FÑ#Ô#Ð#r5   Nc                 óê   — t          j        |dz  |dz  z
  ¦  «        }t                               d|z  ||¬¦  «        }||z  t          j        |¦  «        t                               ||¬¦  «        z  z   S )NrR   r   )r@  rÔ   rÕ   rÕ  )rM   rü   rn  r×  r  )rB   rˆ   r‰   rÔ   rÕ   rÖ  Úigs          r3   rÖ   znorminvgauss_gen._rvs  sy   € õ ”˜˜1™˜q !™t™Ñ$Ô$ˆÝ�\Š\˜Q˜u™W¨4¸lˆ\ÑKÔKˆØ�2‰v�œ ™œ¥d§h¢h°DØ<Hð '/ñ 'Jô 'Jñ Jñ Jð 	Jr5   c                 óÐ   — t          j        |dz  |dz  z
  ¦  «        }||z  }|dz  |dz  z  }d|z  |t          j        |¦  «        z  z  }ddd|dz  z  |dz  z  z   z  |z  }||||fS )NrR   rƒ  rD  r   r   r„  )rB   rˆ   r‰   rÖ  rû   ÚvarianceÚskewnessÚkurtosiss           r3   r   znorminvgauss_gen._stats  s…   € Ý”˜˜1™˜q !™t™Ñ$Ô$ˆØ�5‰yˆØ�a‘4˜% ™(‘?ˆØ˜‘7˜a¥"¤'¨%¡.¤.Ñ0Ñ1ˆØ˜!˜a ! Q¡$™h¨¨A©™oÑ-Ñ.°Ñ6ˆØ�X˜x¨Ð1Ð1r5   r   )r€   r�   r‚   rƒ   r   r  r  r`   rh   r’  ro   rv   r~   rÖ   r   rÎ  rÏ  s   @r3   rÒ  rÒ  …  sÃ   ø€ € € € € ð4ð 4ðj "Ô4€Mð.ð .ð .ðð ð ð
6ð 6ð 6ð 6ð 6ð
Gð Gð Gð$ð $ð $ð($ð ($ð ($ðTJð Jð Jð Jð2ð 2ð 2ð 2ð 2ð 2ð 2r5   rÒ  Únorminvgaussc                   ób   ‡ — e Zd ZdZej        Zd„ Zd„ Zd„ Z	d„ Z
d„ Zd„ Zd„ Zd	„ Zdˆ fd„	Zˆ xZS )Úinvweibull_genuˆ  An inverted Weibull continuous random variable.

    This distribution is also known as the FrÃ©chet distribution or the
    type II extreme value distribution.

    %(before_notes)s

    Notes
    -----
    The probability density function for `invweibull` is:

    .. math::

        f(x, c) = c x^{-c-1} \exp(-x^{-c})

    for :math:`x > 0`, :math:`c > 0`.

    `invweibull` takes ``c`` as a shape parameter for :math:`c`.

    %(after_notes)s

    References
    ----------
    F.R.S. de Gusmao, E.M.M Ortega and G.M. Cordeiro, "The generalized inverse
    Weibull distribution", Stat. Papers, vol. 52, pp. 591-619, 2011.

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r  re   rg   s    r3   rh   zinvweibull_gen._shape_info;  r  r5   c                 óš   — t          j        || dz
  ¦  «        }t          j        || ¦  «        }t          j        | ¦  «        }||z  |z  S r  ©rM   r¾  r´   )rB   rn   r  Úxc1Úxc2s        r3   ro   zinvweibull_gen._pdf>  sG   € åŒh�q˜1˜"˜s™(Ñ#Ô#ˆÝŒh�q˜1˜"‰oŒoˆÝŒf�c�T‰lŒlˆØ�3‰w˜‰}Ðr5   c                 óX   — t          j        || ¦  «        }t          j        | ¦  «        S rK   rø  )rB   rn   r  rù  s       r3   rr   zinvweibull_gen._cdfE  s#   € ÝŒh�q˜1˜"‰oŒoˆÝŒv�s�d‰|Œ|Ðr5   c                 ó6   — t          j        || z   ¦  «         S rK   )rM   r  r
  s      r3   rv   zinvweibull_gen._sfI  s   € Ý”˜!˜a˜R™%˜Ñ Ô Ð Ð r5   c                 óX   — t          j        t          j        |¦  «         d|z  ¦  «        S r?  )rM   r¾  rí   r  s      r3   r{   zinvweibull_gen._ppfL  s"   € ÝŒx�œ ™œ˜
 D¨¡FÑ+Ô+Ð+r5   c                 ó:   — t          j        | ¦  «         d|z  z  S ©Nr¼  r9  rŽ  s      r3   r~   zinvweibull_gen._isfO  s   € Ý”˜1˜"‘”�  A¡Ñ&Ð&r5   c                 ó6   — t          j        d||z  z
  ¦  «        S r[   r-  r{  s      r3   rÿ   zinvweibull_gen._munpR  s   € ÝŒx˜˜A ™E™	Ñ"Ô"Ð"r5   c                 óV   — dt           z   t           |z  z   t          j        |¦  «        z
  S r[   r  r}  s     r3   rï   zinvweibull_gen._entropyU  s"   € Ø•‰x�& 1™*Ñ$¥r¤v¨a¡y¤yÑ0Ð0r5   Nc                 óV   •— |€dn|}t          ¦   «                              ||¬¦  «        S )N)r³   rJ  r  )rB   rC   rD   r“  s      €r3   r’  zinvweibull_gen._fitstartX  s-   ø€ à˜ˆvˆv¨4ˆÝ‰wŒw× Ò  ¨DÐ Ñ1Ô1Ð1r5   rK   )r€   r�   r‚   rƒ   r   r  r  rh   ro   rr   rv   r{   r~   rÿ   rï   r’  rÎ  rÏ  s   @r3   rõ  rõ    sÌ   ø€ € € € € ðð ð: "Ô4€MðEð Eð Eðð ð ðð ð ð!ð !ð !ð,ð ,ð ,ð'ð 'ð 'ð#ð #ð #ð1ð 1ð 1ð2ð 2ð 2ð 2ð 2ð 2ð 2ð 2ð 2ð 2r5   rõ  Ú
invweibullc                   ó8   — e Zd ZdZd„ Zd„ Zd	d„Zd„ Zd„ Zd„ Z	dS )
Újf_skew_t_gena€  Jones and Faddy skew-t distribution.

    %(before_notes)s

    Notes
    -----
    The probability density function for `jf_skew_t` is:

    .. math::

        f(x; a, b) = C_{a,b}^{-1}
                    \left(1+\frac{x}{\left(a+b+x^2\right)^{1/2}}\right)^{a+1/2}
                    \left(1-\frac{x}{\left(a+b+x^2\right)^{1/2}}\right)^{b+1/2}

    for real numbers :math:`a>0` and :math:`b>0`, where
    :math:`C_{a,b} = 2^{a+b-1}B(a,b)(a+b)^{1/2}`, and :math:`B` denotes the
    beta function (`scipy.special.beta`).

    When :math:`a<b`, the distribution is negatively skewed, and when
    :math:`a>b`, the distribution is positively skewed. If :math:`a=b`, then
    we recover the `t` distribution with :math:`2a` degrees of freedom.

    `jf_skew_t` takes :math:`a` and :math:`b` as shape parameters.

    %(after_notes)s

    References
    ----------
    .. [1] M.C. Jones and M.J. Faddy. "A skew extension of the t distribution,
           with applications" *Journal of the Royal Statistical Society*.
           Series B (Statistical Methodology) 65, no. 1 (2003): 159-174.
           :doi:`10.1111/1467-9868.00378`

    %(example)s

    c                 ó‚   — t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }||gS rd  re   re  s      r3   rh   zjf_skew_t_gen._shape_info†  rh  r5   c                 ó(  — d||z   dz
  z  t          j        ||¦  «        z  t          j        ||z   ¦  «        z  }d|t          j        ||z   |dz  z   ¦  «        z  z   |dz   z  }d|t          j        ||z   |dz  z   ¦  «        z  z
  |dz   z  }||z  |z  S ©NrR   r   r‘   )rt   rk  rM   rü   )rB   rn   rˆ   r‰   r  r·  r¸  s          r3   ro   zjf_skew_t_gen._pdf‹  sž   € Ø�!�a‘%˜!‘)Ñ�rœw q¨!™}œ}Ñ,­r¬w°q¸1±u©~¬~Ñ=ˆØ�!•b”g˜a !™e a¨1¡f™nÑ-Ô-Ñ-Ñ-°1°s±7Ñ;ˆØ�!•b”g˜a !™e a¨1¡f™nÑ-Ô-Ñ-Ñ-°1°s±7Ñ;ˆØ�B‰w˜‰{Ðr5   Nc                 ó´   — |                      |||¦  «        }d|z  dz
  t          j        ||z   ¦  «        z  }dt          j        |d|z
  z  ¦  «        z  }||z  S râ  )rk  rM   rü   )rB   rˆ   r‰   rÔ   rÕ   r·  r¸  Úd3s           r3   rÖ   zjf_skew_t_gen._rvs‘  s\   € Ø×Ò˜q ! TÑ*Ô*ˆØ�"‰f�q‰j�BœG A¨¡E™NœNÑ*ˆØ•”˜˜q 2™v™Ñ'Ô'Ñ'ˆØ�B‰wˆr5   c                 óz   — d|t          j        ||z   |dz  z   ¦  «        z  z   dz  }t          j        |||¦  «        S ©Nr   rR   r‘   )rM   rü   rt   ry  )rB   rn   rˆ   r‰   ri  s        r3   rr   zjf_skew_t_gen._cdf—  s@   € Ø�•R”W˜Q ™U Q¨!¡V™^Ñ,Ô,Ñ,Ñ,°Ñ3ˆÝŒz˜!˜Q Ñ"Ô"Ð"r5   c                 ó¾   — t                                |||¦  «        }d|z  dz
  t          j        ||z   ¦  «        z  }dt          j        |d|z
  z  ¦  «        z  }||z  S râ  )rk  re  rM   rü   )rB   rz   rˆ   r‰   r·  r¸  r
  s          r3   r{   zjf_skew_t_gen._ppf›  sZ   € Ý�XŠX�a˜˜AÑÔˆØ�"‰f�q‰j�BœG A¨¡E™NœNÑ*ˆØ•”˜˜q 2™v™Ñ'Ô'Ñ'ˆØ�B‰wˆr5   c                 ó¸   — d„ }|d|z  k    |d|z  k    z  |dk    z  }t          ||||ft          j        |t          j        g¬¦  «        t          j        ¦  «        S )z­Returns the n-th moment(s) where all the following hold:

        - n >= 0
        - a > n / 2
        - b > n / 2

        The result is np.nan in all other cases.
        c                 ón  — ||z   d| z  z  }d| z  t          j        ||¦  «        z  }t          j        | dz   ¦  «        }t          j        |dz  dk    dd¦  «        }t          j        |d| z  z   |z
  |d| z  z
  |z   ¦  «        }t          j        | |¦  «        |z  |z  }||z  |                     ¦   «         z  S )zgComputes E[T^(n_k)] where T is skew-t distributed with
            parameters a_k and b_k.
            r‘   rR   r   r   r¼  )rt   rk  rM   rM  rO  r„  r¢  )	Ún_kÚa_kÚb_kr
  rÏ  ÚindicesrC  rÌ  Ú	sum_termss	            r3   Ú
nth_momentz'jf_skew_t_gen._munp.<locals>.nth_momentª  s»   € ð ˜‘9 #¨¡)Ñ,ˆCØ˜‘H�rœw s¨CÑ0Ô0Ñ0ˆEå”i  a¡Ñ(Ô(ˆGÝ”(˜7 Q™;¨š?¨B°Ñ2Ô2ˆCÝ”˜˜c C™i™¨'Ñ1°3¸¸s¹±?ÀWÑ3LÑMÔMˆAÝœ  WÑ-Ô-°Ñ3°aÑ7ˆIà˜‘; §¢¡¤Ñ0Ð0r5   r‘   r   rR  ©r   rM   rL  rV  r  )rB   r_   rˆ   r‰   r  Únth_moment_valids         r3   rÿ   zjf_skew_t_gen._munp¡  sp   € ð	1ð 	1ð 	1ð   a¡šK¨A°°a±ªKÑ8¸AÀºFÑCÐÝØØ��1ˆIÝŒL˜­R¬Z¨LÐ9Ñ9Ô9ÝŒFñ	
ô 
ð 	
r5   r   )
r€   r�   r‚   rƒ   rh   ro   rÖ   rr   r{   rÿ   r„   r5   r3   r  r  a  s~   € € € € € ð#ð #ðHð ð ð
ð ð ðð ð ð ð#ð #ð #ðð ð ð
ð 
ð 
ð 
ð 
r5   r  Ú	jf_skew_tc                   óJ   — e Zd ZdZej        Zd„ Zd„ Zd„ Z	d„ Z
d„ Zd„ Zd„ Zd	S )
Újohnsonsb_gena!  A Johnson SB continuous random variable.

    %(before_notes)s

    See Also
    --------
    johnsonsu

    Notes
    -----
    The probability density function for `johnsonsb` is:

    .. math::

        f(x, a, b) = \frac{b}{x(1-x)}  \phi(a + b \log \frac{x}{1-x} )

    where :math:`x`, :math:`a`, and :math:`b` are real scalars; :math:`b > 0`
    and :math:`x \in [0,1]`.  :math:`\phi` is the pdf of the normal
    distribution.

    `johnsonsb` takes :math:`a` and :math:`b` as shape parameters.

    %(after_notes)s

    %(example)s

    c                 ó   — |dk    ||k    z  S r®  r„   rÕ  s      r3   r`   zjohnsonsb_gen._argcheckâ  r  r5   c                 ó˜   — t          ddt          j         t          j        fd¦  «        }t          dddt          j        fd¦  «        }||gS ©Nrˆ   Fr  r‰   r   re   re  s      r3   rh   zjohnsonsb_gen._shape_infoå  rx  r5   c                 ór   — t          ||t          j        |¦  «        z  z   ¦  «        }|dz  |d|z
  z  z  |z  S r)  )r·   rt   rø  )rB   rn   rˆ   r‰   Útrms        r3   ro   zjohnsonsb_gen._pdfê  s;   € å˜˜A�bœh q™kœk™MÑ)Ñ*Ô*ˆØ�‰u�a˜˜1™‘g‰˜sÑ"Ð"r5   c                 óP   — t          ||t          j        |¦  «        z  z   ¦  «        S rK   )r½   rt   rø  rq  s       r3   rr   zjohnsonsb_gen._cdfï  s!   € Ý˜˜Q�rœx¨™{œ{™]Ñ*Ñ+Ô+Ð+r5   c                 óV   — t          j        d|z  t          |¦  «        |z
  z  ¦  «        S r  )rt   rô  rÄ   r€  s       r3   r{   zjohnsonsb_gen._ppfò  ó&   € ÝŒx˜˜a™¥9¨Q¡<¤<°!Ñ#3Ñ4Ñ5Ô5Ð5r5   c                 óP   — t          ||t          j        |¦  «        z  z   ¦  «        S rK   )rÇ   rt   rø  rq  s       r3   rv   zjohnsonsb_gen._sfõ  s!   € Ý˜˜A�bœh q™kœk™MÑ)Ñ*Ô*Ð*r5   c                 óV   — t          j        d|z  t          |¦  «        |z
  z  ¦  «        S r  )rt   rô  rÍ   r€  s       r3   r~   zjohnsonsb_gen._isfø  r"  r5   N)r€   r�   r‚   rƒ   r   r  r  r`   rh   ro   rr   r{   rv   r~   r„   r5   r3   r  r  Ä  s‘   € € € € € ðð ð6 "Ô4€Mð"ð "ð "ðð ð ð
#ð #ð #ð
,ð ,ð ,ð6ð 6ð 6ð+ð +ð +ð6ð 6ð 6ð 6ð 6r5   r  Ú	johnsonsbc                   óD   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
dd
„ZdS )Újohnsonsu_gena-  A Johnson SU continuous random variable.

    %(before_notes)s

    See Also
    --------
    johnsonsb

    Notes
    -----
    The probability density function for `johnsonsu` is:

    .. math::

        f(x, a, b) = \frac{b}{\sqrt{x^2 + 1}}
                     \phi(a + b \log(x + \sqrt{x^2 + 1}))

    where :math:`x`, :math:`a`, and :math:`b` are real scalars; :math:`b > 0`.
    :math:`\phi` is the pdf of the normal distribution.

    `johnsonsu` takes :math:`a` and :math:`b` as shape parameters.

    The first four central moments are calculated according to the formulas
    in [1]_.

    %(after_notes)s

    References
    ----------
    .. [1] Taylor Enterprises. "Johnson Family of Distributions".
       https://variation.com/wp-content/distribution_analyzer_help/hs126.htm

    %(example)s

    c                 ó   — |dk    ||k    z  S r®  r„   rÕ  s      r3   r`   zjohnsonsu_gen._argcheck#  r  r5   c                 ó˜   — t          ddt          j         t          j        fd¦  «        }t          dddt          j        fd¦  «        }||gS r  re   re  s      r3   rh   zjohnsonsu_gen._shape_info&  rx  r5   c                 óš   — ||z  }t          ||t          j        |¦  «        z  z   ¦  «        }|dz  t          j        |dz   ¦  «        z  |z  S r  )r·   rM   Úarcsinhrü   )rB   rn   rˆ   r‰   r—  r  s         r3   ro   zjohnsonsu_gen._pdf+  sL   € ð ˆq‰SˆÝ˜˜A¥¤
¨1¡¤Ñ-Ñ-Ñ.Ô.ˆØ�‰u•R”W˜R ™V‘_”_Ñ$ SÑ(Ð(r5   c                 óP   — t          ||t          j        |¦  «        z  z   ¦  «        S rK   )r½   rM   r+  rq  s       r3   rr   zjohnsonsu_gen._cdf2  s"   € Ý˜˜Q¥¤¨A¡¤Ñ.Ñ.Ñ/Ô/Ð/r5   c                 óP   — t          j        t          |¦  «        |z
  |z  ¦  «        S rK   )rM   ÚsinhrÄ   r€  s       r3   r{   zjohnsonsu_gen._ppf5  ó"   € ÝŒw�	 !™œ qÑ(¨AÑ-Ñ.Ô.Ð.r5   c                 óP   — t          ||t          j        |¦  «        z  z   ¦  «        S rK   )rÇ   rM   r+  rq  s       r3   rv   zjohnsonsu_gen._sf8  s"   € Ý˜˜A¥¤
¨1¡¤Ñ-Ñ-Ñ.Ô.Ð.r5   c                 óP   — t          j        t          |¦  «        |z
  |z  ¦  «        S rK   )rM   r.  rÍ   rq  s       r3   r~   zjohnsonsu_gen._isf;  r/  r5   r  c                 ót  — d\  }}}}|dz  }t          j        |¦  «        }	||z  }
d|v r|	dz   t          j        |
¦  «        z  }d|v r5dt          j        |¦  «        z  |	t          j        d|
z  ¦  «        z  dz   z  }d|v r•|	dz  t          j        |¦  «        dz  z  }d	t          j        |
¦  «        z  }|	|	dz   z  t          j        d	|
z  ¦  «        z  }t          j        d¦  «        d|	t          j        d|
z  ¦  «        z  z   d
z  z  }| ||z   z  |z  }d|v r™d	d|	z  z   }d|	dz  z  |	dz   z  t          j        d|
z  ¦  «        z  }|	dz  t          j        d|
z  ¦  «        z  }dd	|	dz  z  z   d|	d	z  z  z   |	dz  z   }dd|	t          j        d|
z  ¦  «        z  z   dz  z  }||z   ||z  z   |z  d	z
  }||||fS )N©NNNNr°  rÊ  r‘   rÉ  rR   r   r  rƒ  r¼  r  r‚  r   rÆ  )rM   r´   r.  rt   r  r"  rü   )rB   rˆ   r‰   r  r@  rA  rB  rC  Úbn2Úexpbn2Úa_br·  r¸  r¹  rÏ  Út4s                   r3   r   zjohnsonsu_gen._stats>  sé  € ð 1‰ˆˆC��Rà�‰fˆÝ”˜‘”ˆØ�!‰eˆà�'ˆ>ˆ>Ø˜#‘+�¥¤¨¡¤Ñ,ˆBØ�'ˆ>ˆ>Ø•b”h˜s‘m”mÑ# V­B¬G°A°c±E©N¬NÑ%:¸QÑ%>Ñ?ˆCØ�'ˆ>ˆ>Ø˜‘�bœh s™mœm¨SÑ0Ñ0ˆBØ•2”7˜3‘<”<‘ˆBØ˜6 A™:Ñ&­¬°°3±©¬Ñ7ˆBÝ”G˜A‘J”J ! f­r¬w°q¸±u©~¬~Ñ&=Ñ"=ÀÑ!EÑEˆEØ�˜˜R™‘ 5Ñ(ˆBØ�'ˆ>ˆ>Ø�Q�v‘X‘ˆBØ�6˜1‘9‘ ¨¡
Ñ+­b¬g°a¸±e©n¬nÑ<ˆBØ˜‘�RœW Q s¡U™^œ^Ñ+ˆBØ�a˜ ™	‘kÑ! A f¨a¡i¡KÑ/°&¸!±)Ñ;ˆBØ�q˜6¥"¤'¨!¨C©%¡.¤.Ñ0Ñ0°1Ñ4Ñ4ˆEØ�r‘'˜B˜r™E‘/ UÑ*¨QÑ.ˆBØ�3˜˜BˆÐr5   Nr  )r€   r�   r‚   rƒ   r`   rh   ro   rr   r{   rv   r~   r   r„   r5   r3   r'  r'  ÿ  sœ   € € € € € ð"ð "ðF"ð "ð "ðð ð ð
)ð )ð )ð0ð 0ð 0ð/ð /ð /ð/ð /ð /ð/ð /ð /ðð ð ð ð ð r5   r'  Ú	johnsonsuc                   ó†   — e Zd ZdZd„ Zdd„Zd„ Zd„ Zd„ Zd„ Z	d	„ Z
d
„ Zd„ Ze eed¬¦  «        d„ ¦   «         ¦   «         ZdS )Úlaplace_gena
  A Laplace continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `laplace` is

    .. math::

        f(x) = \frac{1}{2} \exp(-|x|)

    for a real number :math:`x`.

    %(after_notes)s

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   zlaplace_gen._shape_infos  r£   r5   Nc                 ó2   — |                      dd|¬¦  «        S )Nr   r   r  )ÚlaplacerÓ   s      r3   rÖ   zlaplace_gen._rvsv  s   € Ø×#Ò# A q¨tÐ#Ñ4Ô4Ð4r5   c                 óL   — dt          j        t          |¦  «         ¦  «        z  S r  )rM   r´   r
  r¦   s     r3   ro   zlaplace_gen._pdfy  s   € à•2”6�3˜q™6œ6˜'‘?”?Ñ"Ð"r5   c           	      óð   — t          j        d¬¦  «        5  t          j        |dk    ddt          j        | ¦  «        z  z
  dt          j        |¦  «        z  ¦  «        cd d d ¦  «         S # 1 swxY w Y   d S )Nr5  rn  r   r†   r‘   )rM   r8  rO  r´   r¦   s     r3   rr   zlaplace_gen._cdf}  sÁ   € ÝŒ[˜hÐ'Ñ'Ô'ð 	Hð 	HÝ”8˜A šE 3¨­R¬V°Q°B©Z¬Z©Ñ#7¸½R¼VÀA¹Y¼Y¹ÑGÔGð	Hð 	Hð 	Hð 	Hñ 	Hô 	Hð 	Hð 	Hð 	Hð 	Hð 	Hð 	Høøøð 	Hð 	Hð 	Hð 	Hð 	Hð 	Hs   –AA+Á+A/Á2A/c                 ó.   — |                       | ¦  «        S rK   ©rr   r¦   s     r3   rv   zlaplace_gen._sf�  s   € à�yŠy˜!˜‰}Œ}Ðr5   c                 ó’   — t          j        |dk    t          j        dd|z
  z  ¦  «         t          j        d|z  ¦  «        ¦  «        S rë   ©rM   rO  rí   r­   s     r3   r{   zlaplace_gen._ppf…  s9   € ÝŒx˜˜Cš¥"¤&¨¨A¨a©C©¡/¤/Ð!1µ2´6¸!¸A¹#±;´;Ñ?Ô?Ð?r5   c                 ó.   — |                       |¦  «         S rK   rW  r­   s     r3   r~   zlaplace_gen._isfˆ  s   € à—	’	˜!‘”ˆ}Ðr5   c                 ó   — dS )N)r   rR   r   rƒ  r„   rg   s    r3   r   zlaplace_gen._statsŒ  s   € Øˆzr5   c                 ó0   — t          j        d¦  «        dz   S râ  r.  rg   s    r3   rï   zlaplace_gen._entropy�  s   € ÝŒv�a‰yŒy˜‰{Ðr5   zÒ        This function uses explicit formulas for the maximum likelihood
        estimation of the Laplace distribution parameters, so the keyword
        arguments `loc`, `scale`, and `optimizer` are ignored.

rð   c                 óØ   — t          | |||¦  «        \  }}}|€t          j        |¦  «        }|€9t          j        t          j        ||z
  ¦  «        ¦  «        t          |¦  «        z  }||fS rK   )r  rM   Úmedianr¢  r
  r¡  )rB   rC   rD   r2   ró   rô   s         r3   r@   zlaplace_gen.fit’  sp   € õ 9¸¸tØ9=¸tñEô EÑˆˆd�Fð ˆ<Ý”9˜T‘?”?ˆDàˆ>Ý”f�RœV D¨4¡KÑ0Ô0Ñ1Ô1µS¸±Y´YÑ>ˆFà�Vˆ|Ðr5   r   )r€   r�   r‚   rƒ   rh   rÖ   ro   rr   rv   r{   r~   r   rï   rH   r
   r   r@   r„   r5   r3   r:  r:  _  s÷   € € € € € ðð ð&ð ð ð5ð 5ð 5ð 5ð#ð #ð #ðHð Hð Hðð ð ð@ð @ð @ðð ð ðð ð ðð ð ð ØÐ ð 6Fð Gñ Gô Gðð ñ	Gô Gñ „_ð
ð ð r5   r:  r=  c                   óH   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ ZdS )Úlaplace_asymmetric_genuñ  An asymmetric Laplace continuous random variable.

    %(before_notes)s

    See Also
    --------
    laplace : Laplace distribution

    Notes
    -----
    The probability density function for `laplace_asymmetric` is

    .. math::

       f(x, \kappa) &= \frac{1}{\kappa+\kappa^{-1}}\exp(-x\kappa),\quad x\ge0\\
                    &= \frac{1}{\kappa+\kappa^{-1}}\exp(x/\kappa),\quad x<0\\

    for :math:`-\infty < x < \infty`, :math:`\kappa > 0`.

    `laplace_asymmetric` takes ``kappa`` as a shape parameter for
    :math:`\kappa`. For :math:`\kappa = 1`, it is identical to a
    Laplace distribution.

    %(after_notes)s

    Note that the scale parameter of some references is the reciprocal of
    SciPy's ``scale``. For example, :math:`\lambda = 1/2` in the
    parameterization of [1]_ is equivalent to ``scale = 2`` with
    `laplace_asymmetric`.

    References
    ----------
    .. [1] "Asymmetric Laplace distribution", Wikipedia
            https://en.wikipedia.org/wiki/Asymmetric_Laplace_distribution

    .. [2] Kozubowski TJ and PodgÃ³rski K. A Multivariate and
           Asymmetric Generalization of Laplace Distribution,
           Computational Statistics 15, 531--540 (2000).
           :doi:`10.1007/PL00022717`

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS )NÚkappaFr   r  re   rg   s    r3   rh   z"laplace_asymmetric_gen._shape_infoÖ  s   € Ý˜7 E¨A­r¬v¨;¸ÑGÔGÐHÐHr5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   rÛ  ©rB   rn   rL  s      r3   ro   zlaplace_asymmetric_gen._pdfÙ  s    € ÝŒv�d—l’l 1 eÑ,Ô,Ñ-Ô-Ð-r5   c                 ó€   — d|z  }|t          j        |dk    | |¦  «        z  }|t          j        ||z   ¦  «        z  }|S rK  rC  )rB   rn   rL  Úkapinvrw  s        r3   rÛ   zlaplace_asymmetric_gen._logpdfÜ  sF   € Ø�5‘ˆØ•"”(˜1 š6 E 6¨6Ñ2Ô2Ñ2ˆØ�rŒv�e˜F‘lÑ#Ô#Ñ#ˆØˆ
r5   c                 ó¾   — d|z  }||z   }t          j        |dk    dt          j        | |z  ¦  «        ||z  z  z
  t          j        ||z  ¦  «        ||z  z  ¦  «        S rK  ©rM   rO  r´   ©rB   rn   rL  rP  Ú
kappkapinvs        r3   rr   zlaplace_asymmetric_gen._cdfâ  sk   € Ø�5‘ˆØ˜6‘\ˆ
ÝŒx˜˜QšØ�BœF A 2 e¡8Ñ,Ô,¨f°ZÑ.?Ñ@Ñ@Ýœ˜q ™xÑ(Ô(¨%°
Ñ*:Ñ;ñ=ô =ð 	=r5   c           	      ó¾   — d|z  }||z   }t          j        |dk    t          j        | |z  ¦  «        ||z  z  dt          j        ||z  ¦  «        ||z  z  z
  ¦  «        S rK  rR  rS  s        r3   rv   zlaplace_asymmetric_gen._sfé  sn   € Ø�5‘ˆØ˜6‘\ˆ
ÝŒx˜˜QšÝœ ˜r %™xÑ(Ô(¨&°Ñ*;Ñ<Ø�BœF 1 V¡8Ñ,Ô,¨e°JÑ.>Ñ?Ñ?ñAô Að 	Ar5   c                 óÄ   — d|z  }||z   }t          j        |||z  k    t          j        d|z
  |z  |z  ¦  «         |z  t          j        ||z  |z  ¦  «        |z  ¦  «        S r[   rC  ©rB   rz   rL  rP  rT  s        r3   r{   zlaplace_asymmetric_gen._ppfð  sr   € Ø�5‘ˆØ˜6‘\ˆ
ÝŒx˜˜U :Ñ-Ò-Ýœ  Q¡¨
Ñ 2°5Ñ 8Ñ9Ô9Ð9¸&Ñ@Ýœ˜q ™|¨EÑ1Ñ2Ô2°5Ñ8ñ:ô :ð 	:r5   c                 óÄ   — d|z  }||z   }t          j        |||z  k    t          j        ||z  |z  ¦  «         |z  t          j        d|z
  |z  |z  ¦  «        |z  ¦  «        S r[   rC  rW  s        r3   r~   zlaplace_asymmetric_gen._isf÷  su   € Ø�5‘ˆØ˜6‘\ˆ
ÝŒx˜˜V JÑ.Ò.Ýœ  *¡¨UÑ 2Ñ3Ô3Ð3°FÑ:Ýœ  A¡ zÑ1°%Ñ7Ñ8Ô8¸Ñ>ñ@ô @ð 	@r5   c                 óT  — d|z  }||z
  }||z  ||z  z   }ddt          j        |d¦  «        z
  z  t          j        dt          j        |d¦  «        z   d¦  «        z  }ddt          j        |d¦  «        z   z  t          j        dt          j        |d¦  «        z   d¦  «        z  }||||fS )	Nr   r³   r‚  r   r¼  rE  r*  rR   r§  )rB   rL  rP  Úmnr¤  rB  rC  s          r3   r   zlaplace_asymmetric_gen._statsþ  s®   € Ø�5‘ˆØ�e‰^ˆØ�V‰m˜e E™kÑ)ˆØ�!•B”H˜U AÑ&Ô&Ñ&Ñ'­¬°µ2´8¸EÀ1Ñ3EÔ3EÑ1EÀsÑ(KÔ(KÑKˆØ�!•B”H˜U AÑ&Ô&Ñ&Ñ'­¬°µ2´8¸EÀ1Ñ3EÔ3EÑ1EÀqÑ(IÔ(IÑIˆØ�3˜˜BˆÐr5   c                 ó<   — dt          j        |d|z  z   ¦  «        z   S r[   r.  ©rB   rL  s     r3   rï   zlaplace_asymmetric_gen._entropy  s   € Ø•2”6˜%  %¡™-Ñ(Ô(Ñ(Ð(r5   Nrþ  r„   r5   r3   rJ  rJ  ª  s¯   € € € € € ð*ð *ðVIð Ið Ið.ð .ð .ðð ð ð=ð =ð =ðAð Að Að:ð :ð :ð@ð @ð @ðð ð ð)ð )ð )ð )ð )r5   rJ  Úlaplace_asymmetricc                 ó*  — t          |t          ¦  «        st          j        |¦  «        }|                     dd ¦  «        }|                     dd ¦  «        }| j        r't          | j                             d¦  «        ¦  «        nd}g }g }| j        r | j                             dd¦  «                             ¦   «         }	t          |	¦  «        D ]c\  }
}dt          |
¦  «        z   }|d|z   d|z   g}t          ||¦  «        }|                     |¦  «         |                     |¦  «         |�|||<   Œddd	d
dddh|£}t          |¦  «                             |¦  «        }|rt          d|› d�¦  «        ‚t          |¦  «        |k    rt          d¦  «        ‚d ||h|£vrt!          d¦  «        ‚t          |t          ¦  «        r|                     ¦   «         n|}t          j        |¦  «                             ¦   «         st)          d¦  «        ‚|g|¢|‘|‘R S )Nró   rô   ú,r   ú r‡  Úfix_r,   r-   r.   r/   zUnknown keyword arguments: r  zToo many positional arguments.rõ   rö   )r<   r(   rM   rø   r:   Úshapesr¡  ÚsplitrS  Ú	enumerateÚstrr   rÞ  ÚsetÚ
differencer1   rÛ  r�  rù   rú   r÷   )ÚdistrC   rD   r2   ró   rô   Ú
num_shapesÚfshape_keysÚfshapesrb  rÊ  r  ÚkeyÚnamesrB  Ú
known_keysÚunknown_keysÚ
uncensoreds                     r3   r  r    sD  € Ý�d�LÑ)Ô)ð  ÝŒz˜$ÑÔˆà�8Š8�F˜DÑ!Ô!€DØ�XŠX�h Ñ%Ô%€Fà04´ÐB•�T”[×&Ò& sÑ+Ô+Ñ,Ô,Ð,À€JØ€KØ€Gð
 „{ð 	 Ø”×$Ò$ S¨#Ñ.Ô.×4Ò4Ñ6Ô6ˆÝ˜fÑ%Ô%ð 	 ð 	 ‰DˆAˆqØ�˜A™œ‘,ˆCØ˜# ™' 6¨A¡:Ð.ˆEÝ& t¨UÑ3Ô3ˆCØ×Ò˜sÑ#Ô#Ð#Ø�NŠN˜3ÑÔÐØˆØ��S‘	øð ˜ +¨xØ˜(ð2Ø%0ð2€Jå�t‘9”9×'Ò'¨
Ñ3Ô3€LØð GÝÐE°lÐEÐEÐEÑFÔFÐFå
ˆ4�y„y�:ÒÐÝÐ8Ñ9Ô9Ð9à�D˜&Ð+ 7Ð+Ð+Ð+õ ð 'ñ (ô (ð 	(õ &0°µlÑ%CÔ%CÐM�—’Ñ!Ô!Ð!È€JÝŒ;�zÑ"Ô"×&Ò&Ñ(Ô(ð AÝÐ?Ñ@Ô@Ð@àÐ)�7Ð)˜DÐ) &Ð)Ð)Ð)r5   c                   óJ   — e Zd ZdZej        Zd„ Zd„ Zd„ Z	d„ Z
d„ Zd„ Zd„ Zd	S )
Úlevy_genag  A Levy continuous random variable.

    %(before_notes)s

    See Also
    --------
    levy_stable, levy_l

    Notes
    -----
    The probability density function for `levy` is:

    .. math::

        f(x) = \frac{1}{\sqrt{2\pi x^3}} \exp\left(-\frac{1}{2x}\right)

    for :math:`x > 0`.

    This is the same as the Levy-stable distribution with :math:`a=1/2` and
    :math:`b=1`.

    %(after_notes)s

    Examples
    --------
    >>> import numpy as np
    >>> from scipy.stats import levy
    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots(1, 1)

    Calculate the first four moments:

    >>> mean, var, skew, kurt = levy.stats(moments='mvsk')

    Display the probability density function (``pdf``):

    >>> # `levy` is very heavy-tailed.
    >>> # To show a nice plot, let's cut off the upper 40 percent.
    >>> a, b = levy.ppf(0), levy.ppf(0.6)
    >>> x = np.linspace(a, b, 100)
    >>> ax.plot(x, levy.pdf(x),
    ...        'r-', lw=5, alpha=0.6, label='levy pdf')

    Alternatively, the distribution object can be called (as a function)
    to fix the shape, location and scale parameters. This returns a "frozen"
    RV object holding the given parameters fixed.

    Freeze the distribution and display the frozen ``pdf``:

    >>> rv = levy()
    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

    Check accuracy of ``cdf`` and ``ppf``:

    >>> vals = levy.ppf([0.001, 0.5, 0.999])
    >>> np.allclose([0.001, 0.5, 0.999], levy.cdf(vals))
    True

    Generate random numbers:

    >>> r = levy.rvs(size=1000)

    And compare the histogram:

    >>> # manual binning to ignore the tail
    >>> bins = np.concatenate((np.linspace(a, b, 20), [np.max(r)]))
    >>> ax.hist(r, bins=bins, density=True, histtype='stepfilled', alpha=0.2)
    >>> ax.set_xlim([x[0], x[-1]])
    >>> ax.legend(loc='best', frameon=False)
    >>> plt.show()

    c                 ó   — g S rK   r„   rg   s    r3   rh   zlevy_gen._shape_info‰  r£   r5   c                 óŒ   — dt          j        dt           j        z  |z  ¦  «        z  |z  t          j        dd|z  z  ¦  «        z  S ©Nr   rR   r¼  r  r¦   s     r3   ro   zlevy_gen._pdfŒ  s=   € à•2”7˜1�RœU™7 1™9Ñ%Ô%Ñ%¨Ñ)­B¬F°2°q¸±s±8Ñ,<Ô,<Ñ<Ð<r5   c                 óT   — t          j        t          j        d|z  ¦  «        ¦  «        S r  )rt   ÚerfcrM   rü   r¦   s     r3   rr   zlevy_gen._cdf�  s    € åŒw•r”w˜s Q™wÑ'Ô'Ñ(Ô(Ð(r5   c                 óT   — t          j        t          j        d|z  ¦  «        ¦  «        S r  r  r¦   s     r3   rv   zlevy_gen._sf”  s    € ÝŒv•b”g˜c A™gÑ&Ô&Ñ'Ô'Ð'r5   c                 ó6   — t          |dz  ¦  «        }d||z  z  S ©NrR   r†   rç   ©rB   rz   rB  s      r3   r{   zlevy_gen._ppf—  s    € å˜˜!™‰nŒnˆØ�c˜C‘iÑ Ð r5   c                 ó<   — ddt          j        |¦  «        dz  z  z  S r-  )rt   Úerfinvrø  s     r3   r~   zlevy_gen._isfœ  s   € Ø�!•B”I˜a‘L”L !‘OÑ#Ñ$Ð$r5   c                 ó^   — t           j        t           j        t           j        t           j        fS rK   r  rg   s    r3   r   zlevy_gen._statsŸ  r‘  r5   N©r€   r�   r‚   rƒ   r   r  r  rh   ro   rr   rv   r{   r~   r   r„   r5   r3   rr  rr  >  s”   € € € € € ðGð GðP "Ô4€Mðð ð ð=ð =ð =ð)ð )ð )ð(ð (ð (ð!ð !ð !ð
%ð %ð %ð.ð .ð .ð .ð .r5   rr  Úlevyc                   óJ   — e Zd ZdZej        Zd„ Zd„ Zd„ Z	d„ Z
d„ Zd„ Zd„ Zd	S )
Ú
levy_l_gena“  A left-skewed Levy continuous random variable.

    %(before_notes)s

    See Also
    --------
    levy, levy_stable

    Notes
    -----
    The probability density function for `levy_l` is:

    .. math::
        f(x) = \frac{1}{|x| \sqrt{2\pi |x|}} \exp{ \left(-\frac{1}{2|x|} \right)}

    for :math:`x < 0`.

    This is the same as the Levy-stable distribution with :math:`a=1/2` and
    :math:`b=-1`.

    %(after_notes)s

    Examples
    --------
    >>> import numpy as np
    >>> from scipy.stats import levy_l
    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots(1, 1)

    Calculate the first four moments:

    >>> mean, var, skew, kurt = levy_l.stats(moments='mvsk')

    Display the probability density function (``pdf``):

    >>> # `levy_l` is very heavy-tailed.
    >>> # To show a nice plot, let's cut off the lower 40 percent.
    >>> a, b = levy_l.ppf(0.4), levy_l.ppf(1)
    >>> x = np.linspace(a, b, 100)
    >>> ax.plot(x, levy_l.pdf(x),
    ...        'r-', lw=5, alpha=0.6, label='levy_l pdf')

    Alternatively, the distribution object can be called (as a function)
    to fix the shape, location and scale parameters. This returns a "frozen"
    RV object holding the given parameters fixed.

    Freeze the distribution and display the frozen ``pdf``:

    >>> rv = levy_l()
    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

    Check accuracy of ``cdf`` and ``ppf``:

    >>> vals = levy_l.ppf([0.001, 0.5, 0.999])
    >>> np.allclose([0.001, 0.5, 0.999], levy_l.cdf(vals))
    True

    Generate random numbers:

    >>> r = levy_l.rvs(size=1000)

    And compare the histogram:

    >>> # manual binning to ignore the tail
    >>> bins = np.concatenate(([np.min(r)], np.linspace(a, b, 20)))
    >>> ax.hist(r, bins=bins, density=True, histtype='stepfilled', alpha=0.2)
    >>> ax.set_xlim([x[0], x[-1]])
    >>> ax.legend(loc='best', frameon=False)
    >>> plt.show()

    c                 ó   — g S rK   r„   rg   s    r3   rh   zlevy_l_gen._shape_infoð  r£   r5   c                 óª   — t          |¦  «        }dt          j        dt          j        z  |z  ¦  «        z  |z  t          j        dd|z  z  ¦  «        z  S ru  )r
  rM   rü   rî   r´   ©rB   rn   r  s      r3   ro   zlevy_l_gen._pdfó  sH   € å�‰VŒVˆØ•”˜�2œ5™ ™Ñ$Ô$Ñ$ RÑ'­¬¨r°1°R±4©yÑ(9Ô(9Ñ9Ð9r5   c                 ót   — t          |¦  «        }dt          dt          j        |¦  «        z  ¦  «        z  dz
  S râ  )r
  r½   rM   rü   r…  s      r3   rr   zlevy_l_gen._cdfø  s1   € Ý�‰VŒVˆØ•9˜Q¥¤¨¡¤™_Ñ-Ô-Ñ-°Ñ1Ð1r5   c                 ón   — t          |¦  «        }dt          dt          j        |¦  «        z  ¦  «        z  S râ  )r
  rÇ   rM   rü   r…  s      r3   rv   zlevy_l_gen._sfü  s,   € Ý�‰VŒVˆØ•8˜A¥¤¨¡¤™OÑ,Ô,Ñ,Ð,r5   c                 ó<   — t          |dz   dz  ¦  «        }d||z  z  S )Nr†   rR   r<  rÌ   r{  s      r3   r{   zlevy_l_gen._ppf   s&   € Ý˜˜S™ A™Ñ&Ô&ˆØ�s˜S‘yÑ!Ð!r5   c                 ó2   — dt          |dz  ¦  «        dz  z  S )Nr¼  rR   rç   rø  s     r3   r~   zlevy_l_gen._isf  s   € Ø•)˜A˜a™C‘.”. !Ñ#Ñ#Ð#r5   c                 ó^   — t           j        t           j        t           j        t           j        fS rK   r  rg   s    r3   r   zlevy_l_gen._stats  r‘  r5   Nr  r„   r5   r3   r‚  r‚  ¦  s”   € € € € € ðFð FðN "Ô4€Mðð ð ð:ð :ð :ð
2ð 2ð 2ð-ð -ð -ð"ð "ð "ð$ð $ð $ð.ð .ð .ð .ð .r5   r‚  Úlevy_lc                   óž   ‡ — e Zd ZdZd„ Zdd„Zd„ Zd„ Zd„ Zd„ Z	d	„ Z
d
„ Zd„ Zd„ Zd„ Zd„ Ze ee¦  «        ˆ fd„¦   «         ¦   «         Zˆ xZS )Úlogistic_genaã  A logistic (or Sech-squared) continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `logistic` is:

    .. math::

        f(x) = \frac{\exp(-x)}
                    {(1+\exp(-x))^2}

    `logistic` is a special case of `genlogistic` with ``c=1``.

    Remark that the survival function (``logistic.sf``) is equal to the
    Fermi-Dirac distribution describing fermionic statistics.

    %(after_notes)s

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   zlogistic_gen._shape_info&  r£   r5   Nc                 ó.   — |                      |¬¦  «        S r  )ÚlogisticrÓ   s      r3   rÖ   zlogistic_gen._rvs)  s   € Ø×$Ò$¨$Ð$Ñ/Ô/Ð/r5   c                 óP   — t          j        |                      |¦  «        ¦  «        S rK   rÛ  r¦   s     r3   ro   zlogistic_gen._pdf,  rž  r5   c                 ó„   — t          j        |¦  «         }|dt          j        t          j        |¦  «        ¦  «        z  z
  S r;  )rM   r
  rt   r£  r´   )rB   rn   ri  s      r3   rÛ   zlogistic_gen._logpdf0  s3   € ÝŒV�A‰YŒYˆJˆØ�2�œ¥¤¨¡¤Ñ+Ô+Ñ+Ñ+Ð+r5   c                 ó*   — t          j        |¦  «        S rK   ró  r¦   s     r3   rr   zlogistic_gen._cdf4  ó   € ÝŒx˜‰{Œ{Ðr5   c                 ó*   — t          j        |¦  «        S rK   ©rt   Ú	log_expitr¦   s     r3   rà   zlogistic_gen._logcdf7  s   € ÝŒ|˜A‰ŒÐr5   c                 ó*   — t          j        |¦  «        S rK   r÷  r­   s     r3   r{   zlogistic_gen._ppf:  r”  r5   c                 ó,   — t          j        | ¦  «        S rK   ró  r¦   s     r3   rv   zlogistic_gen._sf=  s   € ÝŒx˜˜‰|Œ|Ðr5   c                 ó,   — t          j        | ¦  «        S rK   r–  r¦   s     r3   rä   zlogistic_gen._logsf@  s   € ÝŒ|˜Q˜BÑÔÐr5   c                 ó,   — t          j        |¦  «         S rK   r÷  r­   s     r3   r~   zlogistic_gen._isfC  s   € Ý”˜‘”ˆ|Ðr5   c                 óB   — dt           j        t           j        z  dz  ddfS )Nr   rD  g333333ó?r+  rg   s    r3   r   zlogistic_gen._statsF  s   € Ø•"”%�œ‘+˜c‘/ 1 gÐ-Ð-r5   c                 ó   — dS r;  r„   rg   s    r3   rï   zlogistic_gen._entropyI  s   € àˆsr5   c                 óÈ  •‡‡
‡‡— |                      dd¦  «        r t          ¦   «         j        ‰g|¢R i |¤ŽS t          | ‰||¦  «        \  Š}}t	          ‰¦  «        Š|                      ‰¦  «        \  }}|                     d|¦  «        |                     d|¦  «        }}|fˆˆfd„	Š
|fˆˆfd„	Šˆ
ˆfd„}|�(|€&t          j        ‰
|f¦  «        }	|	j	        d         }|}nK|�(|€&t          j        ‰|f¦  «        }	|	j	        d         }|}n!t          j        |||f¦  «        }	|	j	        \  }}t          |¦  «        }|	j        r||fn t          ¦   «         j        ‰g|¢R i |¤ŽS )	Nr  Fr,   r-   c                 ól   •— ‰| z
  |z  }t          j        t          j        |¦  «        ¦  «        ‰dz  z
  S r  )rM   r¢  rt   rô  )r,   r-   r  rC   r_   s      €€r3   Údl_dlocz!logistic_gen.fit.<locals>.dl_dloca  s2   ø€ Ø˜‘˜uÑ$ˆAÝ”6�"œ( 1™+œ+Ñ&Ô&¨¨1©Ñ,Ð,r5   c                 ór   •— ‰|z
  | z  }t          j        |t          j        |dz  ¦  «        z  ¦  «        ‰z
  S r  )rM   r¢  rî  )r-   r,   r  rC   r_   s      €€r3   Ú	dl_dscalez#logistic_gen.fit.<locals>.dl_dscalee  s6   ø€ Ø˜‘˜uÑ$ˆAÝ”6˜!�BœG A a¡C™LœL™.Ñ)Ô)¨AÑ-Ð-r5   c                 ó>   •— | \  }} ‰||¦  «         ‰||¦  «        fS rK   r„   )Úparamsr,   r-   r   r¢  s      €€r3   r[  zlogistic_gen.fit.<locals>.funci  s/   ø€ Ø‰JˆC�Ø�7˜3 Ñ&Ô&¨	¨	°%¸Ñ(=Ô(=Ð=Ð=r5   r   )r0   r>   r@   r  r¡  r’  r:   r   r  rn   r
  Úsuccess)rB   rC   rD   r2   ró   rô   r,   r-   r[  r¶  r   r¢  r_   r“  s    `        @@@€r3   r@   zlogistic_gen.fitM  sâ  øøøøø€ ð �8Š8�J Ñ&Ô&ð 	4Ø•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3å8¸¸tØ9=¸tñEô EÑˆˆd�Få�‰IŒIˆð —^’^ DÑ)Ô)‰
ˆˆUà—X’X˜e SÑ)Ô)¨4¯8ª8°G¸UÑ+CÔ+CˆUˆð  &ð 	-ð 	-ð 	-ð 	-ð 	-ð 	-ð 	-ð "&ð 	.ð 	.ð 	.ð 	.ð 	.ð 	.ð 	.ð	>ð 	>ð 	>ð 	>ð 	>ð 	>ð Ð $ ,Ý”- ¨#¨Ñ0Ô0ˆCØ”%˜”(ˆCØˆEˆEØÐ & .Ý”- 	¨E¨8Ñ4Ô4ˆCØ”E˜!”HˆEØˆCˆCå”-  s¨E lÑ3Ô3ˆCØœ‰JˆC�õ �E‘
”
ˆØ #¤ð 6��e��Ø •U‘W”W”[ Ð5¨Ð5Ð5Ð5°Ð5Ð5ð	7r5   r   )r€   r�   r‚   rƒ   rh   rÖ   ro   rÛ   rr   rà   r{   rv   rä   r~   r   rï   rH   r   r   r@   rÎ  rÏ  s   @r3   r�  r�    s  ø€ € € € € ðð ð.ð ð ð0ð 0ð 0ð 0ð'ð 'ð 'ð,ð ,ð ,ðð ð ðð ð ðð ð ðð ð ð ð  ð  ðð ð ð.ð .ð .ðð ð ð ØÐ˜MÑ*Ô*ð07ð 07ð 07ð 07ñ +Ô*ñ „_ð07ð 07ð 07ð 07ð 07r5   r�  r�  c                   óP   — e Zd ZdZd„ Zdd„Zd„ Zd„ Zd„ Zd„ Z	d	„ Z
d
„ Zd„ Zd„ ZdS )Úloggamma_gena½  A log gamma continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `loggamma` is:

    .. math::

        f(x, c) = \frac{\exp(c x - \exp(x))}
                       {\Gamma(c)}

    for all :math:`x, c > 0`. Here, :math:`\Gamma` is the
    gamma function (`scipy.special.gamma`).

    `loggamma` takes ``c`` as a shape parameter for :math:`c`.

    %(after_notes)s

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r  re   rg   s    r3   rh   zloggamma_gen._shape_infož  r  r5   Nc                 ó²   — t          j        |                     |dz   |¬¦  «        ¦  «        t          j        |                     |¬¦  «        ¦  «        |z  z   S )Nr   r  )rM   rí   rÖ  r  rµ  s       r3   rÖ   zloggamma_gen._rvs¡  sU   € õ ”�|×)Ò)¨!¨a©%°dÐ)Ñ;Ô;Ñ<Ô<Ý”&˜×-Ò-°4Ð-Ñ8Ô8Ñ9Ô9¸!Ñ;ñ<ð 	=r5   c                 ó„   — t          j        ||z  t          j        |¦  «        z
  t          j        |¦  «        z
  ¦  «        S rK   ©rM   r´   rt   rÃ  r
  s      r3   ro   zloggamma_gen._pdf¯  s/   € åŒv�a˜‘c�"œ& ™)œ)‘m¥B¤J¨q¡M¤MÑ1Ñ2Ô2Ð2r5   c                 ó`   — ||z  t          j        |¦  «        z
  t          j        |¦  «        z
  S rK   r«  r
  s      r3   rÛ   zloggamma_gen._logpdf³  s%   € Ø�‰s•R”V˜A‘Y”Y‰¥¤¨A¡¤Ñ.Ð.r5   c                 óB   — t          |t          k     ||fd„ d„ ¬¦  «        S )Nc                 ó`   — t          j        || z  t          j        |dz   ¦  «        z
  ¦  «        S r[   r«  rn  s     r3   rå  z#loggamma_gen._cdf.<locals>.<lambda>Æ  s%   € ¥r¤v¨a°©cµB´J¸qÀ¹s±O´OÑ.CÑ'DÔ'D€ r5   c                 óP   — t          j        |t          j        | ¦  «        ¦  «        S rK   )rt   r¯  rM   r´   rn  s     r3   rå  z#loggamma_gen._cdf.<locals>.<lambda>Ç  s   € ­"¬+°a½¼À¹¼Ñ*CÔ*C€ r5   rè  ©r   r"   r
  s      r3   rr   zloggamma_gen._cdf¶  s7   € õ ˜!�hš,¨¨A¨ØDÐDØCÐCðEñ Eô Eð 	Er5   c                 ón   — t          j        ||¦  «        }t          |t          k     |||fd„ d„ ¬¦  «        S )Nc                 ó`   — t          j        |¦  «        t          j        |dz   ¦  «        z   |z  S r[   r<  ©rÀ  rz   r  s      r3   rå  z#loggamma_gen._ppf.<locals>.<lambda>Î  s$   € ­2¬6°!©9¬9µr´zÀ!ÀAÁ#±´Ñ+FÈÑ*I€ r5   c                 ó*   — t          j        | ¦  «        S rK   r.  r³  s      r3   rå  z#loggamma_gen._ppf.<locals>.<lambda>Ï  ó   € ­R¬V°A©Y¬Y€ r5   rè  )rt   r¶  r   r!   ©rB   rz   r  rÀ  s       r3   r{   zloggamma_gen._ppfÉ  sF   € õ ŒN˜1˜aÑ Ô ˆÝ˜!�eš) a¨¨A YØIÐIØ6Ð6ð8ñ 8ô 8ð 	8r5   c                 óB   — t          |t          k     ||fd„ d„ ¬¦  «        S )Nc                 ób   — t          j        || z  t          j        |dz   ¦  «        z
  ¦  «         S r[   )rM   r  rt   rÃ  rn  s     r3   rå  z"loggamma_gen._sf.<locals>.<lambda>Ô  s(   € ­¬°°1±µr´zÀ!ÀAÁ#±´Ñ1FÑ(GÔ(GÐ'G€ r5   c                 óP   — t          j        |t          j        | ¦  «        ¦  «        S rK   )rt   r²  rM   r´   rn  s     r3   rå  z"loggamma_gen._sf.<locals>.<lambda>Õ  s   € ­"¬,°q½"¼&À¹)¼)Ñ*DÔ*D€ r5   rè  r°  r
  s      r3   rv   zloggamma_gen._sfÑ  s5   € å˜!�hš,¨¨A¨ØGÐGØDÐDðFñ Fô Fð 	Fr5   c                 ón   — t          j        ||¦  «        }t          |t          k     |||fd„ d„ ¬¦  «        S )Nc                 ób   — t          j        | ¦  «        t          j        |dz   ¦  «        z   |z  S r[   )rM   r£  rt   rÃ  r³  s      r3   rå  z#loggamma_gen._isf.<locals>.<lambda>Ü  s&   € ­2¬8°Q°B©<¬<½"¼*ÀQÀqÁS¹/¼/Ñ+IÈ1Ñ*L€ r5   c                 ó*   — t          j        | ¦  «        S rK   r.  r³  s      r3   rå  z#loggamma_gen._isf.<locals>.<lambda>Ý  rµ  r5   rè  )rt   rº  r   r!   r¶  s       r3   r~   zloggamma_gen._isf×  sF   € õ ŒO˜A˜qÑ!Ô!ˆÝ˜!�eš) a¨¨A YØLÐLØ6Ð6ð8ñ 8ô 8ð 	8r5   c                 óì   — t          j        |¦  «        }t          j        d|¦  «        }t          j        d|¦  «        t          j        |d¦  «        z  }t          j        d|¦  «        ||z  z  }||||fS )Nr   rR   r¼  rƒ  )rt   rÂ  Ú	polygammarM   r¾  )rB   r  rû   r¤  rñ  Úexcess_kurtosiss         r3   r   zloggamma_gen._statsß  sm   € õ Œz˜!‰}Œ}ˆÝŒl˜1˜aÑ Ô ˆÝ”<  1Ñ%Ô%­¬°°cÑ(:Ô(:Ñ:ˆÝœ, q¨!Ñ,Ô,°°C±Ñ8ˆØ�S˜( OÐ3Ð3r5   c                 óB   — d„ }d„ }t          |dk    |f||¬¦  «        }|S )Nc                 ód   — t          j        | ¦  «        | t          j        | ¦  «        z  z
  | z   }|S rK   )rt   rÃ  rÂ  )r  ræ  s     r3   r¬  z&loggamma_gen._entropy.<locals>.regularé  s+   € Ý”
˜1‘” ¥B¤J¨q¡M¤MÑ 1Ñ1°AÑ5ˆAØˆHr5   c                 ó¢   — dt          j        | ¦  «        z  | dz  dz  z   | dz  dz  z
  | dz  dz  z   }t                               ¦   «         |z   }|S )Nrî  r<  r‚  r±  rû  r¾  éÒ   )rM   rí   r  rï   )r  Útermræ  s      r3   r.  z)loggamma_gen._entropy.<locals>.asymptoticí  sQ   € à�œ˜q™	œ	‘> A s¡F¨1¡HÑ,¨q°#©v°b©yÑ8¸1¸c¹6À#¹:ÑEˆDÝ—’‘” $Ñ&ˆAØˆHr5   é-   r0  rê  )rB   r  r¬  r.  ræ  s        r3   rï   zloggamma_gen._entropyè  sC   € ð	ð 	ð 	ð	ð 	ð 	õ �q˜B’w  ¨¸Ð@Ñ@Ô@ˆØˆr5   r   ©r€   r�   r‚   rƒ   rh   rÖ   ro   rÛ   rr   r{   rv   r~   r   rï   r„   r5   r3   r§  r§  …  sÂ   € € € € € ðð ð0Eð Eð Eð=ð =ð =ð =ð3ð 3ð 3ð/ð /ð /ðEð Eð Eð&8ð 8ð 8ðFð Fð Fð8ð 8ð 8ð4ð 4ð 4ðð ð ð ð r5   r§  Úloggammac                   ó„   ‡ — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Ze ee¦  «        ˆ fd
„¦   «         ¦   «         Zˆ xZS )Úloglaplace_genaT  A log-Laplace continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `loglaplace` is:

    .. math::

        f(x, c) = \begin{cases}\frac{c}{2} x^{ c-1}  &\text{for } 0 < x < 1\\
                               \frac{c}{2} x^{-c-1}  &\text{for } x \ge 1
                  \end{cases}

    for :math:`c > 0`.

    `loglaplace` takes ``c`` as a shape parameter for :math:`c`.

    %(after_notes)s

    Suppose a random variable ``X`` follows the Laplace distribution with
    location ``a`` and scale ``b``.  Then ``Y = exp(X)`` follows the
    log-Laplace distribution with ``c = 1 / b`` and ``scale = exp(a)``.

    References
    ----------
    T.J. Kozubowski and K. Podgorski, "A log-Laplace growth rate model",
    The Mathematical Scientist, vol. 28, pp. 49-60, 2003.

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r  re   rg   s    r3   rh   zloglaplace_gen._shape_info  r  r5   c                 óX   — |dz  }t          j        |dk     || ¦  «        }|||dz
  z  z  S rÔ  ©rM   rO  )rB   rn   r  Úcd2s       r3   ro   zloglaplace_gen._pdf  s8   € ð �‰eˆÝŒH�Q˜’U˜A ˜rÑ"Ô"ˆØ�1�q˜‘s‘8‰|Ðr5   c                 óV   — t          j        |dk     d||z  z  dd|| z  z  z
  ¦  «        S ©Nr   r‘   rÌ  r
  s      r3   rr   zloglaplace_gen._cdf%  s0   € ÝŒx˜˜Aš˜s 1 a¡4™x¨¨3¨q°A°2©w©;©Ñ7Ô7Ð7r5   c                 óV   — t          j        |dk     dd||z  z  z
  d|| z  z  ¦  «        S rÏ  rÌ  r
  s      r3   rv   zloglaplace_gen._sf(  s0   € ÝŒx˜˜Aš˜q 3 q¨!¡t¡8™|¨S°°a°R±©[Ñ9Ô9Ð9r5   c                 ó`   — t          j        |dk     d|z  d|z  z  dd|z
  z  d|z  z  ¦  «        S ©Nr‘   r³   r†   rR   r<  rÌ  r  s      r3   r{   zloglaplace_gen._ppf+  s8   € ÝŒx˜˜Cš # a¡%¨3¨q©5Ñ!1°A°s¸1±u±IÀÀaÁÑ3HÑIÔIÐIr5   c                 ó`   — t          j        |dk    dd|z
  z  d|z  z  d|z  d|z  z  ¦  «        S rÒ  rÌ  r  s      r3   r~   zloglaplace_gen._isf.  s7   € ÝŒx˜˜Cš # s¨Q¡w¡-°3°q±5Ñ!9¸A¸a¹CÀ4ÈÁ6¹?ÑKÔKÐKr5   c                 óÈ   — t          j        d¬¦  «        5  |dz  |dz  }}t          j        ||k     |||z
  z  t           j        ¦  «        cd d d ¦  «         S # 1 swxY w Y   d S )Nr5  r6  rR   )rM   r8  rO  rf   )rB   r_   r  r¨  Ún2s        r3   rÿ   zloglaplace_gen._munp1  s©   € ÝŒ[ Ð)Ñ)Ô)ð 	=ð 	=Ø˜‘T˜1˜a™4�ˆBÝ”8˜B šG R¨2°©7¡^µR´VÑ<Ô<ð	=ð 	=ð 	=ð 	=ñ 	=ô 	=ð 	=ð 	=ð 	=ð 	=ð 	=ð 	=øøøð 	=ð 	=ð 	=ð 	=ð 	=ð 	=s   –4AÁAÁAc                 ó6   — t          j        d|z  ¦  «        dz   S r  r.  r}  s     r3   rï   zloglaplace_gen._entropy6  s   € ÝŒv�c˜!‘e‰}Œ}˜sÑ"Ð"r5   c                 óü  •— t          | |||¦  «        \  }}}}|€, t          t          | ¦  «        | ¦  «        j        |g|¢R i |¤ŽS t	          j        ||k    ¦  «        rt          d|t          j        ¬¦  «        ‚|dk    r||z
  }t                               t	          j	        |¦  «        |�t	          j	        |¦  «        nd |�d|z  nd d¬¦  «        \  }}|}	|€t	          j
        |¦  «        n|}
|€d|z  n|}||	|
fS )NÚ
loglaplacerœ  r   r   r8   )ró   rô   r/   )r  r>   r?   r@   rM   r   rH  rf   r=  rí   r´   )rB   rC   rD   r2   r  ró   rô   rˆ   r‰   r,   r-   r  r“  s               €r3   r@   zloglaplace_gen.fit9  s-  ø€ õ "=¸TÀ4Ø=AÀ4ñ"Iô "IÑˆˆb�$˜ð ˆ<Ø.•5�˜d™œ TÑ*Ô*Ô.¨tÐC°dÐCÐCÐC¸dÐCÐCÐCõ Œ6�$˜$’,ÑÔð 	GÝ˜|°4½r¼vÐFÑFÔFÐFð �1Š9ˆ9Ø˜$‘;ˆDõ �{Š{�2œ6 $™<œ<Ø28Ð2D¥¤ v¡¤ È$Ø*,¨. ! B¡$ $¸dØ"'ð ñ )ô )‰ˆˆ1ð ˆØ#˜^•”�q‘	”	�	°ˆØ�ZˆA�‰EˆE RˆØ�#�uˆ}Ðr5   )r€   r�   r‚   rƒ   rh   ro   rr   rv   r{   r~   rÿ   rï   rH   r   r   r@   rÎ  rÏ  s   @r3   rÉ  rÉ  ú  sæ   ø€ € € € € ðð ð@Eð Eð Eðð ð ð8ð 8ð 8ð:ð :ð :ðJð Jð JðLð Lð Lð=ð =ð =ð
#ð #ð #ð ØÐ˜MÑ*Ô*ðð ð ð ñ +Ô*ñ „_ðð ð ð ð r5   rÉ  rØ  c                 óJ   — t          | dk    | |fd„ t          j         ¦  «        S )Nr   c                 ó¸   — t          j        | ¦  «        dz   d|dz  z  z  t          j        || z  t          j        dt           j        z  ¦  «        z  ¦  «        z
  S r  )rM   rí   rü   rî   ©rn   r  s     r3   rå  z!_lognorm_logpdf.<locals>.<lambda>_  sM   € ¥R¤V¨A¡Y¤Y°¡\ M°Q¸¸A¹±XÑ$>Ý&(¤f¨Q°©UµR´W¸QÅÄ¹YÑ5GÔ5GÑ-GÑ&HÔ&Hñ%I€ r5   r  rÛ  s     r3   Ú_lognorm_logpdfrÜ  ]  s3   € Ý�a˜1’f˜q !˜fðJð Jå”v�gñô ð r5   c                   ó°   ‡ — e Zd ZdZej        Zd„ Zdd„Zd„ Z	d„ Z
d„ Zd„ Zd	„ Zd
„ Zd„ Zd„ Zd„ Zd„ Ze eed¬¦  «        ˆ fd„¦   «         ¦   «         Zˆ xZS )Úlognorm_gena±  A lognormal continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `lognorm` is:

    .. math::

        f(x, s) = \frac{1}{s x \sqrt{2\pi}}
                  \exp\left(-\frac{\log^2(x)}{2s^2}\right)

    for :math:`x > 0`, :math:`s > 0`.

    `lognorm` takes ``s`` as a shape parameter for :math:`s`.

    %(after_notes)s

    Suppose a normally distributed random variable ``X`` has  mean ``mu`` and
    standard deviation ``sigma``. Then ``Y = exp(X)`` is lognormally
    distributed with ``s = sigma`` and ``scale = exp(mu)``.

    %(example)s

    The logarithm of a log-normally distributed random variable is
    normally distributed:

    >>> import numpy as np
    >>> import matplotlib.pyplot as plt
    >>> from scipy import stats
    >>> fig, ax = plt.subplots(1, 1)
    >>> mu, sigma = 2, 0.5
    >>> X = stats.norm(loc=mu, scale=sigma)
    >>> Y = stats.lognorm(s=sigma, scale=np.exp(mu))
    >>> x = np.linspace(*X.interval(0.999))
    >>> y = Y.rvs(size=10000)
    >>> ax.plot(x, X.pdf(x), label='X (pdf)')
    >>> ax.hist(np.log(y), density=True, bins=x, label='log(Y) (histogram)')
    >>> ax.legend()
    >>> plt.show()

    c                 ó@   — t          dddt          j        fd¦  «        gS )Nr  Fr   r  re   rg   s    r3   rh   zlognorm_gen._shape_info’  r  r5   Nc                 óV   — t          j        ||                     |¦  «        z  ¦  «        S rK   ©rM   r´   rÒ   )rB   r  rÔ   rÕ   s       r3   rÖ   zlognorm_gen._rvs•  s%   € ÝŒv�a˜,×6Ò6°tÑ<Ô<Ñ<Ñ=Ô=Ð=r5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   rÛ  ©rB   rn   r  s      r3   ro   zlognorm_gen._pdf˜  rƒ  r5   c                 ó"   — t          ||¦  «        S rK   ©rÜ  rã  s      r3   rÛ   zlognorm_gen._logpdfœ  s   € Ý˜q !Ñ$Ô$Ð$r5   c                 óJ   — t          t          j        |¦  «        |z  ¦  «        S rK   ©r½   rM   rí   rã  s      r3   rr   zlognorm_gen._cdfŸ  s   € Ý�œ ™œ Q™Ñ'Ô'Ð'r5   c                 óJ   — t          t          j        |¦  «        |z  ¦  «        S rK   rY  rã  s      r3   rà   zlognorm_gen._logcdf¢  s   € Ý�BœF 1™IœI¨™MÑ*Ô*Ð*r5   c                 óJ   — t          j        |t          |¦  «        z  ¦  «        S rK   ©rM   r´   rÄ   ©rB   rz   r  s      r3   r{   zlognorm_gen._ppf¥  ó   € ÝŒv�a�) A™,œ,Ñ&Ñ'Ô'Ð'r5   c                 óJ   — t          t          j        |¦  «        |z  ¦  «        S rK   ©rÇ   rM   rí   rã  s      r3   rv   zlognorm_gen._sf¨  s   € Ý�œ˜q™	œ	 A™Ñ&Ô&Ð&r5   c                 óJ   — t          t          j        |¦  «        |z  ¦  «        S rK   )rÊ   rM   rí   rã  s      r3   rä   zlognorm_gen._logsf«  s   € Ý�2œ6 !™9œ9 q™=Ñ)Ô)Ð)r5   c                 óJ   — t          j        |t          |¦  «        z  ¦  «        S rK   ©rM   r´   rÍ   rë  s      r3   r~   zlognorm_gen._isf®  rì  r5   c                 óÜ   — t          j        ||z  ¦  «        }t          j        |¦  «        }||dz
  z  }t          j        |dz
  ¦  «        d|z   z  }t          j        g d¢|¦  «        }||||fS ©Nr   rR   )r   rR   rƒ  r   rÀ  )rM   r´   rü   Úpolyval)rB   r  rñ  r@  rA  rB  rC  s          r3   r   zlognorm_gen._stats±  sm   € ÝŒF�1�Q‘3‰KŒKˆÝŒW�Q‰ZŒZˆØ��1‘‰gˆÝŒW�Q�q‘S‰\Œ\˜1˜Q™3ÑˆÝŒZÐ*Ð*Ð*¨AÑ.Ô.ˆØ�3˜˜BˆÐr5   c                 ó€   — ddt          j        dt           j        z  ¦  «        z   dt          j        |¦  «        z  z   z  S ©Nr‘   r   rR   rì   )rB   r  s     r3   rï   zlognorm_gen._entropy¹  s1   € Ø�a�"œ& ¥2¤5¡™/œ/Ñ)¨Aµ´°q±	´	©MÑ9Ñ:Ð:r5   aF          When `method='MLE'` and
        the location parameter is fixed by using the `floc` argument,
        this function uses explicit formulas for the maximum likelihood
        estimation of the log-normal shape and scale parameters, so the
        `optimizer`, `loc` and `scale` keyword arguments are ignored.
        If the location is free, a likelihood maximum is found by
        setting its partial derivative wrt to location to 0, and
        solving by substituting the analytical expressions of shape
        and scale (or provided parameters).
        See, e.g., equation 3.1 in
        A. Clifford Cohen & Betty Jones Whitten (1980)
        Estimation in the Three-Parameter Lognormal Distribution,
        Journal of the American Statistical Association, 75:370, 399-404
        https://doi.org/10.2307/2287466
        

rð   c                 óP  •‡ ‡‡‡‡— |                      dd¦  «        r t          ¦   «         j        ‰g|¢R i |¤ŽS t          ‰ ‰||¦  «        }|\  ŠŠ}Št	          j        ‰¦  «        }ˆˆˆfd„Šˆˆfd„}ˆˆˆ fd„}|�€;t	          j        |¦  «        }	||	z
  }
 ||
¦  «        } ||
¦  «        }d|	z  }|dk    r||z
  }
 ||
¦  «        }|dz  }|dk    °t	          j        |
¦  «        rt	          j        |¦  «        s t          ¦   «         j        ‰g|¢R i |¤ŽS t	          j        t	          j	        |
t          j
         ¦  «        |
dz
  ¦  «        } ||¦  «        }d|
|z
  z  }t	          j        |¦  «        r¥t	          j        |¦  «        r‘t	          j        |¦  «        t	          j        |¦  «        k    rg|
|z
  } ||¦  «        }|dz  }t	          j        |¦  «        r>t	          j        |¦  «        r*t	          j        |¦  «        t	          j        |¦  «        k    °gt	          j        |¦  «        rt	          j        |¦  «        s t          ¦   «         j        ‰g|¢R i |¤ŽS t          |||
f¬	¦  «        }|j        s t          ¦   «         j        ‰g|¢R i |¤ŽS  ||j        ¦  «        }||k    r|j        n||	z
  }n$||k    rt          d
dt          j
        ¬¦  «        ‚|} ‰|¦  «        \  }}‰                      |¦  «        r|dk    s t          ¦   «         j        ‰g|¢R i |¤ŽS |||fS )Nr  Fc                 ó  •— ‰�‰€t          j        ‰| z
  ¦  «        }‰p%t          j        |                     ¦   «         ¦  «        }‰p=t          j        t          j        |t          j        |¦  «        z
  dz  ¦  «        ¦  «        }||fS r  )rM   rí   r´   rû   rü   )r,   Úlndatar-   rw  rC   rô   Úfshapes       €€€r3   Úget_shape_scalez(lognorm_gen.fit.<locals>.get_shape_scaleÕ  sw   ø€ ð ˆ~  Ýœ  s¡
Ñ+Ô+�ØÐ3�bœf V§[¢[¡]¤]Ñ3Ô3ˆEØÐK�bœg¥b¤g¨v½¼¸u¹¼Ñ/EÈÑ.IÑ&JÔ&JÑKÔKˆEØ˜%�<Ðr5   c                 ó”   •—  ‰| ¦  «        \  }}‰| z
  }t          j        dt          j        ||z  ¦  «        |dz  z  z   |z  ¦  «        S r-  ©rM   r¢  rí   )r,   rw  r-   ÚshiftedrC   rû  s       €€r3   ÚdL_dLocz lognorm_gen.fit.<locals>.dL_dLocÞ  sP   ø€ à*˜?¨3Ñ/Ô/‰LˆE�5Ø˜S‘jˆGÝ”6˜1�rœv g¨e¡mÑ4Ô4°U¸A±XÑ=Ñ=¸wÑFÑGÔGÐGr5   c                 óT   •—  ‰| ¦  «        \  }}‰                      || |f‰¦  «         S rK   )Únnlf)r,   rw  r-   rC   rû  rB   s      €€€r3   Úllzlognorm_gen.fit.<locals>.llä  s4   ø€ à*˜?¨3Ñ/Ô/‰LˆE�5Ø—I’I˜u c¨5Ð1°4Ñ8Ô8Ð8Ð8r5   rR   g�íµ ÷Æ°¾r   rà  Úlognormr…   rœ  r   )r0   r>   r@   r  rM   rK  Úspacingrù   r¢  Ú	nextafterrf   rN   r)   Ú	convergedr  rH  r`   )rB   rC   rD   r2   Ú
parametersró   rM  rÿ  r  r  rP   ÚdL_dLoc_rbrackÚ	ll_rbrackrè  rO   ÚdL_dLoc_lbrackr¶  Úll_rootr,   rw  r-   rô   rú  rû  r“  s   ``                   @@@€r3   r@   zlognorm_gen.fit¼  sÝ  øøøøøø€ ð$ �8Š8�J Ñ&Ô&ð 	4Ø•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3å0°°t¸TÀ4ÑHÔHˆ
Ø%/Ñ"ˆˆf�d˜FÝ”6˜$‘<”<ˆð	 ð 	 ð 	 ð 	 ð 	 ð 	 ð 	 ð	Hð 	Hð 	Hð 	Hð 	Hð 	Hð	9ð 	9ð 	9ð 	9ð 	9ð 	9ð 	9ð
 ‰<õ ”j Ñ*Ô*ˆGØ Ñ'ˆFð %˜W V™_œ_ˆNØ˜˜6™
œ
ˆIØ˜‘KˆEØ  EÒ)Ð)Ø! EÑ)�Ø!( ¨¡¤�Ø˜‘
�ð ! EÒ)Ð)õ
 ”;˜vÑ&Ô&ð 8­b¬k¸.Ñ.IÔ.Ið 8ð #•u‘w”w”{ 4Ð7¨$Ð7Ð7Ð7°$Ð7Ð7Ð7õ
 ”Z¥¤¨Vµb´f°WÑ =Ô =¸vÀa¹xÑHÔHˆFØ$˜W V™_œ_ˆNØ˜ &™Ñ)ˆEÝ”;˜vÑ&Ô&ð ­2¬;°~Ñ+FÔ+Fð Ý”w˜~Ñ.Ô.µ"´'¸.Ñ2IÔ2IÒIÐIØ %™�Ø!( ¨¡¤�Ø˜‘
�õ	 ”;˜vÑ&Ô&ð ­2¬;°~Ñ+FÔ+Fð Ý”w˜~Ñ.Ô.µ"´'¸.Ñ2IÔ2IÒIÐIõ ”;˜vÑ&Ô&ð 8­b¬k¸.Ñ.IÔ.Ið 8Ø"•u‘w”w”{ 4Ð7¨$Ð7Ð7Ð7°$Ð7Ð7Ð7õ ˜g°¸Ð/?Ð@Ñ@Ô@ˆCØ”=ð 8Ø"•u‘w”w”{ 4Ð7¨$Ð7Ð7Ð7°$Ð7Ð7Ð7ð
 �b˜œ‘l”lˆGØ%¨	Ò1Ð1�#”(�(°xÀÑ7GˆCˆCð �xÒÐÝ" 9°B½b¼fÐEÑEÔEÐEØˆCà&� sÑ+Ô+‰ˆˆuØ—’˜uÑ%Ô%ð 	4¨%°!ª)¨)Ø•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3Ø�c˜5Ð Ð r5   r   )r€   r�   r‚   rƒ   r   r  r  rh   rÖ   ro   rÛ   rr   rà   r{   rv   rä   r~   r   rï   rH   r	   r@   rÎ  rÏ  s   @r3   rÞ  rÞ  d  sD  ø€ € € € € ð*ð *ðV "Ô4€MðEð Eð Eð>ð >ð >ð >ð*ð *ð *ð%ð %ð %ð(ð (ð (ð+ð +ð +ð(ð (ð (ð'ð 'ð 'ð*ð *ð *ð(ð (ð (ðð ð ð;ð ;ð ;ð ØÐ˜}ð 5ð ñ ô ð Z!ð Z!ð Z!ð Z!ñ!ô ñ „_ð"Z!ð Z!ð Z!ð Z!ð Z!r5   rÞ  r  c                   ó^   — e Zd ZdZej        Zd„ Zdd„Zd„ Z	d„ Z
d„ Zd„ Zd	„ Zd
„ Zd„ Zd„ ZdS )Ú
gibrat_genaB  A Gibrat continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `gibrat` is:

    .. math::

        f(x) = \frac{1}{x \sqrt{2\pi}} \exp(-\frac{1}{2} (\log(x))^2)

    `gibrat` is a special case of `lognorm` with ``s=1``.

    %(after_notes)s

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   zgibrat_gen._shape_infoC  r£   r5   Nc                 óP   — t          j        |                     |¦  «        ¦  «        S rK   rá  rÓ   s      r3   rÖ   zgibrat_gen._rvsF  s    € ÝŒv�l×2Ò2°4Ñ8Ô8Ñ9Ô9Ð9r5   c                 óP   — t          j        |                      |¦  «        ¦  «        S rK   rÛ  r¦   s     r3   ro   zgibrat_gen._pdfI  rž  r5   c                 ó"   — t          |d¦  «        S r  rå  r¦   s     r3   rÛ   zgibrat_gen._logpdfM  s   € Ý˜q #Ñ&Ô&Ð&r5   c                 óD   — t          t          j        |¦  «        ¦  «        S rK   rç  r¦   s     r3   rr   zgibrat_gen._cdfP  s   € Ý�œ ™œÑ#Ô#Ð#r5   c                 óD   — t          j        t          |¦  «        ¦  «        S rK   rê  r­   s     r3   r{   zgibrat_gen._ppfS  ó   € ÝŒv•i ‘l”lÑ#Ô#Ð#r5   c                 óD   — t          t          j        |¦  «        ¦  «        S rK   rî  r¦   s     r3   rv   zgibrat_gen._sfV  s   € Ý�œ˜q™	œ	Ñ"Ô"Ð"r5   c                 óD   — t          j        t          |¦  «        ¦  «        S rK   rñ  rø  s     r3   r~   zgibrat_gen._isfY  r  r5   c                 óÆ   — t           j        }t          j        |¦  «        }||dz
  z  }t          j        |dz
  ¦  «        d|z   z  }t          j        g d¢|¦  «        }||||fS ró  )rM   Úerü   rô  )rB   rñ  r@  rA  rB  rC  s         r3   r   zgibrat_gen._stats\  sc   € ÝŒDˆÝŒW�Q‰ZŒZˆØ�1�q‘5‰kˆÝŒW�Q˜‘U‰^Œ^˜q 1™uÑ%ˆÝŒZÐ*Ð*Ð*¨AÑ.Ô.ˆØ�3˜˜BˆÐr5   c                 óP   — dt          j        dt           j        z  ¦  «        z  dz   S r­  rì   rg   s    r3   rï   zgibrat_gen._entropyd  s"   € Ø•R”V˜A¥¤™IÑ&Ô&Ñ&¨Ñ,Ð,r5   r   )r€   r�   r‚   rƒ   r   r  r  rh   rÖ   ro   rÛ   rr   r{   rv   r~   r   rï   r„   r5   r3   r  r  -  sÃ   € € € € € ðð ð& "Ô4€Mðð ð ð:ð :ð :ð :ð'ð 'ð 'ð'ð 'ð 'ð$ð $ð $ð$ð $ð $ð#ð #ð #ð$ð $ð $ðð ð ð-ð -ð -ð -ð -r5   r  Úgibratc                   óP   — e Zd ZdZd„ Zdd„Zd„ Zd„ Zd„ Zd„ Z	d	„ Z
d
„ Zd„ Zd„ ZdS )Úmaxwell_gena  A Maxwell continuous random variable.

    %(before_notes)s

    Notes
    -----
    A special case of a `chi` distribution,  with ``df=3``, ``loc=0.0``,
    and given ``scale = a``, where ``a`` is the parameter used in the
    Mathworld description [1]_.

    The probability density function for `maxwell` is:

    .. math::

        f(x) = \sqrt{2/\pi}x^2 \exp(-x^2/2)

    for :math:`x >= 0`.

    %(after_notes)s

    References
    ----------
    .. [1] http://mathworld.wolfram.com/MaxwellDistribution.html

    %(example)s
    c                 ó   — g S rK   r„   rg   s    r3   rh   zmaxwell_gen._shape_info†  r£   r5   Nc                 ó<   — t                                d||¬¦  «        S )NrD  rÕ  ©rË  r×  rÓ   s      r3   rÖ   zmaxwell_gen._rvs‰  s   € Ý�wŠw�s °LˆwÑAÔAÐAr5   c                 óT   — t           |z  |z  t          j        | |z  dz  ¦  «        z  S r;  )r&   rM   r´   r¦   s     r3   ro   zmaxwell_gen._pdfŒ  s+   € å˜qÑ  Ñ"¥2¤6¨1¨"¨Q©$¨s©(Ñ#3Ô#3Ñ3Ð3r5   c                 ó°   — t          j        d¬¦  «        5  t          dt          j        |¦  «        z  z   d|z  |z  z
  cd d d ¦  «         S # 1 swxY w Y   d S )Nr5  r6  rR   r‘   )rM   r8  r'   rí   r¦   s     r3   rÛ   zmaxwell_gen._logpdf�  sš   € åŒ[ Ð)Ñ)Ô)ð 	?ð 	?Ý&¨­2¬6°!©9¬9©Ñ4°s¸1±u¸Q±wÑ>ð	?ð 	?ð 	?ð 	?ñ 	?ô 	?ð 	?ð 	?ð 	?ð 	?ð 	?ð 	?øøøð 	?ð 	?ð 	?ð 	?ð 	?ð 	?s   –(AÁAÁAc                 ó8   — t          j        d||z  dz  ¦  «        S ©Nr¼  r³   r®  r¦   s     r3   rr   zmaxwell_gen._cdf•  s   € ÝŒ{˜3  !¡ C¡Ñ(Ô(Ð(r5   c                 óV   — t          j        dt          j        d|¦  «        z  ¦  «        S rÃ  rµ  r­   s     r3   r{   zmaxwell_gen._ppf˜  s#   € ÝŒw�q�œ¨¨QÑ/Ô/Ñ/Ñ0Ô0Ð0r5   c                 ó8   — t          j        d||z  dz  ¦  «        S r#  r±  r¦   s     r3   rv   zmaxwell_gen._sf›  s   € ÝŒ|˜C  1¡ S¡Ñ)Ô)Ð)r5   c                 óV   — t          j        dt          j        d|¦  «        z  ¦  «        S rÃ  r¹  r­   s     r3   r~   zmaxwell_gen._isfž  s#   € ÝŒw�q�œ¨¨aÑ0Ô0Ñ0Ñ1Ô1Ð1r5   c                 óR  — dt           j        z  dz
  }dt          j        dt           j        z  ¦  «        z  ddt           j        z  z
  t          j        d¦  «        ddt           j        z  z
  z  |dz  z  dt           j        z  t           j        z  d	t           j        z  z   d
z
  |dz  z  fS )Nrƒ  r*  rR   r³   é    r³  r¼  rÅ  é    i€  ©rM   rî   rü   ©rB   rB  s     r3   r   zmaxwell_gen._stats¡  s�   € Ø•”‰g�a‰iˆØ•"”'˜#�bœe™)Ñ$Ô$Ñ$Ø�!•B”E‘'‘	Ý”˜‘
”
˜B˜r¥"¤%™x™KÑ(¨¨c©Ñ1Ø•R”U‘�2œ5‘ 3¥r¤u¡9Ñ,¨sÑ2°c¸3±hÑ>ð@ð 	@r5   c                 ó`   — t           dt          j        dt          j        z  ¦  «        z  z   dz
  S r­  )r#   rM   rí   rî   rg   s    r3   rï   zmaxwell_gen._entropy¨  s%   € Ý˜�BœF 1¥R¤U¡7™OœOÑ+Ñ+¨CÑ/Ð/r5   r   rÆ  r„   r5   r3   r  r  k  sÀ   € € € € € ðð ð4ð ð ðBð Bð Bð Bð4ð 4ð 4ð?ð ?ð ?ð
)ð )ð )ð1ð 1ð 1ð*ð *ð *ð2ð 2ð 2ð@ð @ð @ð0ð 0ð 0ð 0ð 0r5   r  Úmaxwellc                   ó6   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	dS )	Ú
mielke_genaâ  A Mielke Beta-Kappa / Dagum continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `mielke` is:

    .. math::

        f(x, k, s) = \frac{k x^{k-1}}{(1+x^s)^{1+k/s}}

    for :math:`x > 0` and :math:`k, s > 0`. The distribution is sometimes
    called Dagum distribution ([2]_). It was already defined in [3]_, called
    a Burr Type III distribution (`burr` with parameters ``c=s`` and
    ``d=k/s``).

    `mielke` takes ``k`` and ``s`` as shape parameters.

    %(after_notes)s

    References
    ----------
    .. [1] Mielke, P.W., 1973 "Another Family of Distributions for Describing
           and Analyzing Precipitation Data." J. Appl. Meteor., 12, 275-280
    .. [2] Dagum, C., 1977 "A new model for personal income distribution."
           Economie Appliquee, 33, 327-367.
    .. [3] Burr, I. W. "Cumulative frequency functions", Annals of
           Mathematical Statistics, 13(2), pp 215-232 (1942).

    %(example)s

    c                 ó‚   — t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }||gS )Nr  Fr   r  r  re   )rB   ÚikÚi_ss      r3   rh   zmielke_gen._shape_infoÑ  ó>   € Ý˜˜U Q­¬ K°Ñ@Ô@ˆÝ˜˜e a­¬ [°.ÑAÔAˆØ�CˆyÐr5   c                 óB   — |||dz
  z  z  d||z  z   d|dz  |z  z   z  z  S r  r„   ©rB   rn   r  r  s       r3   ro   zmielke_gen._pdfÖ  s2   € Ø��Q�s‘U‘‰|˜s 1 a¡4™x¨3¨q°©u°Q©w©;Ñ7Ñ7Ð7r5   c                 ó   — t          j        d¬¦  «        5  t          j        |¦  «        t          j        |¦  «        |dz
  z  z   t          j        ||z  ¦  «        d||z  z   z  z
  cd d d ¦  «         S # 1 swxY w Y   d S )Nr5  r6  r   )rM   r8  rí   r£  r5  s       r3   rÛ   zmielke_gen._logpdfÙ  sÌ   € åŒ[ Ð)Ñ)Ô)ð 	Lð 	LÝ”6˜!‘9”9�rœv a™yœy¨!¨a©%Ñ0Ñ0µ2´8¸A¸q¹D±>´>À1ÀqÈÁsÁ7Ñ3KÑKð	Lð 	Lð 	Lð 	Lñ 	Lô 	Lð 	Lð 	Lð 	Lð 	Lð 	Lð 	Løøøð 	Lð 	Lð 	Lð 	Lð 	Lð 	Ls   –AA3Á3A7Á:A7c                 ó0   — ||z  d||z  z   |dz  |z  z  z  S r  r„   r5  s       r3   rr   zmielke_gen._cdfÞ  s&   € Ø�!‰t�s˜1˜a™4‘x 1 S¡5¨¡7Ñ+Ñ+Ð+r5   c                 ó`   — t          ||dz  |z  ¦  «        }t          |d|z
  z  d|z  ¦  «        S r  rþ  )rB   rz   r  r  Úqsks        r3   r{   zmielke_gen._ppfá  s3   € Ý�!�Q�s‘U˜1‘W‰oŒoˆÝ�3˜˜C™‘= # a¡%Ñ(Ô(Ð(r5   c                 óN   — d„ }t          ||k     |||f|t          j        ¦  «        S )Nc                 óœ   — t          j        || z   |z  ¦  «        t          j        d| |z  z
  ¦  «        z  t          j        ||z  ¦  «        z  S r[   r-  )r_   r  r  s      r3   r  z$mielke_gen._munp.<locals>.nth_momentæ  s@   € å”8˜Q˜q™S !™GÑ$Ô$¥R¤X¨a°°!±©e¡_¤_Ñ4µR´X¸aÀ¹c±]´]ÑBÐBr5   r  )rB   r_   r  r  r  s        r3   rÿ   zmielke_gen._munpå  s6   € ð	Cð 	Cð 	Cõ ˜!˜aš% ! Q¨ ¨J½¼Ñ?Ô?Ð?r5   N)
r€   r�   r‚   rƒ   rh   ro   rÛ   rr   r{   rÿ   r„   r5   r3   r/  r/  ¯  s�   € € € € € ð ð  ðBð ð ð
8ð 8ð 8ðLð Lð Lð
,ð ,ð ,ð)ð )ð )ð@ð @ð @ð @ð @r5   r/  Úmielkec                   óT   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Zd„ Zd„ ZdS )Ú
kappa4_genap  Kappa 4 parameter distribution.

    %(before_notes)s

    Notes
    -----
    The probability density function for kappa4 is:

    .. math::

        f(x, h, k) = (1 - k x)^{1/k - 1} (1 - h (1 - k x)^{1/k})^{1/h-1}

    if :math:`h` and :math:`k` are not equal to 0.

    If :math:`h` or :math:`k` are zero then the pdf can be simplified:

    h = 0 and k != 0::

        kappa4.pdf(x, h, k) = (1.0 - k*x)**(1.0/k - 1.0)*
                              exp(-(1.0 - k*x)**(1.0/k))

    h != 0 and k = 0::

        kappa4.pdf(x, h, k) = exp(-x)*(1.0 - h*exp(-x))**(1.0/h - 1.0)

    h = 0 and k = 0::

        kappa4.pdf(x, h, k) = exp(-x)*exp(-exp(-x))

    kappa4 takes :math:`h` and :math:`k` as shape parameters.

    The kappa4 distribution returns other distributions when certain
    :math:`h` and :math:`k` values are used.

    +------+-------------+----------------+------------------+
    | h    | k=0.0       | k=1.0          | -inf<=k<=inf     |
    +======+=============+================+==================+
    | -1.0 | Logistic    |                | Generalized      |
    |      |             |                | Logistic(1)      |
    |      |             |                |                  |
    |      | logistic(x) |                |                  |
    +------+-------------+----------------+------------------+
    |  0.0 | Gumbel      | Reverse        | Generalized      |
    |      |             | Exponential(2) | Extreme Value    |
    |      |             |                |                  |
    |      | gumbel_r(x) |                | genextreme(x, k) |
    +------+-------------+----------------+------------------+
    |  1.0 | Exponential | Uniform        | Generalized      |
    |      |             |                | Pareto           |
    |      |             |                |                  |
    |      | expon(x)    | uniform(x)     | genpareto(x, -k) |
    +------+-------------+----------------+------------------+

    (1) There are at least five generalized logistic distributions.
        Four are described here:
        https://en.wikipedia.org/wiki/Generalized_logistic_distribution
        The "fifth" one is the one kappa4 should match which currently
        isn't implemented in scipy:
        https://en.wikipedia.org/wiki/Talk:Generalized_logistic_distribution
        https://www.mathwave.com/help/easyfit/html/analyses/distributions/gen_logistic.html
    (2) This distribution is currently not in scipy.

    References
    ----------
    J.C. Finney, "Optimization of a Skewed Logistic Distribution With Respect
    to the Kolmogorov-Smirnov Test", A Dissertation Submitted to the Graduate
    Faculty of the Louisiana State University and Agricultural and Mechanical
    College, (August, 2004),
    https://digitalcommons.lsu.edu/gradschool_dissertations/3672

    J.R.M. Hosking, "The four-parameter kappa distribution". IBM J. Res.
    Develop. 38 (3), 25 1-258 (1994).

    B. Kumphon, A. Kaew-Man, P. Seenoi, "A Rainfall Distribution for the Lampao
    Site in the Chi River Basin, Thailand", Journal of Water Resource and
    Protection, vol. 4, 866-869, (2012).
    :doi:`10.4236/jwarp.2012.410101`

    C. Winchester, "On Estimation of the Four-Parameter Kappa Distribution", A
    Thesis Submitted to Dalhousie University, Halifax, Nova Scotia, (March
    2000).
    http://www.nlc-bnc.ca/obj/s4/f2/dsk2/ftp01/MQ57336.pdf

    %(after_notes)s

    %(example)s

    c                 ón   — t          j        ||¦  «        d         j        }t          j        |d¬¦  «        S )Nr   T©Ú
fill_value)rM   rï  rw  Úfull)rB   ræ  r  rw  s       r3   r`   zkappa4_gen._argcheckI  s1   € ÝÔ# A qÑ)Ô)¨!Ô,Ô2ˆÝŒw�u¨Ð.Ñ.Ô.Ð.r5   c                 ó®   — t          ddt          j         t          j        fd¦  «        }t          ddt          j         t          j        fd¦  «        }||gS )Nræ  Fr  r  re   )rB   Úihr1  s      r3   rh   zkappa4_gen._shape_infoM  sG   € Ý˜˜U¥b¤f W­b¬fÐ$5°~ÑFÔFˆÝ˜˜U¥b¤f W­b¬fÐ$5°~ÑFÔFˆØ�Bˆxˆr5   c           
      ó  — t          j        |dk    |dk    ¦  «        t          j        |dk    |dk    ¦  «        t          j        |dk    |dk     ¦  «        t          j        |dk    |dk    ¦  «        t          j        |dk    |dk    ¦  «        t          j        |dk    |dk     ¦  «        g}d„ }d„ }d„ }d„ }t          |||||||g||gt           j        ¬¦  «        }d„ }d„ }t          |||||||g||gt           j        ¬¦  «        }	||	fS )	Nr   c                 ó:   — dt          j        | | ¦  «        z
  |z  S r  )rM   rn  ©ræ  r  s     r3   r–  z#kappa4_gen._get_support.<locals>.f0Z  s    € Ø�"œ.¨¨Q¨BÑ/Ô/Ñ/°Ñ2Ð2r5   c                 ó*   — t          j        | ¦  «        S rK   r.  rG  s     r3   r™  z#kappa4_gen._get_support.<locals>.f1]  s   € Ý”6˜!‘9”9Ðr5   c                 óv   — t          j        t          j        | ¦  «        ¦  «        }t           j         |d d …<   |S rK   ©rM   r–  rw  rf   ©ræ  r  rˆ   s      r3   Úf3z#kappa4_gen._get_support.<locals>.f3`  s/   € Ý”�œ !™œÑ%Ô%ˆAÝ”F�7ˆAˆaˆaˆa‰DØˆHr5   c                 ó   — d|z  S r  r„   rG  s     r3   Úf5z#kappa4_gen._get_support.<locals>.f5e  ó   € Ø�q‘5ˆLr5   ©Údefaultc                 ó   — d|z  S r  r„   rG  s     r3   r–  z#kappa4_gen._get_support.<locals>.f0m  rO  r5   c                 ót   — t          j        t          j        | ¦  «        ¦  «        }t           j        |d d …<   |S rK   rJ  rK  s      r3   r™  z#kappa4_gen._get_support.<locals>.f1p  s-   € Ý”�œ !™œÑ%Ô%ˆAÝ”6ˆAˆaˆaˆa‰DØˆHr5   ©rM   rB  r   r  )
rB   ræ  r  Úcondlistr–  r™  rL  rN  r¤  r£  s
             r3   r“   zkappa4_gen._get_supportR  s`  € Ý”N 1 q¢5¨!¨aª%Ñ0Ô0Ý”N 1 q¢5¨!¨qª&Ñ1Ô1Ý”N 1 q¢5¨!¨aª%Ñ0Ô0Ý”N 1¨¢6¨1¨qª5Ñ1Ô1Ý”N 1¨¢6¨1°ª6Ñ2Ô2Ý”N 1¨¢6¨1¨qª5Ñ1Ô1ð3ˆð	3ð 	3ð 	3ð	ð 	ð 	ð	ð 	ð 	ð
	ð 	ð 	õ ˜Ø˜b " b¨"¨bÐ1Ø˜Q˜Ý!#¤ð)ñ )ô )ˆð
	ð 	ð 	ð	ð 	ð 	õ
 ˜Ø˜b " b¨"¨bÐ1Ø˜Q˜Ý!#¤ð)ñ )ô )ˆð �2ˆvˆr5   c                 óT   — t          j        |                      |||¦  «        ¦  «        S rK   rÛ  ©rB   rn   ræ  r  s       r3   ro   zkappa4_gen._pdf{  rr  r5   c                 óF  — t          j        |dk    |dk    ¦  «        t          j        |dk    |dk    ¦  «        t          j        |dk    |dk    ¦  «        t          j        |dk    |dk    ¦  «        g}d„ }d„ }d„ }d„ }t          |||||g|||gt           j        ¬¦  «        S )Nr   c                 ó˜   — t          j        d|z  dz
  | | z  ¦  «        t          j        d|z  dz
  | d|| z  z
  d|z  z  z  ¦  «        z   S )zŒpdf = (1.0 - k*x)**(1.0/k - 1.0)*(
                      1.0 - h*(1.0 - k*x)**(1.0/k))**(1.0/h-1.0)
               logpdf = ...
            r†   rf  ©rn   ræ  r  s      r3   r–  zkappa4_gen._logpdf.<locals>.f0†  s\   € õ
 ”J˜s 1™u s™{¨Q¨B¨q©DÑ1Ô1Ý”J˜s 1™u s™{¨Q¨B°°a¸±c±	¸SÀ¹UÑ/CÑ,CÑDÔDñEð Fr5   c                 ó^   — t          j        d|z  dz
  | | z  ¦  «        d|| z  z
  d|z  z  z
  S )z~pdf = (1.0 - k*x)**(1.0/k - 1.0)*np.exp(-(
                      1.0 - k*x)**(1.0/k))
               logpdf = ...
            r†   rf  rZ  s      r3   r™  zkappa4_gen._logpdf.<locals>.f1Ž  s:   € õ
 ”:˜c !™e c™k¨A¨2¨a©4Ñ0Ô0°C¸!¸A¹#±IÀÀQÁÑ3GÑGÐGr5   c                 ón   — |  t          j        d|z  dz
  | t          j        |  ¦  «        z  ¦  «        z   S )z]pdf = np.exp(-x)*(1.0 - h*np.exp(-x))**(1.0/h - 1.0)
               logpdf = ...
            r†   )rt   rt  rM   r´   rZ  s      r3   ré  zkappa4_gen._logpdf.<locals>.f2•  s5   € ð �2�œ
 3 q¡5¨3¡;°°µ2´6¸1¸"±:´:±Ñ>Ô>Ñ>Ð>r5   c                 ó4   — |  t          j        |  ¦  «        z
  S )zDpdf = np.exp(-x-np.exp(-x))
               logpdf = ...
            r9  rZ  s      r3   rL  zkappa4_gen._logpdf.<locals>.f3›  s   € ð �2�œ ˜r™
œ
‘?Ð"r5   rP  rT  ©	rB   rn   ræ  r  rU  r–  r™  ré  rL  s	            r3   rÛ   zkappa4_gen._logpdf€  sÜ   € Ý”N 1¨¢6¨1°ª6Ñ2Ô2Ý”N 1¨¢6¨1°ª6Ñ2Ô2Ý”N 1¨¢6¨1°ª6Ñ2Ô2Ý”N 1¨¢6¨1°ª6Ñ2Ô2ð4ˆð
	Fð 	Fð 	Fð	Hð 	Hð 	Hð	?ð 	?ð 	?ð	#ð 	#ð 	#õ ˜8Ø  B¨Ð+Ø˜q !˜9Ý#%¤6ð+ñ +ô +ð 	+r5   c                 óT   — t          j        |                      |||¦  «        ¦  «        S rK   r¶  rW  s       r3   rr   zkappa4_gen._cdf¦  r  r5   c                 óF  — t          j        |dk    |dk    ¦  «        t          j        |dk    |dk    ¦  «        t          j        |dk    |dk    ¦  «        t          j        |dk    |dk    ¦  «        g}d„ }d„ }d„ }d„ }t          |||||g|||gt           j        ¬¦  «        S )Nr   c                 óV   — d|z  t          j        | d|| z  z
  d|z  z  z  ¦  «        z  S )zVcdf = (1.0 - h*(1.0 - k*x)**(1.0/k))**(1.0/h)
               logcdf = ...
            r†   r	  rZ  s      r3   r–  zkappa4_gen._logcdf.<locals>.f0¯  s5   € ð ˜‘E�2œ8 Q B¨¨a°©c©	°S¸±UÑ';Ñ$;Ñ<Ô<Ñ<Ð<r5   c                 ó    — d|| z  z
  d|z  z   S )zLcdf = np.exp(-(1.0 - k*x)**(1.0/k))
               logcdf = ...
            r†   r„   rZ  s      r3   r™  zkappa4_gen._logcdf.<locals>.f1µ  s   € ð ˜1˜Q™3‘Y # a¡%Ñ(Ð(Ð(r5   c                 ód   — d|z  t          j        | t          j        |  ¦  «        z  ¦  «        z  S )zLcdf = (1.0 - h*np.exp(-x))**(1.0/h)
               logcdf = ...
            r†   )rt   r£  rM   r´   rZ  s      r3   ré  zkappa4_gen._logcdf.<locals>.f2»  s-   € ð ˜‘E�2œ8 Q B¥r¤v¨q¨b¡z¤z¡MÑ2Ô2Ñ2Ð2r5   c                 ó.   — t          j        |  ¦  «         S )zBcdf = np.exp(-np.exp(-x))
               logcdf = ...
            r9  rZ  s      r3   rL  zkappa4_gen._logcdf.<locals>.f3Á  s   € õ ”F˜A˜2‘J”J�;Ðr5   rP  rT  r^  s	            r3   rà   zkappa4_gen._logcdf©  sÖ   € Ý”N 1¨¢6¨1°ª6Ñ2Ô2Ý”N 1¨¢6¨1°ª6Ñ2Ô2Ý”N 1¨¢6¨1°ª6Ñ2Ô2Ý”N 1¨¢6¨1°ª6Ñ2Ô2ð4ˆð
	=ð 	=ð 	=ð	)ð 	)ð 	)ð	3ð 	3ð 	3ð	ð 	ð 	õ ˜8Ø  B¨Ð+Ø˜q !˜9Ý#%¤6ð+ñ +ô +ð 	+r5   c                 óF  — t          j        |dk    |dk    ¦  «        t          j        |dk    |dk    ¦  «        t          j        |dk    |dk    ¦  «        t          j        |dk    |dk    ¦  «        g}d„ }d„ }d„ }d„ }t          |||||g|||gt           j        ¬¦  «        S )Nr   c                 ó0   — d|z  dd| |z  z
  |z  |z  z
  z  S r  r„   ©rz   ræ  r  s      r3   r–  zkappa4_gen._ppf.<locals>.f0Ò  s(   € Ø�q‘5˜# #¨¨A©¡,°Ñ!1°AÑ 5Ñ5Ñ6Ð6r5   c                 óD   — d|z  dt          j        | ¦  «         |z  z
  z  S r  r.  rg  s      r3   r™  zkappa4_gen._ppf.<locals>.f1Õ  s$   € Ø�q‘5˜#¥"¤&¨¡)¤) ¨a¡Ñ/Ñ0Ð0r5   c                 ó^   — t          j        | |z   ¦  «         t          j        |¦  «        z   S )z,ppf = -np.log((1.0 - (q**h))/h)
            rŒ  rg  s      r3   ré  zkappa4_gen._ppf.<locals>.f2Ø  s*   € õ ”H˜q !™t˜WÑ%Ô%Ð%­¬¨q©	¬	Ñ1Ð1r5   c                 óR   — t          j        t          j        | ¦  «         ¦  «         S rK   r.  rg  s      r3   rL  zkappa4_gen._ppf.<locals>.f3Ý  s   € Ý”F�BœF 1™IœI˜:Ñ&Ô&Ð&Ð&r5   rP  rT  )	rB   rz   ræ  r  rU  r–  r™  ré  rL  s	            r3   r{   zkappa4_gen._ppfÌ  sÖ   € Ý”N 1¨¢6¨1°ª6Ñ2Ô2Ý”N 1¨¢6¨1°ª6Ñ2Ô2Ý”N 1¨¢6¨1°ª6Ñ2Ô2Ý”N 1¨¢6¨1°ª6Ñ2Ô2ð4ˆð
	7ð 	7ð 	7ð	1ð 	1ð 	1ð	2ð 	2ð 	2ð
	'ð 	'ð 	'õ ˜8Ø  B¨Ð+Ø˜q !˜9Ý#%¤6ð+ñ +ô +ð 	+r5   c                 ó‚   — t          j        |dk     |dk    ¦  «        |dk     g}d„ }d„ }t          |||g||gd¬¦  «        S )Nr   c                 óB   — d| z  |z                        t          ¦  «        S r?  ©ÚastyperÈ  rG  s     r3   r–  z&kappa4_gen._get_stats_info.<locals>.f0ë  s   € Ø˜‘F˜1‘H×$Ò$¥SÑ)Ô)Ð)r5   c                 ó<   — d|z                        t          ¦  «        S r?  rm  rG  s     r3   r™  z&kappa4_gen._get_stats_info.<locals>.f1î  s   € Ø˜‘F—?’?¥3Ñ'Ô'Ð'r5   rC  rP  )rM   rB  r   )rB   ræ  r  rU  r–  r™  s         r3   Ú_get_stats_infozkappa4_gen._get_stats_infoå  sf   € åŒN˜1˜qš5 ! q¢&Ñ)Ô)Ø�ŠEð
ˆð
	*ð 	*ð 	*ð	(ð 	(ð 	(õ ˜8 b¨" X°°1¨v¸qÐAÑAÔAÐAr5   c                 ó|   ‡— |                       ||¦  «        Šˆfd„t          dd¦  «        D ¦   «         }|d d …         S )Nc                 ó\   •— g | ](}t          j        |‰k     ¦  «        rd nt           j        ‘Œ)S rK   ©rM   r   r  )rù  rò  Úmaxrs     €r3   rú  z%kappa4_gen._stats.<locals>.<listcomp>õ  s2   ø€ ÐMÐMÐM¸A�2œ6 ! d¢(Ñ+Ô+Ð7�4�4µ´ÐMÐMÐMr5   r   rC  )rp  rþ  )rB   ræ  r  Úoutputsrt  s       @r3   r   zkappa4_gen._statsó  sG   ø€ Ø×#Ò# A qÑ)Ô)ˆØMÐMÐMÐMÅÀqÈ!ÁÄÐMÑMÔMˆØ�q�q�qŒzÐr5   c                 ó¸   — |                       |d         |d         ¦  «        }||k    rt          j        S t          j        | j        dd|f|z   ¬¦  «        d         S ©Nr   r   rJ  )rp  rM   r  r   ra  Ú_mom_integ1)rB   rÊ  rD   rt  s       r3   Ú_mom1_sczkappa4_gen._mom1_scø  sV   € Ø×#Ò# D¨¤G¨T°!¬WÑ5Ô5ˆØ�Š9ˆ9Ý”6ˆMÝŒ~˜dÔ.°°1¸A¸4À¹9ÐEÑEÔEÀaÔHÐHr5   N)r€   r�   r‚   rƒ   r`   rh   r“   ro   rÛ   rr   rà   r{   rp  r   ry  r„   r5   r3   r>  r>  ð  sÑ   € € € € € ðWð Wðp/ð /ð /ðð ð ð
'ð 'ð 'ðR-ð -ð -ð
$+ð $+ð $+ðL-ð -ð -ð!+ð !+ð !+ðF+ð +ð +ð2Bð Bð Bðð ð ð
Ið Ið Ið Ið Ir5   r>  Úkappa4c                   óL   ‡ — e Zd ZdZd„ Zd„ Zd„ Zˆ fd„Zd„ Zd„ Z	d„ Z
d	„ Zˆ xZS )
Ú
kappa3_gena*  Kappa 3 parameter distribution.

    %(before_notes)s

    Notes
    -----
    The probability density function for `kappa3` is:

    .. math::

        f(x, a) = a (a + x^a)^{-(a + 1)/a}

    for :math:`x > 0` and :math:`a > 0`.

    `kappa3` takes ``a`` as a shape parameter for :math:`a`.

    References
    ----------
    P.W. Mielke and E.S. Johnson, "Three-Parameter Kappa Distribution Maximum
    Likelihood and Likelihood Ratio Tests", Methods in Weather Research,
    701-707, (September, 1973),
    :doi:`10.1175/1520-0493(1973)101<0701:TKDMLE>2.3.CO;2`

    B. Kumphon, "Maximum Entropy and Maximum Likelihood Estimation for the
    Three-Parameter Kappa Distribution", Open Journal of Statistics, vol 2,
    415-419 (2012), :doi:`10.4236/ojs.2012.24050`

    %(after_notes)s

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r  re   rg   s    r3   rh   zkappa3_gen._shape_info#  r  r5   c                 ó*   — ||||z  z   d|z  dz
  z  z  S r;  r„   r
  s      r3   ro   zkappa3_gen._pdf&  s"   € à�!�a˜‘d‘(˜d 1™f Q™hÑ'Ñ'Ð'r5   c                 ó$   — ||||z  z   d|z  z  z  S r?  r„   r
  s      r3   rr   zkappa3_gen._cdf*  s   € Ø�!�a˜‘d‘(˜d 1™fÑ%Ñ%Ð%r5   c           	      óX  •— t          j        ||¦  «        \  }}t          ¦   «                              ||¦  «        }d}||k     }t	          j        t	          j        d||         z  ||         ||         ||          z  z  ¦  «        ¦  «         }||k    }||         |         ||<   |||<   |S )Ng{®Gáz„?r<  )rM   rï  r>   rv   rt   r  rt  )	rB   rn   rˆ   ÚsfÚcutoffrô  Úsf2Úi2r“  s	           €r3   rv   zkappa3_gen._sf-  s¥   ø€ ÝÔ" 1 aÑ(Ô(‰ˆˆ1Ý‰WŒW�[Š[˜˜AÑÔˆð
 ˆØ�ŠKˆÝŒx�œ
 4¨!¨A¬$¡;°°!´°q¸´t¸aÀ¼d¸U±{Ñ0BÑCÔCÑDÔDÐDˆØ�6Š\ˆØ�Q”%˜”)ˆˆB‰àˆˆ1‰Øˆ	r5   c                 ó&   — ||| z  dz
  z  d|z  z  S r  r„   r  s      r3   r{   zkappa3_gen._ppf=  s   € Ø�1�q�b‘5˜3‘;‘ 3 q¡5Ñ)Ð)r5   c                 ón   — t          j        | | ¦  «        }t          j        |¦  «        }||z  d|z  z  S r  r@  )rB   rz   rˆ   ÚlgrÏ  s        r3   r~   zkappa3_gen._isf@  s7   € ÝŒZ˜˜˜Q˜BÑÔˆÝ”˜‘”ˆØ�E‘	˜S 1™WÑ%Ð%r5   c                 óP   ‡— ˆfd„t          dd¦  «        D ¦   «         }|d d …         S )Nc                 ó\   •— g | ](}t          j        |‰k     ¦  «        rd nt           j        ‘Œ)S rK   rs  )rù  rô  rˆ   s     €r3   rú  z%kappa3_gen._stats.<locals>.<listcomp>F  s0   ø€ ÐJÐJÐJ¸�2œ6 ! a¢%™=œ=Ð4�4�4­b¬fÐJÐJÐJr5   r   rC  )rþ  )rB   rˆ   ru  s    ` r3   r   zkappa3_gen._statsE  s2   ø€ ØJÐJÐJÐJ½eÀAÀq¹k¼kÐJÑJÔJˆØ�q�q�qŒzÐr5   c                 ó¤   — t          j        ||d         k    ¦  «        rt           j        S t          j        | j        dd|f|z   ¬¦  «        d         S rw  )rM   r   r  r   ra  rx  )rB   rÊ  rD   s      r3   ry  zkappa3_gen._mom1_scI  sJ   € ÝŒ6�!�t˜A”w’,ÑÔð 	Ý”6ˆMÝŒ~˜dÔ.°°1¸A¸4À¹9ÐEÑEÔEÀaÔHÐHr5   )r€   r�   r‚   rƒ   rh   ro   rr   rv   r{   r~   r   ry  rÎ  rÏ  s   @r3   r|  r|    s¶   ø€ € € € € ðð ð@Eð Eð Eð(ð (ð (ð&ð &ð &ðð ð ð ð ð *ð *ð *ð&ð &ð &ð
ð ð ðIð Ið Ið Ið Ið Ið Ir5   r|  Úkappa3c                   óD   — e Zd ZdZd„ Zdd„Zd„ Zd„ Zd„ Zd„ Z	d	„ Z
d
„ ZdS )Ú	moyal_genaÄ  A Moyal continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `moyal` is:

    .. math::

        f(x) = \exp(-(x + \exp(-x))/2) / \sqrt{2\pi}

    for a real number :math:`x`.

    %(after_notes)s

    This distribution has utility in high-energy physics and radiation
    detection. It describes the energy loss of a charged relativistic
    particle due to ionization of the medium [1]_. It also provides an
    approximation for the Landau distribution. For an in depth description
    see [2]_. For additional description, see [3]_.

    References
    ----------
    .. [1] J.E. Moyal, "XXX. Theory of ionization fluctuations",
           The London, Edinburgh, and Dublin Philosophical Magazine
           and Journal of Science, vol 46, 263-280, (1955).
           :doi:`10.1080/14786440308521076` (gated)
    .. [2] G. Cordeiro et al., "The beta Moyal: a useful skew distribution",
           International Journal of Research and Reviews in Applied Sciences,
           vol 10, 171-192, (2012).
           http://www.arpapress.com/Volumes/Vol10Issue2/IJRRAS_10_2_02.pdf
    .. [3] C. Walck, "Handbook on Statistical Distributions for
           Experimentalists; International Report SUF-PFY/96-01", Chapter 26,
           University of Stockholm: Stockholm, Sweden, (2007).
           http://www.stat.rice.edu/~dobelman/textfiles/DistributionsHandbook.pdf

    .. versionadded:: 1.1.0

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   zmoyal_gen._shape_info}  r£   r5   Nc                 óh   — t                                dd||¬¦  «        }t          j        |¦  «         S )Nr‘   rR   )rˆ   r-   rÔ   rÕ   )rÖ  r×  rM   rí   )rB   rÔ   rÕ   rØ  s       r3   rÖ   zmoyal_gen._rvs€  s3   € Ý�YŠY˜ A¨DØ$0ð ñ 2ô 2ˆå”�r‘
”
ˆ{Ðr5   c                 ó    — t          j        d|t          j        | ¦  «        z   z  ¦  «        t          j        dt           j        z  ¦  «        z  S ©Nrî  rR   )rM   r´   rü   rî   r¦   s     r3   ro   zmoyal_gen._pdf…  s:   € ÝŒv�d˜a¥"¤&¨!¨¡*¤*™nÑ-Ñ.Ô.µ´¸½2¼5¹Ñ1AÔ1AÑAÐAr5   c                 ó~   — t          j        t          j        d|z  ¦  «        t          j        d¦  «        z  ¦  «        S r‘  )rt   rw  rM   r´   rü   r¦   s     r3   rr   zmoyal_gen._cdfˆ  s-   € ÝŒw•r”v˜d Q™hÑ'Ô'­"¬'°!©*¬*Ñ4Ñ5Ô5Ð5r5   c                 ó~   — t          j        t          j        d|z  ¦  «        t          j        d¦  «        z  ¦  «        S r‘  )rt   rê  rM   r´   rü   r¦   s     r3   rv   zmoyal_gen._sf‹  s-   € ÝŒv•b”f˜T A™XÑ&Ô&­¬°©¬Ñ3Ñ4Ô4Ð4r5   c                 ó\   — t          j        dt          j        |¦  «        dz  z  ¦  «         S r  )rM   rí   rt   Úerfcinvr¦   s     r3   r{   zmoyal_gen._ppfŽ  s'   € Ý”�q�2œ: a™=œ=¨!Ñ+Ñ+Ñ,Ô,Ð,Ð,r5   c                 óð   — t          j        d¦  «        t           j        z   }t           j        dz  dz  }dt          j        d¦  «        z  t          j        d¦  «        z  t           j        dz  z  }d}||||fS )NrR   é   rƒ  rJ  )rM   rí   Úeuler_gammarî   rü   rt   rZ  r?  s        r3   r   zmoyal_gen._stats‘  sa   € ÝŒV�A‰YŒY�œÑ'ˆÝŒe�Q‰h˜‰lˆØ•"”'˜!‘*”*‰_�rœw q™zœzÑ)­B¬E°1©HÑ4ˆØˆØ�3˜˜BˆÐr5   c                 ób  — |dk    r!t          j        d¦  «        t           j        z   S |dk    r7t           j        dz  dz  t          j        d¦  «        t           j        z   dz  z   S |dk    rwdt           j        dz  z  t          j        d¦  «        t           j        z   z  }t          j        d¦  «        t           j        z   dz  }dt	          j        d¦  «        z  }||z   |z   S |dk    r´d	t	          j        d¦  «        z  t          j        d¦  «        t           j        z   z  }dt           j        dz  z  t          j        d¦  «        t           j        z   dz  z  }t          j        d¦  «        t           j        z   d
z  }dt           j        d
z  z  d
z  }||z   |z   |z   S |                      |¦  «        S )Nr†   rR   r³   rD  r¼  rƒ  r  rJ  é8   r   rÆ  )rM   rí   r˜  rî   rt   rZ  ry  )rB   r_   Útmp1r:  Útmp3Útmp4s         r3   rÿ   zmoyal_gen._munp˜  sc  € Ø�Š8ˆ8Ý”6˜!‘9”9�rœ~Ñ-Ð-Ø�#ŠXˆXÝ”5˜!‘8˜a‘<¥2¤6¨!¡9¤9­r¬~Ñ#=ÀÑ"AÑAÐAØ�#ŠXˆXØ�œ ™‘>¥R¤V¨A¡Y¤Y­r¬~Ñ%=Ñ>ˆDÝ”F˜1‘I”I�bœnÑ,¨qÑ0ˆDØ�œ ™
œ
‘?ˆDØ˜$‘; Ñ%Ð%Ø�#ŠXˆXØ�BœG A™JœJÑ&­"¬&°©)¬)µb´nÑ*DÑEˆDØ•r”u˜a‘x‘<¥2¤6¨!¡9¤9­r¬~Ñ#=ÀÑ"AÑAˆDÝ”F˜1‘I”I¥¤Ñ.°Ñ2ˆDØ•r”u˜a‘x‘< !Ñ#ˆDØ˜$‘; Ñ%¨Ñ,Ð,ð —=’= Ñ#Ô#Ð#r5   r   )r€   r�   r‚   rƒ   rh   rÖ   ro   rr   rv   r{   r   rÿ   r„   r5   r3   r�  r�  R  sŸ   € € € € € ð)ð )ðTð ð ðð ð ð ð
Bð Bð Bð6ð 6ð 6ð5ð 5ð 5ð-ð -ð -ðð ð ð$ð $ð $ð $ð $r5   r�  Úmoyalc                   ó^   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Zd„ Zdd„Zdd„ZdS )Únakagami_gena`  A Nakagami continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `nakagami` is:

    .. math::

        f(x, \nu) = \frac{2 \nu^\nu}{\Gamma(\nu)} x^{2\nu-1} \exp(-\nu x^2)

    for :math:`x >= 0`, :math:`\nu > 0`. The distribution was introduced in
    [2]_, see also [1]_ for further information.

    `nakagami` takes ``nu`` as a shape parameter for :math:`\nu`.

    %(after_notes)s

    References
    ----------
    .. [1] "Nakagami distribution", Wikipedia
           https://en.wikipedia.org/wiki/Nakagami_distribution
    .. [2] M. Nakagami, "The m-distribution - A general formula of intensity
           distribution of rapid fading", Statistical methods in radio wave
           propagation, Pergamon Press, 1960, 3-36.
           :doi:`10.1016/B978-0-08-009306-2.50005-4`

    %(example)s

    c                 ó   — |dk    S r®  r„   )rB   Únus     r3   r`   znakagami_gen._argcheckÑ  s   € Ø�AŠvˆr5   c                 ó@   — t          dddt          j        fd¦  «        gS )Nr¢  Fr   r  re   rg   s    r3   rh   znakagami_gen._shape_infoÔ  r¤  r5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   rÛ  ©rB   rn   r¢  s      r3   ro   znakagami_gen._pdf×  r_  r5   c                 óÊ   — t          j        d¦  «        t          j        ||¦  «        z   t          j        |¦  «        z
  t          j        d|z  dz
  |¦  «        z   ||dz  z  z
  S râ  )rM   rí   rt   ru  rÃ  r¥  s      r3   rÛ   znakagami_gen._logpdfÚ  s^   € õ ”�q‘	”	�BœH R¨Ñ,Ô,Ñ,­r¬z¸"©~¬~Ñ=Ý”˜˜2™ ™ 1Ñ%Ô%ñ&Ø(*¨1¨a©4©ñ0ð 	1r5   c                 ó8   — t          j        |||z  |z  ¦  «        S rK   r®  r¥  s      r3   rr   znakagami_gen._cdfà  s   € ÝŒ{˜2˜r !™t A™vÑ&Ô&Ð&r5   c                 ó\   — t          j        d|z  t          j        ||¦  «        z  ¦  «        S r  rµ  )rB   rz   r¢  s      r3   r{   znakagami_gen._ppfã  s'   € ÝŒw�s˜2‘v�bœn¨R°Ñ3Ô3Ñ3Ñ4Ô4Ð4r5   c                 ó8   — t          j        |||z  |z  ¦  «        S rK   r±  r¥  s      r3   rv   znakagami_gen._sfæ  s   € ÝŒ|˜B  1¡ Q¡Ñ'Ô'Ð'r5   c                 ó\   — t          j        d|z  t          j        ||¦  «        z  ¦  «        S r[   r¹  )rB   rñ  r¢  s      r3   r~   znakagami_gen._isfé  s'   € ÝŒw�q˜‘t�bœo¨b°!Ñ4Ô4Ñ4Ñ5Ô5Ð5r5   c                 ó"  — t          j        |d¦  «        t          j        |¦  «        z  }d||z  z
  }|dd|z  |z  z
  z  dz  |z  t          j        |d¦  «        z  }d|dz  z  |z  d|z  d	z
  |d	z  z  z   d	|z  z
  dz   }|||dz  z  z  }||||fS )
Nr‘   r†   r   r   r³   r¼  éúÿÿÿr*  rR   )rt   r½  rM   rü   r¾  )rB   r¢  r@  rA  rB  rC  s         r3   r   znakagami_gen._statsì  s²   € ÝŒW�R˜ÑÔ�bœg b™kœkÑ)ˆØ�"�R‘%‰iˆØ�1�q˜‘t˜C‘x‘<Ñ  3Ñ&¨Ñ+­b¬h°s¸CÑ.@Ô.@Ñ@ˆØ��A‘‰X�b‰[˜A˜b™D ™F B¨¡E™>Ñ)¨!¨B©$Ñ.°Ñ2ˆØ
ˆb��c‘‰kÑˆØ�3˜˜BˆÐr5   c                 óÔ  — t          j        |¦  «        }t          j        |¦  «        }t          j        |¦  «        }||dz
  t          j        |¦  «        z  z
  }dt          j        |¦  «        z  t          j        d¦  «        z
  }||z   |z   }t          j         	                    ¦   «         }|dk    }||         |z   dd||         z  z  z
  ||<   | 
                    |¦  «        d         S )Nr‘   rî  rR   g     jè@r   r½  r„   )rM   rw  r¦  rt   rÃ  rÂ  rí   rð  r  rï   rN  )	rB   r¢  rw  r+  r,  r  ræ  Únorm_entropyrô  s	            r3   rï   znakagami_gen._entropyô  sÊ   € Ý”˜‘”ˆåŒ]˜2ÑÔˆÝŒJ�r‰NŒNˆØ�"�s‘(�bœj¨™nœnÑ,Ñ,ˆØ•2”6˜"‘:”:Ñ¥¤ q¡	¤	Ñ)ˆØ�‰E�A‰Iˆå”z×*Ò*Ñ,Ô,ˆð �ŠHˆà�Œt�lÑ" Q¨¨2¨a¬5©¡\Ñ1ˆˆ!‰Ø�yŠy˜ÑÔ Ô#Ð#r5   Nc                 óZ   — t          j        |                     ||¬¦  «        |z  ¦  «        S r  )rM   rü   rå  )rB   r¢  rÔ   rÕ   s       r3   rÖ   znakagami_gen._rvs  s*   € åŒw�|×2Ò2°2¸DÐ2ÑAÔAÀBÑFÑGÔGÐGr5   c                 ó  — t          |t          ¦  «        r|                     ¦   «         }|€
d| j        z  }t	          j        |¦  «        }t	          j        t	          j        ||z
  dz  ¦  «        t          |¦  «        z  ¦  «        }|||fz   S )N)r†   rR   )	r<   r(   r�  ÚnumargsrM   rK  rü   r¢  r¡  )rB   rC   rD   r,   r-   s        r3   r’  znakagami_gen._fitstart	  s~   € Ý�d�LÑ)Ô)ð 	$Ø—>’>Ñ#Ô#ˆDØˆ<Ø˜DœLÑ(ˆDõ Œf�T‰lŒlˆÝ”�œ  s¡
¨Q™Ñ/Ô/µ#°d±)´)Ñ;Ñ<Ô<ˆØ�s˜E�lÑ"Ð"r5   r   rK   )r€   r�   r‚   rƒ   r`   rh   ro   rÛ   rr   r{   rv   r~   r   rï   rÖ   r’  r„   r5   r3   r   r   ±  sã   € € € € € ðð ð>ð ð ðFð Fð Fð+ð +ð +ð1ð 1ð 1ð'ð 'ð 'ð5ð 5ð 5ð(ð (ð (ð6ð 6ð 6ðð ð ð$ð $ð $ð"Hð Hð Hð Hð	#ð 	#ð 	#ð 	#ð 	#ð 	#r5   r   Únakagamic                 ó0  — |dz  dz
  }t          j        | ¦  «        t          j        |¦  «        }}t          j        |dz  | |z  ¦  «        d||z
  dz  z  z
  }t          j        |||z  ¦  «        dz  }t          |dk    ||fd„ t           j         ¬¦  «        S )Nr³   r†   r‘   rR   r   c                 ó0   — | t          j        |¦  «        z   S rK   r.  )rò  r  s     r3   rå  z_ncx2_log_pdf.<locals>.<lambda>%  s   € �q�2œ6 !™9œ9‘}€ r5   )r‡  r   )rM   rü   rt   ru  Úiver   rf   )rn   r£  rQ  Údf2r¿  Únsr¶  Úcorrs           r3   Ú_ncx2_log_pdfr¹    s¡   € ð ˆS‰&�3‰,€CÝŒW�Q‰ZŒZ�œ ™œˆ€BÝ
Œ(�3�s‘7˜A˜b™DÑ
!Ô
! C¨¨b©°1©Ñ$4Ñ
4€CÝŒ6�#�r˜"‘uÑÔ Ñ#€DåØˆqŠØ	ˆdˆØ
$Ð
$Ý”6�'ð	ñ ô ð r5   c                   óP   — e Zd ZdZd„ Zd„ Zdd„Zd„ Zd„ Zd„ Z	d	„ Z
d
„ Zd„ Zd„ ZdS )Úncx2_genaø  A non-central chi-squared continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `ncx2` is:

    .. math::

        f(x, k, \lambda) = \frac{1}{2} \exp(-(\lambda+x)/2)
            (x/\lambda)^{(k-2)/4}  I_{(k-2)/2}(\sqrt{\lambda x})

    for :math:`x >= 0`, :math:`k > 0` and :math:`\lambda \ge 0`.
    :math:`k` specifies the degrees of freedom (denoted ``df`` in the
    implementation) and :math:`\lambda` is the non-centrality parameter
    (denoted ``nc`` in the implementation). :math:`I_\nu` denotes the
    modified Bessel function of first order of degree :math:`\nu`
    (`scipy.special.iv`).

    `ncx2` takes ``df`` and ``nc`` as shape parameters.

    %(after_notes)s

    %(example)s

    c                 óF   — |dk    t          j        |¦  «        z  |dk    z  S r®  rd  ©rB   r£  rQ  s      r3   r`   zncx2_gen._argcheckE  s"   € Ø�Q’�"œ+ b™/œ/Ñ)¨R°1ªWÑ5Ð5r5   c                 ó‚   — t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }||gS )Nr£  Fr   r  rQ  rd   re   ©rB   ÚidfÚincs      r3   rh   zncx2_gen._shape_infoH  s>   € Ý˜˜u q­"¬& k°>ÑBÔBˆÝ˜˜u q­"¬& k°=ÑAÔAˆØ�SˆzÐr5   Nc                 ó0   — |                      |||¦  «        S rK   )Únoncentral_chisquare)rB   r£  rQ  rÔ   rÕ   s        r3   rÖ   zncx2_gen._rvsM  s   € Ø×0Ò0°°R¸Ñ>Ô>Ð>r5   c                 ó~   — t          j        |t          ¬¦  «        |dk    z  }t          ||||ft          d„ ¬¦  «        S )NrË  r   c                 ó8   — t                                | |¦  «        S rK   )r¦  rÛ   ©rn   r£  Ú_s      r3   rå  z"ncx2_gen._logpdf.<locals>.<lambda>S  s   € ­d¯lªl¸1¸bÑ.AÔ.A€ r5   r0  )rM   Ú	ones_likeÚboolr   r¹  ©rB   rn   r£  rQ  Úconds        r3   rÛ   zncx2_gen._logpdfP  sL   € ÝŒ|˜A¥TÐ*Ñ*Ô*¨b°AªgÑ6ˆÝ˜$  B¨ ­}ØAÐAðCñ Cô Cð 	Cr5   c                 óæ   — t          j        |t          ¬¦  «        |dk    z  }t          j        d¬¦  «        5  t	          ||||ft
          j        d„ ¬¦  «        cd d d ¦  «         S # 1 swxY w Y   d S )NrË  r   r5  rn  c                 ó8   — t                                | |¦  «        S rK   )r¦  ro   rÆ  s      r3   rå  zncx2_gen._pdf.<locals>.<lambda>Y  ó   € µ$·)²)¸A¸rÑ2BÔ2B€ r5   r0  )rM   rÈ  rÉ  r8  r   rk   Ú	_ncx2_pdfrÊ  s        r3   ro   zncx2_gen._pdfU  óÓ   € ÝŒ|˜A¥TÐ*Ñ*Ô*¨b°AªgÑ6ˆÝŒ[˜hÐ'Ñ'Ô'ð 	Dð 	DÝ˜d Q¨¨B Kµ3´=Ø!BÐ!BðDñ Dô Dð	Dð 	Dð 	Dð 	Dñ 	Dô 	Dð 	Dð 	Dð 	Dð 	Dð 	Dð 	Døøøð 	Dð 	Dð 	Dð 	Dð 	Dð 	Dó   ¸!A&Á&A*Á-A*c                 óæ   — t          j        |t          ¬¦  «        |dk    z  }t          j        d¬¦  «        5  t	          ||||ft
          j        d„ ¬¦  «        cd d d ¦  «         S # 1 swxY w Y   d S )NrË  r   r5  rn  c                 ó8   — t                                | |¦  «        S rK   )r¦  rr   rÆ  s      r3   rå  zncx2_gen._cdf.<locals>.<lambda>_  rÎ  r5   r0  )rM   rÈ  rÉ  r8  r   rk   Ú	_ncx2_cdfrÊ  s        r3   rr   zncx2_gen._cdf[  rÐ  rÑ  c                 óæ   — t          j        |t          ¬¦  «        |dk    z  }t          j        d¬¦  «        5  t	          ||||ft
          j        d„ ¬¦  «        cd d d ¦  «         S # 1 swxY w Y   d S )NrË  r   r5  rn  c                 ó8   — t                                | |¦  «        S rK   )r¦  r{   rÆ  s      r3   rå  zncx2_gen._ppf.<locals>.<lambda>e  rÎ  r5   r0  )rM   rÈ  rÉ  r8  r   rk   Ú	_ncx2_ppf)rB   rz   r£  rQ  rË  s        r3   r{   zncx2_gen._ppfa  rÐ  rÑ  c                 óæ   — t          j        |t          ¬¦  «        |dk    z  }t          j        d¬¦  «        5  t	          ||||ft
          j        d„ ¬¦  «        cd d d ¦  «         S # 1 swxY w Y   d S )NrË  r   r5  rn  c                 ó8   — t                                | |¦  «        S rK   )r¦  rv   rÆ  s      r3   rå  zncx2_gen._sf.<locals>.<lambda>k  s   € µ$·(²(¸1¸b±/´/€ r5   r0  )rM   rÈ  rÉ  r8  r   rk   Ú_ncx2_sfrÊ  s        r3   rv   zncx2_gen._sfg  sÓ   € ÝŒ|˜A¥TÐ*Ñ*Ô*¨b°AªgÑ6ˆÝŒ[˜hÐ'Ñ'Ô'ð 	Cð 	CÝ˜d Q¨¨B Kµ3´<Ø!AÐ!AðCñ Cô Cð	Cð 	Cð 	Cð 	Cñ 	Cô 	Cð 	Cð 	Cð 	Cð 	Cð 	Cð 	Cøøøð 	Cð 	Cð 	Cð 	Cð 	Cð 	CrÑ  c                 óæ   — t          j        |t          ¬¦  «        |dk    z  }t          j        d¬¦  «        5  t	          ||||ft
          j        d„ ¬¦  «        cd d d ¦  «         S # 1 swxY w Y   d S )NrË  r   r5  rn  c                 ó8   — t                                | |¦  «        S rK   )r¦  r~   rÆ  s      r3   rå  zncx2_gen._isf.<locals>.<lambda>q  rÎ  r5   r0  )rM   rÈ  rÉ  r8  r   rk   Ú	_ncx2_isfrÊ  s        r3   r~   zncx2_gen._isfm  rÐ  rÑ  c                 ó
  — ||z   }d„ }d |||d¦  «        z  }t          j        d¦  «         |||d¦  «        z  t          j         |||d¦  «        dz  ¦  «        z  }d |||d¦  «        z   |||d¦  «        dz  z  }||||fS )Nc                 ó   — | ||z  z   S rK   r„   )r  r«  r  s      r3   Ú	k_plus_clz"ncx2_gen._stats.<locals>.k_plus_clu  s   € Ø�q˜‘s‘7ˆNr5   r³   rÓ  rƒ  rß  rJ  rR   r„  )rB   r£  rQ  Ú
_ncx2_meanrà  Ú_ncx2_varianceÚ_ncx2_skewnessÚ_ncx2_kurtosis_excesss           r3   r   zncx2_gen._statss  sÃ   € Ø˜"‘Wˆ
ð	ð 	ð 	à 	 	¨"¨b°#Ñ 6Ô 6Ñ6ˆÝœ' #™,œ,¨¨°2°r¸1Ñ)=Ô)=Ñ=Ýœ' ) )¨B°°CÑ"8Ô"8¸!Ñ";Ñ<Ô<ñ=ˆà!%¨	¨	°"°b¸#Ñ(>Ô(>Ñ!>Ø!* ¨2¨r°3Ñ!7Ô!7¸Ñ!:ñ";Ðð ØØØ!ð	
ð 	
r5   r   )r€   r�   r‚   rƒ   r`   rh   rÖ   rÛ   ro   rr   r{   rv   r~   r   r„   r5   r3   r»  r»  )  sË   € € € € € ðð ð66ð 6ð 6ðð ð ð
?ð ?ð ?ð ?ðCð Cð Cð
Dð Dð DðDð Dð DðDð Dð DðCð Cð CðDð Dð Dð
ð 
ð 
ð 
ð 
r5   r»  Úncx2c                   óR   — e Zd ZdZd„ Zd„ Zdd„Zd„ Zd„ Zd„ Z	d	„ Z
d
„ Zd„ Zdd„ZdS )Úncf_gena  A non-central F distribution continuous random variable.

    %(before_notes)s

    See Also
    --------
    scipy.stats.f : Fisher distribution

    Notes
    -----
    The probability density function for `ncf` is:

    .. math::

        f(x, n_1, n_2, \lambda) =
            \exp\left(\frac{\lambda}{2} +
                      \lambda n_1 \frac{x}{2(n_1 x + n_2)}
                \right)
            n_1^{n_1/2} n_2^{n_2/2} x^{n_1/2 - 1} \\
            (n_2 + n_1 x)^{-(n_1 + n_2)/2}
            \gamma(n_1/2) \gamma(1 + n_2/2) \\
            \frac{L^{\frac{n_1}{2}-1}_{n_2/2}
                \left(-\lambda n_1 \frac{x}{2(n_1 x + n_2)}\right)}
            {B(n_1/2, n_2/2)
                \gamma\left(\frac{n_1 + n_2}{2}\right)}

    for :math:`n_1, n_2 > 0`, :math:`\lambda \ge 0`.  Here :math:`n_1` is the
    degrees of freedom in the numerator, :math:`n_2` the degrees of freedom in
    the denominator, :math:`\lambda` the non-centrality parameter,
    :math:`\gamma` is the logarithm of the Gamma function, :math:`L_n^k` is a
    generalized Laguerre polynomial and :math:`B` is the beta function.

    `ncf` takes ``df1``, ``df2`` and ``nc`` as shape parameters. If ``nc=0``,
    the distribution becomes equivalent to the Fisher distribution.

    %(after_notes)s

    %(example)s

    c                 ó*   — |dk    |dk    z  |dk    z  S r®  r„   )rB   Údf1r¶  rQ  s       r3   r`   zncf_gen._argcheck°  s   € Ø�a’˜C !šGÑ$¨¨aªÑ0Ð0r5   c                 óÀ   — t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }|||gS )Nré  Fr   r  r¶  rQ  rd   re   )rB   Úidf1Úidf2rÁ  s       r3   rh   zncf_gen._shape_info³  sZ   € Ý˜% ¨­B¬F¨°^ÑDÔDˆÝ˜% ¨­B¬F¨°^ÑDÔDˆÝ˜˜u q­"¬& k°=ÑAÔAˆØ�d˜CÐ Ð r5   Nc                 ó2   — |                      ||||¦  «        S rK   )Únoncentral_f)rB   rÁ  rÂ  rQ  rÔ   rÕ   s         r3   rÖ   zncf_gen._rvs¹  s   € Ø×(Ò(¨¨c°2°tÑ<Ô<Ð<r5   c                 ó0   — t          j        ||||¦  «        S rK   )rk   Ú_ncf_pdf©rB   rn   rÁ  rÂ  rQ  s        r3   ro   zncf_gen._pdf¼  s   € õ Œ|˜A˜s C¨Ñ,Ô,Ð,r5   c                 ó0   — t          j        ||||¦  «        S rK   )rk   Ú_ncf_cdfrñ  s        r3   rr   zncf_gen._cdfÅ  s   € ÝŒ|˜A˜s C¨Ñ,Ô,Ð,r5   c                 óŽ   — t          j        d¬¦  «        5  t          j        ||||¦  «        cd d d ¦  «         S # 1 swxY w Y   d S rm  )rM   r8  rk   Ú_ncf_ppf)rB   rz   rÁ  rÂ  rQ  s        r3   r{   zncf_gen._ppfÈ  óŒ   € ÝŒ[˜hÐ'Ñ'Ô'ð 	1ð 	1Ý”<  3¨¨RÑ0Ô0ð	1ð 	1ð 	1ð 	1ñ 	1ô 	1ð 	1ð 	1ð 	1ð 	1ð 	1ð 	1øøøð 	1ð 	1ð 	1ð 	1ð 	1ð 	1ó   –:º>Á>c                 ó0   — t          j        ||||¦  «        S rK   )rk   Ú_ncf_sfrñ  s        r3   rv   zncf_gen._sfÌ  s   € ÝŒ{˜1˜c 3¨Ñ+Ô+Ð+r5   c                 óŽ   — t          j        d¬¦  «        5  t          j        ||||¦  «        cd d d ¦  «         S # 1 swxY w Y   d S rm  )rM   r8  rk   Ú_ncf_isfrñ  s        r3   r~   zncf_gen._isfÏ  rö  r÷  c                 ó<  — |dz  |z  |z  }t          j        |d|z  z   ¦  «        t          j        d|z  |z
  ¦  «        z   t          j        |dz  ¦  «        z
  }|t          j        | dz  |z   ¦  «        z  }|t          j        |d|z  z   d|z  d|z  ¦  «        z  }|S )Nr†   r‘   r³   )rt   rÃ  rM   r´   Úhyp1f1)rB   r_   rÁ  rÂ  rQ  rB  rÄ  s          r3   rÿ   zncf_gen._munpÓ  s    € Ø�S‰y˜‰}˜qÑ ˆÝŒz˜!˜C ™G™)Ñ$Ô$¥r¤z°#°c±'¸!±)Ñ'<Ô'<Ñ<½r¼zÈ#ÈcÉ'Ñ?RÔ?RÑRˆØ�rŒv�r�c˜C‘i ‘nÑ%Ô%Ñ%ˆØ�rŒy˜˜3˜s™7™ C¨¡G¨S°©VÑ4Ô4Ñ4ˆØˆ
r5   r  c                 óÖ   — t          j        |||¦  «        }t          j        |||¦  «        }d|v rt          j        |||¦  «        nd }d|v rt          j        |||¦  «        nd }||||fS ©Nr  r  )rk   Ú	_ncf_meanÚ_ncf_varianceÚ_ncf_skewnessÚ_ncf_kurtosis_excess)	rB   rÁ  rÂ  rQ  r  r@  rA  rB  rC  s	            r3   r   zncf_gen._statsÚ  s‡   € ÝŒ]˜3  RÑ(Ô(ˆÝÔ  S¨"Ñ-Ô-ˆØ03°w°°�SÔ˜s C¨Ñ,Ô,Ð,ÀDˆà  G˜^˜^õ Ô%Ø��bñô ð Ø15ð 	à�3˜˜BˆÐr5   r   r  )r€   r�   r‚   rƒ   r`   rh   rÖ   ro   rr   r{   rv   r~   rÿ   r   r„   r5   r3   rç  rç  ‡  s¿   € € € € € ð'ð 'ðP1ð 1ð 1ð!ð !ð !ð=ð =ð =ð =ð-ð -ð -ð-ð -ð -ð1ð 1ð 1ð,ð ,ð ,ð1ð 1ð 1ðð ð ðð ð ð ð ð r5   rç  Úncfc                   óP   — e Zd ZdZd„ Zdd„Zd„ Zd„ Zd„ Zd„ Z	d	„ Z
d
„ Zd„ Zd„ ZdS )Út_gena‹  A Student's t continuous random variable.

    For the noncentral t distribution, see `nct`.

    %(before_notes)s

    See Also
    --------
    nct

    Notes
    -----
    The probability density function for `t` is:

    .. math::

        f(x, \nu) = \frac{\Gamma((\nu+1)/2)}
                        {\sqrt{\pi \nu} \Gamma(\nu/2)}
                    (1+x^2/\nu)^{-(\nu+1)/2}

    where :math:`x` is a real number and the degrees of freedom parameter
    :math:`\nu` (denoted ``df`` in the implementation) satisfies
    :math:`\nu > 0`. :math:`\Gamma` is the gamma function
    (`scipy.special.gamma`).

    %(after_notes)s

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r¢  re   rg   s    r3   rh   zt_gen._shape_info  r¤  r5   Nc                 ó0   — |                      ||¬¦  «        S r  )Ú
standard_tr§  s       r3   rÖ   z
t_gen._rvs  s   € Ø×&Ò& r°Ð&Ñ5Ô5Ð5r5   c                 óR   ‡ — t          |t          j        k    ||fd„ ˆ fd„¬¦  «        S )Nc                 ó6   — t                                | ¦  «        S rK   )r  ro   ©rn   r£  s     r3   rå  zt_gen._pdf.<locals>.<lambda>  s   € �DŸIšI a™LœL€ r5   c                 óT   •— t          j        ‰                     | |¦  «        ¦  «        S rK   rÛ  )rn   r£  rB   s     €r3   rå  zt_gen._pdf.<locals>.<lambda>  s#   ø€ Ý”�t—|’| A rÑ*Ô*Ñ+Ô+ð r5   r0  r  r©  s   `  r3   ro   z
t_gen._pdf  sC   ø€ ÝØ•"”&ŠL˜1˜b˜'Ø(Ð(ðð ð ð ð
ñ 
ô 
ð 	
r5   c                 óT   — d„ }d„ }t          |t          j        k    ||f||¬¦  «        S )Nc                 ó  — t          j        t          j        d|z  d¦  «        ¦  «        dt          j        |¦  «        t          j        t           j        ¦  «        z   z  z
  |dz   dz  t          j        | | z  |z  ¦  «        z  z
  S rö  )rM   rí   rt   r½  rî   r£  r	  s     r3   Út_logpdfzt_gen._logpdf.<locals>.t_logpdf  so   € Ý”F�2œ7 3¨¡8¨SÑ1Ô1Ñ2Ô2Ø�RœV B™ZœZ­"¬&µ´©-¬-Ñ7Ñ8ñ9à˜A‘v˜q‘j¥¤¨!¨a©%°©(Ñ!3Ô!3Ñ3ñ4ð 5r5   c                 ó6   — t                                | ¦  «        S rK   )r  rÛ   r	  s     r3   Únorm_logpdfz"t_gen._logpdf.<locals>.norm_logpdf  s   € Ý—<’< ‘?”?Ð"r5   r0  r  )rB   rn   r£  r	  r	  s        r3   rÛ   zt_gen._logpdf  sC   € ð	5ð 	5ð 	5ð
	#ð 	#ð 	#õ ˜"¥¤š,¨¨B¨	°[ÀXÐNÑNÔNÐNr5   c                 ó,   — t          j        ||¦  «        S rK   ©rt   Ústdtrr©  s      r3   rr   z
t_gen._cdf   rÕ  r5   c                 ó.   — t          j        || ¦  «        S rK   r	  r©  s      r3   rv   z	t_gen._sf#  s   € ÝŒx˜˜Q˜BÑÔÐr5   c                 ó,   — t          j        ||¦  «        S rK   ©rt   Ústdtritr·  s      r3   r{   z
t_gen._ppf&  s   € ÝŒz˜"˜aÑ Ô Ð r5   c                 ó.   — t          j        ||¦  «         S rK   r	  r·  s      r3   r~   z
t_gen._isf)  s   € Ý”
˜2˜qÑ!Ô!Ð!Ð!r5   c                 óþ  — t          j        |¦  «        }t          j        |dk    dt           j        ¦  «        }|dk    |dk    z  |dk    t          j        |¦  «        z  |f}d„ d„ d„ f}t          |||ft           j        ¦  «        }t          j        |dk    dt           j        ¦  «        }|dk    |dk    z  |dk    t          j        |¦  «        z  |f}d	„ d
„ d„ f}t          |||ft           j        ¦  «        }||||fS )Nr   r…   rR   c                 óJ   — t          j        t           j        | j        ¦  «        S rK   ©rM   Úbroadcast_torf   rw  rÃ  s    r3   rå  zt_gen._stats.<locals>.<lambda>5  ó   € ¥¤µ´¸¼Ñ!BÔ!B€ r5   c                 ó   — | | dz
  z  S r;  r„   rÃ  s    r3   rå  zt_gen._stats.<locals>.<lambda>6  s   €   r¨#¡v¡€ r5   c                 ó6   — t          j        d| j        ¦  «        S r[   ©rM   r	  rw  rÃ  s    r3   rå  zt_gen._stats.<locals>.<lambda>7  ó   € ¥¤°°B´HÑ!=Ô!=€ r5   rƒ  r   c                 óJ   — t          j        t           j        | j        ¦  «        S rK   r	  rÃ  s    r3   rå  zt_gen._stats.<locals>.<lambda>?  r	  r5   c                 ó   — d| dz
  z  S )NrE  rJ  r„   rÃ  s    r3   rå  zt_gen._stats.<locals>.<lambda>@  s   €  ¨¨3©¡€ r5   c                 ó6   — t          j        d| j        ¦  «        S r®  r"	  rÃ  s    r3   rå  zt_gen._stats.<locals>.<lambda>A  r#	  r5   )rM   ÚisposinfrO  rf   rù   r   r  )	rB   r£  Úinfinite_dfr@  rU  Ú
choicelistrA  rB  rC  s	            r3   r   zt_gen._stats,  s  € å”k "‘o”oˆåŒX�b˜1’f˜c¥2¤6Ñ*Ô*ˆà˜!’V  a¢Ñ(Ø˜!’V�rœ{¨2™œÑ.Øð!ˆð CÐBØ.Ð.Ø=Ð=ð?ˆ
õ ˜( J°°µr´vÑ>Ô>ˆåŒX�b˜1’f˜c¥2¤6Ñ*Ô*ˆà˜!’V  a¢Ñ(Ø˜!’V�rœ{¨2™œÑ.Øð!ˆð CÐBØ/Ð/Ø=Ð=ð?ˆ
õ ˜ :°¨uµb´fÑ=Ô=ˆà�3˜˜BˆÐr5   c                 ó”   — |t           j        k    rt                               ¦   «         S d„ }d„ }t	          |dk    |f||¬¦  «        }|S )Nc                 óî   — | dz  }| dz   dz  }|t          j        |¦  «        t          j        |¦  «        z
  z  t          j        t          j        | ¦  «        t          j        |d¦  «        z  ¦  «        z   S r  )rt   rÂ  rM   rí   rü   rk  )r£  ÚhalfÚhalf1s      r3   r¬  zt_gen._entropy.<locals>.regularJ  si   € Ø�a‘4ˆDØ˜!‘V˜Q‘JˆEØ�2œ: eÑ,Ô,­r¬z¸$Ñ/?Ô/?Ñ?Ñ@Ý”f�RœW R™[œ[­¬°°sÑ);Ô);Ñ;Ñ<Ô<ñ=ð >r5   c                 óž   — t                                ¦   «         d| z  z   | dz  dz  z   | dz  dz  z
  | dz  dz  z
  d| d	z  z  z   | d
z  dz  z   }|S )Nr   r°  r   r±  r‚  r²  r*  g333333Ó?r¾  rÀ  )r  rï   )r£  ræ  s     r3   r.  z"t_gen._entropy.<locals>.asymptoticP  si   € õ —’‘” 1 R¡4Ñ'¨2¨s©7°A©+Ñ5¸¸S¹À!¹ÑCØ˜‘G˜Q‘;ñØ!% r¨3¡w¡ñ0Ø35°s±7¸A±+ñ>ˆAàˆHr5   éd   r0  )rM   rf   r  rï   r   )rB   r£  r¬  r.  ræ  s        r3   rï   zt_gen._entropyF  s\   € Ø•”Š<ˆ<Ý—=’=‘?”?Ð"ð	>ð 	>ð 	>ð	ð 	ð 	õ �r˜S’y 2 &¨J¸7ÐCÑCÔCˆØˆr5   r   rÊ  r„   r5   r3   r	  r	  æ  s¿   € € € € € ðð ð<Fð Fð Fð6ð 6ð 6ð 6ð
ð 
ð 
ð
Oð 
Oð 
Oðð ð ð ð  ð  ð!ð !ð !ð"ð "ð "ðð ð ð4ð ð ð ð r5   r	  r˜  c                   óL   — e Zd ZdZd„ Zd„ Zdd„Zd„ Zd„ Zd„ Z	d	„ Z
d
„ Zdd„ZdS )Únct_gena†  A non-central Student's t continuous random variable.

    %(before_notes)s

    Notes
    -----
    If :math:`Y` is a standard normal random variable and :math:`V` is
    an independent chi-square random variable (`chi2`) with :math:`k` degrees
    of freedom, then

    .. math::

        X = \frac{Y + c}{\sqrt{V/k}}

    has a non-central Student's t distribution on the real line.
    The degrees of freedom parameter :math:`k` (denoted ``df`` in the
    implementation) satisfies :math:`k > 0` and the noncentrality parameter
    :math:`c` (denoted ``nc`` in the implementation) is a real number.

    %(after_notes)s

    %(example)s

    c                 ó   — |dk    ||k    z  S r®  r„   r½  s      r3   r`   znct_gen._argcheckx  s   € Ø�Q’˜2 š8Ñ$Ð$r5   c                 ó˜   — t          dddt          j        fd¦  «        }t          ddt          j         t          j        fd¦  «        }||gS )Nr£  Fr   r  rQ  re   r¿  s      r3   rh   znct_gen._shape_info{  sC   € Ý˜˜u q­"¬& k°>ÑBÔBˆÝ˜˜u­¬ wµ´Ð&7¸ÑHÔHˆØ�SˆzÐr5   Nc                 óÎ   — t                                |||¬¦  «        }t                               |||¬¦  «        }|t          j        |¦  «        z  t          j        |¦  «        z  S )Nr´  rÕ  )r  r×  r¦  rM   rü   )rB   r£  rQ  rÔ   rÕ   r_   r¨  s          r3   rÖ   znct_gen._rvs€  sO   € Ý�HŠH˜ $°\ˆHÑBÔBˆÝ�XŠX�b˜t°,ˆXÑ?Ô?ˆØ•2”7˜2‘;”;‰¥¤¨¡¤Ñ,Ð,r5   c                 óD  — |dz  }|dz  }||z  }||z  |z  }||z   }|dz  t          j        |¦  «        z  t          j        |dz   ¦  «        z   |t          j        d¦  «        z  ||z  dz  z   |dz  t          j        |¦  «        z  z   t          j        |dz  ¦  «        z   z
  }t          j        |¦  «        }	|d|z  z  }
t          j        d¦  «        |z  |z  t          j        |dz  dz   d|
¦  «        z  t          j        |t          j        |dz   dz  ¦  «        z  ¦  «        z  }t          j        |dz   dz  d|
¦  «        t          j        t          j        |¦  «        t          j        |dz  dz   ¦  «        z  ¦  «        z  }|	||z   z  }	t          j	        |	dd ¦  «        S )Nr†   r³   r   rR   r¼  r‘   r   )
rM   rí   rt   rÃ  r´   rü   rý  rø   rÖ  Úclip)rB   rn   r£  rQ  r_   r—  rå  rÛ  Útrm1r   ÚvalFÚtrm2s               r3   ro   znct_gen._pdf…  s„  € àˆs‰FˆØ�‰VˆØˆq‰SˆØ�"‰u�R‰xˆØ�2‰vˆØ�"‘•R”V˜A‘Y”Y‘¥¤¨A¨a©C¡¤Ñ0Ø•R”V˜A‘Y”Y‘;  B¡ q¡Ñ(¨A¨a©Cµ´¸±´Ñ+=Ñ=Ý”Z  !¡‘_”_ñ%ñ&ˆõ ŒV�D‰\Œ\ˆØ�q˜‘v‰ˆÝ”˜‘
”
˜2‘˜a‘¥¤	¨!¨A©#¨a©%°°dÑ ;Ô ;Ñ;Ý”*˜T¥"¤(¨A¨a©C°©7Ñ"3Ô"3Ñ3Ñ4Ô4ñ5ˆå”	˜1˜Q™3 ™' 3¨Ñ-Ô-Ý”*�RœW T™]œ]­2¬8°A°a±C¸±E©?¬?Ñ:Ñ;Ô;ñ<ˆà
ˆd�4‰i‰ˆÝŒw�r˜1˜dÑ#Ô#Ð#r5   c                 ó´   — t          j        d¬¦  «        5  t          j        t          j        |||¦  «        dd¦  «        cd d d ¦  «         S # 1 swxY w Y   d S ©Nr5  rn  r   r   )rM   r8  r6	  rk   Ú_nct_cdf©rB   rn   r£  rQ  s       r3   rr   znct_gen._cdf˜  s˜   € ÝŒ[˜hÐ'Ñ'Ô'ð 	:ð 	:Ý”7�3œ<¨¨2¨rÑ2Ô2°A°qÑ9Ô9ð	:ð 	:ð 	:ð 	:ñ 	:ô 	:ð 	:ð 	:ð 	:ð 	:ð 	:ð 	:øøøð 	:ð 	:ð 	:ð 	:ð 	:ð 	:r9  c                 óŒ   — t          j        d¬¦  «        5  t          j        |||¦  «        cd d d ¦  «         S # 1 swxY w Y   d S rm  )rM   r8  rk   Ú_nct_ppf)rB   rz   r£  rQ  s       r3   r{   znct_gen._ppfœ  óŠ   € ÝŒ[˜hÐ'Ñ'Ô'ð 	+ð 	+Ý”<  2 rÑ*Ô*ð	+ð 	+ð 	+ð 	+ñ 	+ô 	+ð 	+ð 	+ð 	+ð 	+ð 	+ð 	+øøøð 	+ð 	+ð 	+ð 	+ð 	+ð 	+rr  c                 ó´   — t          j        d¬¦  «        5  t          j        t          j        |||¦  «        dd¦  «        cd d d ¦  «         S # 1 swxY w Y   d S r;	  )rM   r8  r6	  rk   Ú_nct_sfr=	  s       r3   rv   znct_gen._sf   s˜   € ÝŒ[˜hÐ'Ñ'Ô'ð 	9ð 	9Ý”7�3œ; q¨"¨bÑ1Ô1°1°aÑ8Ô8ð	9ð 	9ð 	9ð 	9ñ 	9ô 	9ð 	9ð 	9ð 	9ð 	9ð 	9ð 	9øøøð 	9ð 	9ð 	9ð 	9ð 	9ð 	9r9  c                 óŒ   — t          j        d¬¦  «        5  t          j        |||¦  «        cd d d ¦  «         S # 1 swxY w Y   d S rm  )rM   r8  rk   Ú_nct_isfr=	  s       r3   r~   znct_gen._isf¤  r@	  rr  r  c                 óÎ   — t          j        ||¦  «        }t          j        ||¦  «        }d|v rt          j        ||¦  «        nd }d|v rt          j        ||¦  «        nd }||||fS rÿ  )rk   Ú	_nct_meanÚ_nct_varianceÚ_nct_skewnessÚ_nct_kurtosis_excess)rB   r£  rQ  r  r@  rA  rB  rC  s           r3   r   znct_gen._stats¨  sq   € ÝŒ]˜2˜rÑ"Ô"ˆÝÔ  BÑ'Ô'ˆØ*-°¨.¨.�SÔ˜r 2Ñ&Ô&Ð&¸dˆØ14¸°°�SÔ% b¨"Ñ-Ô-Ð-ÀTˆØ�3˜˜BˆÐr5   r   r  )r€   r�   r‚   rƒ   r`   rh   rÖ   ro   rr   r{   rv   r~   r   r„   r5   r3   r1	  r1	  _  s¯   € € € € € ðð ð0%ð %ð %ðð ð ð
-ð -ð -ð -ð
$ð $ð $ð&:ð :ð :ð+ð +ð +ð9ð 9ð 9ð+ð +ð +ðð ð ð ð ð r5   r1	  Únctc                   ó†   ‡ — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	dd	„Z
d
„ Ze ee¦  «        ˆ fd„¦   «         ¦   «         Zˆ xZS )Ú
pareto_genaL  A Pareto continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `pareto` is:

    .. math::

        f(x, b) = \frac{b}{x^{b+1}}

    for :math:`x \ge 1`, :math:`b > 0`.

    `pareto` takes ``b`` as a shape parameter for :math:`b`.

    %(after_notes)s

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r€  re   rg   s    r3   rh   zpareto_gen._shape_infoÉ  r  r5   c                 ó   — ||| dz
  z  z  S r[   r„   r‚  s      r3   ro   zpareto_gen._pdfÌ  s   € à�1˜�r˜!‘t‘9‰}Ðr5   c                 ó   — d|| z  z
  S r[   r„   r‚  s      r3   rr   zpareto_gen._cdfÐ  s   € Ø�1˜�r‘7‰{Ðr5   c                 ó.   — t          d|z
  d|z  ¦  «        S )Nr   r<  rþ  r�  s      r3   r{   zpareto_gen._ppfÓ  s   € Ý�1�Q‘3˜˜Q™ÑÔÐr5   c                 ó   — || z  S rK   r„   r‚  s      r3   rv   zpareto_gen._sfÖ  s   € Ø�A�2‰wˆr5   c                 ó2   — t          j        |d|z  ¦  «        S r?  r§  r�  s      r3   r~   zpareto_gen._isfÙ  s   € ÝŒx˜˜4 !™8Ñ$Ô$Ð$r5   r  c                 óX  — d\  }}}}d|v ri|dk    }t          j        ||¦  «        }t          j        t          j        |¦  «        t           j        ¬¦  «        }t          j        ||||dz
  z  ¦  «         d|v rr|dk    }t          j        ||¦  «        }t          j        t          j        |¦  «        t           j        ¬¦  «        }t          j        ||||dz
  z  |dz
  dz  z  ¦  «         d	|v rž|d
k    }t          j        ||¦  «        }t          j        t          j        |¦  «        t           j        ¬¦  «        }d|dz   z  t          j        |dz
  ¦  «        z  |dz
  t          j        |¦  «        z  z  }	t          j        |||	¦  «         d|v r•|dk    }t          j        ||¦  «        }t          j        t          j        |¦  «        t           j        ¬¦  «        }dt          j        g d¢|¦  «        z  t          j        g d¢|¦  «        z  }	t          j        |||	¦  «         ||||fS )Nr3  rÊ  r   r@  r†   rÉ  rR   r³   r  rƒ  rD  r  r   rE  )r†   r†   r¬  r  )r†   g      Àrß  r…   )	rM   ÚextractrB  rw  rf   Úplacer  rü   rô  )
rB   r‰   r  r@  rA  rB  rC  ÚmaskÚbtrÑ  s
             r3   r   zpareto_gen._statsÜ  sü  € Ø0‰ˆˆC��RØ�'ˆ>ˆ>Ø�q’5ˆDÝ”˜D !Ñ$Ô$ˆBÝ”�œ !™œµ´Ð8Ñ8Ô8ˆBÝŒH�R˜˜r R¨¡V™}Ñ-Ô-Ð-Ø�'ˆ>ˆ>Ø�q’5ˆDÝ”˜D !Ñ$Ô$ˆBÝ”'�"œ( 1™+œ+µ"´&Ð9Ñ9Ô9ˆCÝŒH�S˜$  b¨¡f¡°°C±¸!±Ñ ;Ñ<Ô<Ð<Ø�'ˆ>ˆ>Ø�q’5ˆDÝ”˜D !Ñ$Ô$ˆBÝ”�œ !™œµ´Ð8Ñ8Ô8ˆBØ˜˜S™‘>¥B¤G¨B°©HÑ$5Ô$5Ñ5¸"¸s¹(ÅbÄgÈbÁkÄkÑ9QÑRˆDÝŒH�R˜˜tÑ$Ô$Ð$Ø�'ˆ>ˆ>Ø�q’5ˆDÝ”˜D !Ñ$Ô$ˆBÝ”�œ !™œµ´Ð8Ñ8Ô8ˆBØ�œ
Ð#5Ð#5Ð#5°rÑ:Ô:Ñ:Ý”JÐ5Ð5Ð5°rÑ:Ô:ñ;ˆDåŒH�R˜˜tÑ$Ô$Ð$Ø�3˜˜BˆÐr5   c                 ó<   — dd|z  z   t          j        |¦  «        z
  S r…  r.  r}  s     r3   rï   zpareto_gen._entropy÷  ó   € Ø�3�q‘5‰y�2œ6 !™9œ9Ñ$Ð$r5   c                 ó  •‡‡‡‡‡‡‡— t          | ‰||¦  «        }|\  ŠŠ}}|�9t          j        ‰¦  «        |z
  |pdk     rt          ddt          j        ¬¦  «        ‚‰j        d         Šˆˆfd„Š||cxu r�€Cn �n?ˆfd„Šˆfd„Šˆˆˆˆˆfd„Šˆfd	„}t          |                     d
d¦  «        ¦  «        }|dz  |dz  }
}	 ||	|
¦  «        sB|	dk    s|
t          j        k     r,|	dz  }	|
dz  }
 ||	|
¦  «        s|	dk    °|
t          j        k     °,t          ‰|	|
g¬¦  «        }|j	        rx|j
        }t          j        ‰¦  «        |z
  }‰p ‰||¦  «        }||z   t          j        ‰¦  «        k     s,t          j        ‰¦  «        |z
  }t          j        |d¦  «        }|||fS  t          ¦   «         j        ‰fi |¤ŽS |€t          j        ‰¦  «        |z
  }n|}|pt          j        ‰¦  «        |z
  }‰p ‰||¦  «        }|||fS )Nr   Úparetor   rœ  c                 ób   •— ‰t          j        t          j        ‰|z
  | z  ¦  «        ¦  «        z  S rK   rý  )r-   ÚlocationrC   Úndatas     €€r3   Ú	get_shapez!pareto_gen.fit.<locals>.get_shape  s-   ø€ ð �2œ6¥"¤&¨$°©/¸UÑ)BÑ"CÔ"CÑDÔDÑDÐDr5   c                 ó   •— ‰| z  |z  S rK   r„   )rw  r-   r^	  s     €r3   Ú	dL_dScalez!pareto_gen.fit.<locals>.dL_dScale  s   ø€ ð ˜u‘} uÑ,Ð,r5   c                 óD   •— | dz   t          j        d‰|z
  z  ¦  «        z  S r[   rÜ  )rw  r]	  rC   s     €r3   ÚdL_dLocationz$pareto_gen.fit.<locals>.dL_dLocation  s'   ø€ ð  ™	¥R¤V¨A°¸±Ñ,AÑ%BÔ%BÑBÐBr5   c                 ó€   •— t          j        ‰¦  «        | z
  }‰p ‰| |¦  «        } ‰||¦  «         ‰|| ¦  «        z
  S rK   )rM   rK  )r-   r]	  rw  rc	  ra	  rC   rú  r_	  s      €€€€€r3   rß  z$pareto_gen.fit.<locals>.fun_to_solve  sP   ø€ õ œ6 $™<œ<¨%Ñ/�ØÐ< ) )¨E°8Ñ"<Ô"<�Ø#�| E¨8Ñ4Ô4°y°yÀÈÑ7NÔ7NÑNÐNr5   c                 ó|   •— t          j         ‰| ¦  «        ¦  «        t          j         ‰|¦  «        ¦  «        k    S rK   rL   ©rO   rP   rß  s     €r3   rQ   z.pareto_gen.fit.<locals>.interval_contains_root#  s;   ø€ åœ  ¨VÑ 4Ô 4Ñ5Ô5Ýœ  ¨VÑ 4Ô 4Ñ5Ô5ò6ð 7r5   r-   rR   rà  )r  rM   rK  rH  rf   rw  rL  r:   r)   r  r  r  r>   r@   )rB   rC   rD   r2   r  ró   rô   rQ   rµ  rO   rP   r¶  r-   r,   rw  rc	  ra	  rú  rß  r_	  r^	  r“  s    `             @@@@@@€r3   r@   zpareto_gen.fitú  sâ  øøøøøøøø€ õ 1°°t¸TÀ4ÑHÔHˆ
Ø%/Ñ"ˆˆf�d˜Fð Ð¥¤ t¡¤¨tÑ 3°v°{ÀÒ CÐ CÝ˜x¨q½¼Ð?Ñ?Ô?Ð?à”
˜1”ˆð	Eð 	Eð 	Eð 	Eð 	Eð 	Eð
 �6Ð!Ð!Ð!Ð!Ñ!Ð!Ð!Ñ!ð-ð -ð -ð -ð -ð
Cð Cð Cð Cð Cð
Oð Oð Oð Oð Oð Oð Oð Oð Oð7ð 7ð 7ð 7ð 7õ   §¢¨°!Ñ 4Ô 4Ñ5Ô5ˆKØ(¨1™_¨k¸A©o�FˆFð .Ð-¨f°fÑ=Ô=ð Ø š
˜
 f­r¬v¢o oØ˜!‘�Ø˜!‘�ð .Ð-¨f°fÑ=Ô=ð Ø š
˜
 f­r¬v¢o oõ ˜l°V¸VÐ4DÐEÑEÔEˆCØŒ}ð 1Øœ�Ý”f˜T‘l”l UÑ*�ØÐ7 ) )¨E°3Ñ"7Ô"7�ð  ™¥r¤v¨d¡|¤|Ò3Ð3ÝœF 4™LœL¨3Ñ.�EÝœL¨°Ñ2Ô2�EØ˜c 5Ð(Ð(à"•u‘w”w”{ 4Ð0Ð0¨4Ð0Ð0Ð0Øˆ\Ý”&˜‘,”, Ñ'ˆCˆCàˆCð Ð,�"œ& ™,œ,¨Ñ,ˆØÐ/˜)˜) E¨3Ñ/Ô/ˆØ�c˜5Ð Ð r5   r  )r€   r�   r‚   rƒ   rh   ro   rr   r{   rv   r~   r   rï   rH   r   r   r@   rÎ  rÏ  s   @r3   rL	  rL	  ³  sí   ø€ € € € € ðð ð*Eð Eð Eðð ð ðð ð ð ð  ð  ðð ð ð%ð %ð %ðð ð ð ð6%ð %ð %ð ØÐ˜MÑ*Ô*ðR!ð R!ð R!ð R!ñ +Ô*ñ „_ðR!ð R!ð R!ð R!ð R!r5   rL	  r[	  c                   óN   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Zd„ ZdS )Ú	lomax_gena§  A Lomax (Pareto of the second kind) continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `lomax` is:

    .. math::

        f(x, c) = \frac{c}{(1+x)^{c+1}}

    for :math:`x \ge 0`, :math:`c > 0`.

    `lomax` takes ``c`` as a shape parameter for :math:`c`.

    `lomax` is a special case of `pareto` with ``loc=-1.0``.

    %(after_notes)s

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r  re   rg   s    r3   rh   zlomax_gen._shape_infol  r  r5   c                 ó$   — |dz  d|z   |dz   z  z  S r  r„   r
  s      r3   ro   zlomax_gen._pdfo  s   € à�‰u�c˜!‘e˜q ™uÑ%Ñ%Ð%r5   c                 ó`   — t          j        |¦  «        |dz   t          j        |¦  «        z  z
  S r[   r¿  r
  s      r3   rÛ   zlomax_gen._logpdfs  s&   € ÝŒv�a‰yŒy˜A˜a™C¥¤¨!¡¤Ñ,Ñ,Ð,r5   c                 óX   — t          j        | t          j        |¦  «        z  ¦  «         S rK   r  r
  s      r3   rr   zlomax_gen._cdfv  s#   € Ý”˜!˜�BœH Q™KœK™Ñ(Ô(Ð(Ð(r5   c                 óV   — t          j        | t          j        |¦  «        z  ¦  «        S rK   )rM   r´   rt   r£  r
  s      r3   rv   zlomax_gen._sfy  s    € ÝŒv�q�b�œ !™œ‘nÑ%Ô%Ð%r5   c                 ó2   — | t          j        |¦  «        z  S rK   r	  r
  s      r3   rä   zlomax_gen._logsf|  s   € Øˆr•"”(˜1‘+”+‰~Ðr5   c                 óX   — t          j        t          j        | ¦  «         |z  ¦  «        S rK   r  r  s      r3   r{   zlomax_gen._ppf  s"   € ÝŒx�œ 1 "™œ˜ a™Ñ(Ô(Ð(r5   c                 ó   — |d|z  z  dz
  S r;  r„   r  s      r3   r~   zlomax_gen._isf‚  s   € Ø�4˜!‘8‰}˜qÑ Ð r5   c                 óR   — t                                |dd¬¦  «        \  }}}}||||fS )Nr<  rA  )r,   r  )r[	  rð  r[  s         r3   r   zlomax_gen._stats…  s/   € Ý Ÿ,š, q¨d¸F˜,ÑCÔC‰ˆˆC��RØ�3˜˜BˆÐr5   c                 ó<   — dd|z  z   t          j        |¦  «        z
  S r…  r.  r}  s     r3   rï   zlomax_gen._entropy‰  s   € Ø��Q‘‰w•r”v˜a‘y”yÑ Ð r5   N)r€   r�   r‚   rƒ   rh   ro   rÛ   rr   rv   rä   r{   r~   r   rï   r„   r5   r3   rh	  rh	  T  s·   € € € € € ðð ð.Eð Eð Eð&ð &ð &ð-ð -ð -ð)ð )ð )ð&ð &ð &ðð ð ð)ð )ð )ð!ð !ð !ðð ð ð!ð !ð !ð !ð !r5   rh	  Úlomaxc                   ó–   ‡ — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zdd„Zd„ Ze eed¬¦  «        ˆ fd„¦   «         ¦   «         Zˆ xZS )Úpearson3_gena�  A pearson type III continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `pearson3` is:

    .. math::

        f(x, \kappa) = \frac{|\beta|}{\Gamma(\alpha)}
                       (\beta (x - \zeta))^{\alpha - 1}
                       \exp(-\beta (x - \zeta))

    where:

    .. math::

            \beta = \frac{2}{\kappa}

            \alpha = \beta^2 = \frac{4}{\kappa^2}

            \zeta = -\frac{\alpha}{\beta} = -\beta

    :math:`\Gamma` is the gamma function (`scipy.special.gamma`).
    Pass the skew :math:`\kappa` into `pearson3` as the shape parameter
    ``skew``.

    %(after_notes)s

    %(example)s

    References
    ----------
    R.W. Vogel and D.E. McMartin, "Probability Plot Goodness-of-Fit and
    Skewness Estimation Procedures for the Pearson Type 3 Distribution", Water
    Resources Research, Vol.27, 3149-3158 (1991).

    L.R. Salvosa, "Tables of Pearson's Type III Function", Ann. Math. Statist.,
    Vol.1, 191-198 (1930).

    "Using Modern Computing Tools to Fit the Pearson Type III Distribution to
    Aviation Loads Data", Office of Aviation Research (2003).

    c                 ó  — d}d}d}t          j        d||¦  «        \  }}}|                     ¦   «         }t          j        |¦  «        |k     }| }d||         |z  z  }	||	z  dz  }
||
|	z  z
  }|	||         |z
  z  }||||||	|
|fS )Nr…   r†   g�íµ ÷Æð>r³   rR   )rM   rï  ÚcopyrÔ  )rB   rn   r  r,   r-   Únorm2pearson_transitionÚansrV	  Úinvmaskrk  r  rZ  Útransxs                r3   Ú_preprocesszpearson3_gen._preprocess¾  s´   € ð
 ˆØˆð #+ÐåÔ*¨3°°4Ñ8Ô8‰ˆˆQ�Ø�hŠh‰jŒjˆõ Œ{˜4Ñ Ô Ð#:Ò:ˆØ�%ˆà�d˜7”m eÑ+Ñ,ˆØ˜‘ Ñ!ˆØ�U˜T‘\Ñ!ˆà˜˜7œ dÑ*Ñ+ˆØ�A�v˜t W¨d°E¸4Ð?Ð?r5   c                 ó*   — t          j        |¦  «        S rK   rd  )rB   r  s     r3   r`   zpearson3_gen._argcheckÚ  s   € õ
 Œ{˜4Ñ Ô Ð r5   c                 óV   — t          ddt          j         t          j        fd¦  «        gS )Nr  Fr  re   rg   s    r3   rh   zpearson3_gen._shape_infoá  s$   € Ý˜6 5­B¬F¨7µB´FÐ*;¸^ÑLÔLÐMÐMr5   c                 ó*   — d}d}|}d|dz  z  }||||fS )Nr…   r†   r¼  rR   r„   )rB   r  rÊ  rÉ  r  r  s         r3   r   zpearson3_gen._statsä  s,   € ØˆØˆØˆØ��a‘‰KˆØ�!�Q˜ˆzÐr5   c                 óÊ   — t          j        |                      ||¦  «        ¦  «        }|j        dk    rt          j        |¦  «        rdS |S d|t          j        |¦  «        <   |S )Nr   r…   )rM   r´   rÛ   r+  rb  )rB   rn   r  ry	  s       r3   ro   zpearson3_gen._pdfë  s]   € õ
 Œf�T—\’\ ! TÑ*Ô*Ñ+Ô+ˆØŒ8�qŠ=ˆ=ÝŒx˜‰}Œ}ð Ø�sØˆJØ ˆ�BŒH�S‰MŒMÑØˆ
r5   c                 ó  — |                       ||¦  «        \  }}}}}}}}	t          j        t          ||         ¦  «        ¦  «        ||<   t          j        t	          |¦  «        ¦  «        t
                               ||¦  «        z   ||<   |S rK   )r|	  rM   rí   r·   r
  rÖ  r³  )
rB   rn   r  ry	  r{	  rV	  rz	  rk  r  rÇ  s
             r3   rÛ   zpearson3_gen._logpdfø  s€   € ð ×Ò˜Q Ñ%Ô%ñ 	6ˆˆQ�˜˜g t¨U°Aõ ”F�9 Q t¤WÑ-Ô-Ñ.Ô.ˆˆD‰	õ ”v�c $™iœiÑ(Ô(­5¯<ª<¸ÀÑ+FÔ+FÑFˆˆG‰Øˆ
r5   c                 óä  — |                       ||¦  «        \  }}}}}}}}t          ||         ¦  «        ||<   t          j        ||j        ¦  «        }t          j        ||dk    ¦  «        }	||         dk    }
t                               ||
         ||
         ¦  «        ||	<   t          j        ||dk     ¦  «        }||         dk     }t                               ||         ||         ¦  «        ||<   |S r®  )	r|	  r½   rM   r	  rw  rB  rÖ  rš   r�  ©rB   rn   r  ry	  r{	  rV	  rz	  rÇ  r  Ú	invmask1aÚ	invmask1bÚ	invmask2aÚ	invmask2bs                r3   rr   zpearson3_gen._cdf   så   € à×Ò˜Q Ñ%Ô%ñ 	3ˆˆQ�˜˜g q¨%°õ ˜a œgÑ&Ô&ˆˆD‰	åŒ˜t W¤]Ñ3Ô3ˆÝ”N 7¨D°1ªHÑ5Ô5ˆ	Ø˜”M AÒ%ˆ	õ Ÿš 6¨)Ô#4°e¸IÔ6FÑGÔGˆˆI‰õ ”N 7¨D°1ªHÑ5Ô5ˆ	Ø˜”M AÒ%ˆ	åŸš &¨Ô"3°U¸9Ô5EÑFÔFˆˆI‰àˆ
r5   c                 óä  — |                       ||¦  «        \  }}}}}}}}t          ||         ¦  «        ||<   t          j        ||j        ¦  «        }t          j        ||dk    ¦  «        }	||         dk    }
t                               ||
         ||
         ¦  «        ||	<   t          j        ||dk     ¦  «        }||         dk     }t                               ||         ||         ¦  «        ||<   |S r®  )	r|	  rÇ   rM   r	  rw  rB  rÖ  r�  rš   rƒ	  s                r3   rv   zpearson3_gen._sf   sá   € à×Ò˜Q Ñ%Ô%ñ 	3ˆˆQ�˜˜g q¨%°õ ˜Q˜tœWÑ%Ô%ˆˆD‰	åŒ˜t W¤]Ñ3Ô3ˆÝ”N 7¨D°1ªHÑ5Ô5ˆ	Ø˜”M AÒ%ˆ	ÝŸš &¨Ô"3°U¸9Ô5EÑFÔFˆˆI‰å”N 7¨D°1ªHÑ5Ô5ˆ	Ø˜”M AÒ%ˆ	ÝŸš 6¨)Ô#4°e¸IÔ6FÑGÔGˆˆI‰àˆ
r5   Nc                 ó6  — t          j        ||¦  «        }|                      dg|¦  «        \  }}}}}}}	}
|                     ¦   «         }|j        |z
  }|                     |¦  «        ||<   |                     |	|¦  «        |z  |
z   ||<   |dk    r|d         }|S )Nr   r„   )rM   r	  r|	  r¢  rÔ   rÒ   rå  )rB   r  rÔ   rÕ   ry	  rÇ  rV	  rz	  rk  r  rZ  ÚnsmallÚnbigs                r3   rÖ   zpearson3_gen._rvs0   s©   € ÝŒ˜t TÑ*Ô*ˆà×Ò˜a˜S $Ñ'Ô'ñ 	4ˆˆQ��4˜ $¨¨tð —’‘”ˆØŒy˜6Ñ!ˆØ ×0Ò0°Ñ8Ô8ˆˆD‰	Ø#×2Ò2°5¸$Ñ?Ô?ÀÑDÀtÑKˆˆG‰à�2Š:ˆ:Ø�a”&ˆCØˆ
r5   c                 óì   — |                       ||¦  «        \  }}}}}}}}	t          ||         ¦  «        ||<   ||         }d||dk              z
  ||dk     <   t          j        ||¦  «        |z  |	z   ||<   |S rK  )r|	  rÄ   rt   r¶  )
rB   rz   r  ry	  rÇ  rV	  rz	  rk  r  rZ  s
             r3   r{   zpearson3_gen._ppf>   s…   € à×Ò˜Q Ñ%Ô%ñ 	4ˆˆQ��4˜ $¨¨tå˜a œgÑ&Ô&ˆˆD‰	ØˆgŒJˆØ˜!˜D 1šHœ+‘oˆˆ$�Š(‰Ý”~ e¨QÑ/Ô/°Ñ4°tÑ;ˆˆG‰Øˆ
r5   ze        Note that method of moments (`method='MM'`) is not
        available for this distribution.

rð   c                 ó®   •— |                      dd ¦  «        dk    rt          d¦  «        ‚ t          t          | ¦  «        | ¦  «        j        |g|¢R i |¤ŽS )Nr/   ÚMMzhFit `method='MM'` is not available for the Pearson3 distribution. Please try the default `method='MLE'`.)r:   ÚNotImplementedErrorr>   r?   r@   r  s       €r3   r@   zpearson3_gen.fitG   sn   ø€ ð
 �8Š8�H˜dÑ#Ô# tÒ+Ð+Ý%ð 'Dñ Eô Eð Eð /•5�˜d™œ TÑ*Ô*Ô.¨tÐC°dÐCÐCÐC¸dÐCÐCÐCr5   r   )r€   r�   r‚   rƒ   r|	  r`   rh   r   ro   rÛ   rr   rv   rÖ   r{   rH   r	   r   r@   rÎ  rÏ  s   @r3   ru	  ru	  �  s  ø€ € € € € ð,ð ,ðZ@ð @ð @ð8!ð !ð !ðNð Nð Nðð ð ðð ð ðð ð ðð ð ð0ð ð ð"ð ð ð ðð ð ð ØÐ˜}ð 50ð 1ñ 1ô 1ðDð Dð Dð Dñ1ô 1ñ „_ðDð Dð Dð Dð Dr5   ru	  Úpearson3c                   óž   ‡ — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Zd„ Zˆ fd„Ze eed¬¦  «        ˆ fd„¦   «         ¦   «         Zˆ xZS )Úpowerlaw_gena¨  A power-function continuous random variable.

    %(before_notes)s

    See Also
    --------
    pareto

    Notes
    -----
    The probability density function for `powerlaw` is:

    .. math::

        f(x, a) = a x^{a-1}

    for :math:`0 \le x \le 1`, :math:`a > 0`.

    `powerlaw` takes ``a`` as a shape parameter for :math:`a`.

    %(after_notes)s

    For example, the support of `powerlaw` can be adjusted from the default
    interval ``[0, 1]`` to the interval ``[c, c+d]`` by setting ``loc=c`` and
    ``scale=d``. For a power-law distribution with infinite support, see
    `pareto`.

    `powerlaw` is a special case of `beta` with ``b=1``.

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r  re   rg   s    r3   rh   zpowerlaw_gen._shape_infox   r  r5   c                 ó   — |||dz
  z  z  S r  r„   r
  s      r3   ro   zpowerlaw_gen._pdf{   s   € à��Q�s‘U‘‰|Ðr5   c                 ó\   — t          j        |¦  «        t          j        |dz
  |¦  «        z   S r[   )rM   rí   rt   ru  r
  s      r3   rÛ   zpowerlaw_gen._logpdf   s%   € ÝŒv�a‰yŒy�2œ8 A¨¡E¨1Ñ-Ô-Ñ-Ð-r5   c                 ó   — ||dz  z  S r  r„   r
  s      r3   rr   zpowerlaw_gen._cdf‚   s   € Ø�1�S‘5‰zÐr5   c                 ó0   — |t          j        |¦  «        z  S rK   r.  r
  s      r3   rà   zpowerlaw_gen._logcdf…   r/  r5   c                 ó(   — t          |d|z  ¦  «        S r  rþ  r  s      r3   r{   zpowerlaw_gen._ppfˆ   s   € Ý�1�c˜!‘e‰}Œ}Ðr5   c                 ó.   — t          j        ||¦  «         S rK   )rt   rR  )rB   rñ  rˆ   s      r3   rv   zpowerlaw_gen._sf‹   s   € Ý”˜˜A‘”ˆÐr5   c                 ó   — |||z   z  S rK   r„   )rB   r_   rˆ   s      r3   rÿ   zpowerlaw_gen._munpŽ   s   € à�A˜‘E‰{Ðr5   c                 óÔ   — ||dz   z  ||dz   z  |dz   dz  z  d|dz
  |dz   z  z  t          j        |dz   |z  ¦  «        z  dt          j        g d¢|¦  «        z  ||dz   z  |dz   z  z  fS )	Nr†   r³   rR   r°  rD  r‚  )r   r¼  r¬  rR   r   )rM   rü   rô  r  s     r3   r   zpowerlaw_gen._stats’   s‹   € Ø�Q˜‘W‘Ø�Q˜‘W‘  S¡¨Q¡Ñ.Ø˜˜S™ Q¨¡WÑ-Ñ.µ´¸!¸c¹'ÀQ¹Ñ1GÔ1GÑGØ•B”J˜~˜~˜~¨qÑ1Ô1Ñ1°Q¸!¸c¹'±]ÀaÈ!ÁeÑ5LÑMðOð 	Or5   c                 ó<   — dd|z  z
  t          j        |¦  «        z
  S r…  r.  r  s     r3   rï   zpowerlaw_gen._entropy˜   rY	  r5   c                 ód   •— t          ¦   «                              ||¦  «        |dk    |dk    z  z  S ©Nr   r   )r>   r  )rB   rn   rˆ   r“  s      €r3   r  zpowerlaw_gen._support_mask›   s4   ø€ Ý‘”×%Ò% a¨Ñ+Ô+Ø˜’F˜q AšvÑ&ñ(ð 	)r5   a:          Notes specifically for ``powerlaw.fit``: If the location is a free
        parameter and the value returned for the shape parameter is less than
        one, the true maximum likelihood approaches infinity. This causes
        numerical difficulties, and the resulting estimates are approximate.
        

rð   c                 óN  •‡‡‡‡‡‡‡‡— |                      dd¦  «        r t          ¦   «         j        ‰g|¢R i |¤ŽS t          t	          j        ‰¦  «        ¦  «        dk    r t          ¦   «         j        ‰g|¢R i |¤ŽS t          | ‰||¦  «        \  ŠŠ}}‰|                      ‰¦  «        fg}|                      |i ¦  «        d         }|�W‰ 	                    ¦   «         |k    st          ddd¦  «        ‚|�,‰                     ¦   «         ||z   k    st          ddd¦  «        ‚|�>|dk    rt          d¦  «        ‚|t	          j        ‰¦  «        k    rd}t          |¦  «        ‚d„ Šd	„ Š|�|� ‰‰||¦  «        ||fS |�²t	          j        ‰ 	                    ¦   «         t          j         ¦  «        }	‰p ‰‰|	|¦  «        }
 ||
|	|f‰¦  «        }t	          j        ‰                     ¦   «         |z
  t          j        ¦  «        }‰p ‰‰||¦  «        } ||||f‰¦  «        }||k     r|
|	|fS |||fS |�  ‰‰|¦  «        }‰p ‰‰||¦  «        }|||fS ˆˆˆˆfd
„}d„ Šd„ Šˆˆˆˆˆfd„Šˆˆˆˆˆˆfd„Šˆˆˆˆˆˆfd„}‰�‰dk    r
 |¦   «         S ‰�‰dk    r
 |¦   «         S  |¦   «         }|                      |‰¦  «        } |¦   «         }|                      |‰¦  «        }||k    r|d         dk    r|S ||k    r|d         dk    r|S  t          ¦   «         j        ‰g|¢R i |¤ŽS )Nr  Fr   Úpowerlawr   zKNegative or zero `fscale` is outside the range allowed by the distribution.z0`fscale` must be greater than the range of data.c                 óª   — t          | ¦  «        }| t          j        t          j        | |z
  ¦  «        ¦  «        |t          j        |¦  «        z  z
  z  S rK   )r¡  rM   r¢  rí   )rC   r,   r-   r®  s       r3   r_	  z#powerlaw_gen.fit.<locals>.get_shapeã   sE   € õ �D‘	”	ˆAØ�3�"œ&¥¤¨¨s©
Ñ!3Ô!3Ñ4Ô4°q½¼À¹¼±ÑFÑGÐGr5   c                 ó0   — |                       ¦   «         |z
  S rK   )rc  )rC   r,   s     r3   Ú	get_scalez#powerlaw_gen.fit.<locals>.get_scaleê   s   € ð —8’8‘:”: Ñ#Ð#r5   c                  ó°  •— t          j        ‰                     ¦   «         t           j         ¦  «        } t          j        | ¦  «        t          j        | j        ¦  «        j        k     r3t          j        | ¦  «        t          j        | j        ¦  «        j        z  } t          j         ‰‰| ¦  «        t           j        ¦  «        }‰p ‰‰| |¦  «        }|| |fS rK   )	rM   r  rK  rf   r
  râ  rÌ  rã  rN   )r,   r-   rw  rC   rú  r£	  r_	  s      €€€€r3   Úfit_loc_scale_w_shape_lt_1z4powerlaw_gen.fit.<locals>.fit_loc_scale_w_shape_lt_1!  s§   ø€ Ý”,˜tŸxšx™zœz­B¬F¨7Ñ3Ô3ˆCÝŒv�c‰{Œ{�RœX c¤iÑ0Ô0Ô5Ò5Ð5Ý”g˜c‘l”l¥R¤X¨c¬iÑ%8Ô%8Ô%=Ñ=�Ý”L  ¨4°Ñ!5Ô!5µr´vÑ>Ô>ˆEØÐ9˜i˜i¨¨c°5Ñ9Ô9ˆEØ˜#˜uÐ$Ð$r5   c                 ó*   — | j         d          |z  |z  S r®  )rw  )rC   rw  r-   s      r3   ra	  z#powerlaw_gen.fit.<locals>.dL_dScale !  s   € ð ”J˜q”M�> EÑ)¨EÑ1Ð1r5   c                 óB   — |dz
  t          j        d|| z
  z  ¦  «        z  S r[   rÜ  )rC   rw  r,   s      r3   rc	  z&powerlaw_gen.fit.<locals>.dL_dLocation%!  s&   € ð ˜A‘I¥¤¨¨S°4©ZÑ(8Ñ!9Ô!9Ñ9Ð9r5   c                 ó�   •— t          j         ‰‰| ¦  «        t           j         ¦  «        }‰p ‰‰| |¦  «        } ‰‰|| ¦  «        S rK   ©rM   r  rf   )r,   r-   rw  rc	  rC   rú  r£	  r_	  s      €€€€€r3   ÚdL_dLocation_starz+powerlaw_gen.fit.<locals>.dL_dLocation_star*!  sR   ø€ õ ”L  ¨4°Ñ!5Ô!5½¼°wÑ?Ô?ˆEØÐ9˜i˜i¨¨c°5Ñ9Ô9ˆEØ�<  e¨SÑ1Ô1Ð1r5   c                 ó¬   •— t          j         ‰‰| ¦  «        t           j         ¦  «        }‰p ‰‰| |¦  «        } ‰‰||¦  «         ‰‰|| ¦  «        z
  S rK   r©	  )	r,   r-   rw  rc	  ra	  rC   rú  r£	  r_	  s	      €€€€€€r3   rß  z&powerlaw_gen.fit.<locals>.fun_to_solve1!  sj   ø€ õ ”L  ¨4°Ñ!5Ô!5½¼°wÑ?Ô?ˆEØÐ9˜i˜i¨¨c°5Ñ9Ô9ˆEØ�I˜d E¨5Ñ1Ô1Ø"�l 4¨°Ñ4Ô4ñ5ð 6r5   c                  óÂ  •— t          j        ‰
                     ¦   «         t           j         ¦  «        } ‰
                     ¦   «         | z
  } ‰	| ¦  «        dk    r+‰
                     ¦   «         |z
  } |dz  } ‰	| ¦  «        dk    °+ˆfd„}| dz
  }d} ||| ¦  «        sJ|t           j         k    r9‰
                     ¦   «         |z
  }|dz  } ||| ¦  «        s|t           j         k    °9t	          j        ‰|| f¬¦  «        }t          j        |j        t           j         ¦  «        }t          j         ‰‰
|¦  «        t           j        ¦  «        }‰p ‰‰
||¦  «        }|||fS )Nr   rR   c                 ó|   •— t          j         ‰| ¦  «        ¦  «        t          j         ‰|¦  «        ¦  «        k    S rK   rL   rf	  s     €r3   rQ   zTpowerlaw_gen.fit.<locals>.fit_loc_scale_w_shape_gt_1.<locals>.interval_contains_rootE!  s;   ø€ åœ  ¨VÑ 4Ô 4Ñ5Ô5Ýœ7 < <°Ñ#7Ô#7Ñ8Ô8ò9ð :r5   r   r†   rà  )rM   r  rK  rf   r   r)   r  )rP   rè  rQ   rO   rô  r  r,   r-   rw  rª	  rC   rú  rß  r£	  r_	  s            €€€€€€r3   Úfit_loc_scale_w_shape_gt_1z4powerlaw_gen.fit.<locals>.fit_loc_scale_w_shape_gt_19!  s…  ø€ õ ”\ $§(¢(¡*¤*­r¬v¨gÑ6Ô6ˆFð —X’X‘Z”Z &Ñ(ˆEØ#Ð# FÑ+Ô+¨aÒ/Ð/ØŸš™œ eÑ+�Ø˜‘
�ð $Ð# FÑ+Ô+¨aÒ/Ð/ð:ð :ð :ð :ð :ð
 ˜a‘ZˆFð
 ˆAØ-Ð-¨f°fÑ=Ô=ð Ø¥"¤& Ò(Ð(ØŸ(š(™*œ* q™.�Ø�Q‘�ð .Ð-¨f°fÑ=Ô=ð Ø¥"¤& Ò(Ð(õ Ô'¨¸vÀvÐ>NÐOÑOÔOˆDå”,˜tœy­2¬6¨'Ñ2Ô2ˆCÝ”L  ¨4°Ñ!5Ô!5µr´vÑ>Ô>ˆEØÐ9˜i˜i¨¨c°5Ñ9Ô9ˆEØ˜#˜uÐ$Ð$r5   )r0   r>   r@   r¡  rM   Úuniquer  r’  Ú_reduce_funcrK  rH  rc  r÷   Úptpr  rf   r  )rB   rC   rD   r2   ró   rô   Úpenalized_nllf_argsÚpenalized_nllfrV   Úloc_lt1Ú	shape_lt1Úll_lt1Úloc_gt1Ú	shape_gt1Úll_gt1r-   rw  r¥	  r®	  Úfit_shape_lt1Úfit_shape_gt1rc	  rª	  ra	  rú  rß  r£	  r_	  r“  s    `                   @@@@@@@€r3   r@   zpowerlaw_gen.fitŸ   s™  øøøøøøøøø€ ðP �8Š8�J Ñ&Ô&ð 	4Ø•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3å�rŒy˜‰ŒÑÔ 1Ò$Ð$Ø•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3å%@ÀÀtØAEÀtñ&Mô &MÑ"ˆˆf�d˜Fà# d§n¢n°TÑ&:Ô&:Ð%<Ð=ÐØ×*Ò*Ð+>ÀÑCÔCÀAÔFˆð
 ÐØ—8’8‘:”: Ò$Ð$Ý" :¨q°!Ñ4Ô4Ð4ØÐ!¨$¯(ª(©*¬*¸¸v¹Ò*EÐ*EÝ" :¨q°!Ñ4Ô4Ð4àÐØ˜Š{ˆ{Ý ð "Fñ Gô Gð Gà�œ ™œÒ%Ð%ØH�Ý  ‘o”oÐ%ð	Hð 	Hð 	Hð	$ð 	$ð 	$ð Ð $Ð"2Ø�9˜T 4¨Ñ0Ô0°$¸Ð>Ð>ð Ðå”l 4§8¢8¡:¤:µ´¨wÑ7Ô7ˆGØÐB ) )¨D°'¸6Ñ"BÔ"BˆIØ#�^ Y°¸Ð$@À$ÑGÔGˆFõ ”l 4§8¢8¡:¤:°Ñ#6½¼Ñ?Ô?ˆGØÐB ) )¨D°'¸6Ñ"BÔ"BˆIØ#�^ Y°¸Ð$@À$ÑGÔGˆFà˜ŠˆØ  '¨6Ð1Ð1à  '¨6Ð1Ð1ð ÐØ�I˜d DÑ)Ô)ˆEØÐ:˜i˜i¨¨d°EÑ:Ô:ˆEØ˜$ Ð%Ð%ð
	%ð 	%ð 	%ð 	%ð 	%ð 	%ð 	%ð 	%ð	2ð 	2ð 	2ð
	:ð 	:ð 	:ð
	2ð 	2ð 	2ð 	2ð 	2ð 	2ð 	2ð 	2ð 	2ð	6ð 	6ð 	6ð 	6ð 	6ð 	6ð 	6ð 	6ð 	6ð 	6ð!	%ð !	%ð !	%ð !	%ð !	%ð !	%ð !	%ð !	%ð !	%ð !	%ðH Ð &¨A¢+ +Ø-Ð-Ñ/Ô/Ð/ØÐ F¨Q¢J JØ-Ð-Ñ/Ô/Ð/ð 3Ð2Ñ4Ô4ˆØ—’˜=¨$Ñ/Ô/ˆà2Ð2Ñ4Ô4ˆØ—’˜=¨$Ñ/Ô/ˆà�VÒÐ ¨aÔ 0°AÒ 5Ð 5Ø Ð Ø�fŠ_ˆ_ ¨qÔ!1°AÒ!5Ð!5Ø Ð à•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3r5   )r€   r�   r‚   rƒ   rh   ro   rÛ   rr   rà   r{   rv   rÿ   r   rï   r  rH   r	   r   r@   rÎ  rÏ  s   @r3   r’	  r’	  W   s3  ø€ € € € € ðð ð@Eð Eð Eðð ð ð.ð .ð .ðð ð ðð ð ðð ð ðð ð ðð ð ðOð Oð Oð%ð %ð %ð)ð )ð )ð )ð )ð ØÐ˜}ð 5ð ñ ô ðH4ð H4ð H4ð H4ñô ñ „_ðH4ð H4ð H4ð H4ð H4r5   r’	  r 	  c                   óP   — e Zd ZdZej        Zd„ Zd„ Zd„ Z	d„ Z
d„ Zd„ Zd„ Zd	„ Zd
S )Úpowerlognorm_genañ  A power log-normal continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `powerlognorm` is:

    .. math::

        f(x, c, s) = \frac{c}{x s} \phi(\log(x)/s)
                     (\Phi(-\log(x)/s))^{c-1}

    where :math:`\phi` is the normal pdf, and :math:`\Phi` is the normal cdf,
    and :math:`x > 0`, :math:`s, c > 0`.

    `powerlognorm` takes :math:`c` and :math:`s` as shape parameters.

    %(after_notes)s

    %(example)s

    c                 ó‚   — t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }||gS )Nr  Fr   r  r  re   )rB   r!  r2  s      r3   rh   zpowerlognorm_gen._shape_infoŽ!  r3  r5   c                 óT   — t          j        |                      |||¦  «        ¦  «        S rK   rÛ  ©rB   rn   r  r  s       r3   ro   zpowerlognorm_gen._pdf“!  r  r5   c                 ó   — t          j        |¦  «        t          j        |¦  «        z
  t          j        |¦  «        z
  t          t          j        |¦  «        |z  ¦  «        z   t          t          j        |¦  «         |z  ¦  «        |dz
  z  z   S r  ©rM   rí   rº   rÀ   rÀ	  s       r3   rÛ   zpowerlognorm_gen._logpdf–!  so   € Ý”�q‘	”	�BœF 1™IœIÑ%­¬¨q©	¬	Ñ1Ý�RœV A™YœY¨™]Ñ+Ô+ñ,å�bœf Q™iœi˜Z¨!™^Ñ,Ô,°°B±Ñ7ñ8ð 	9r5   c                 óV   — t          j        |                      |||¦  «        ¦  «         S rK   ra  rÀ	  s       r3   rr   zpowerlognorm_gen._cdf›!  rb  r5   c                 ó6   — |                       d|z
  ||¦  «        S r[   )r~   ©rB   rz   r  r  s       r3   r{   zpowerlognorm_gen._ppfž!  s   € Ø�yŠy˜˜Q™  1Ñ%Ô%Ð%r5   c                 óT   — t          j        |                      |||¦  «        ¦  «        S rK   r6  rÀ	  s       r3   rv   zpowerlognorm_gen._sf¡!  r7  r5   c                 óR   — t          t          j        |¦  «         |z  ¦  «        |z  S rK   rY  rÀ	  s       r3   rä   zpowerlognorm_gen._logsf¤!  s#   € Ý�RœV A™YœY˜J¨™NÑ+Ô+¨aÑ/Ð/r5   c                 óX   — t          j        t          |d|z  z  ¦  «         |z  ¦  «        S r[   rê  rÅ	  s       r3   r~   zpowerlognorm_gen._isf§!  s*   € ÝŒv•y  Q q¡S¡Ñ*Ô*Ð*¨QÑ.Ñ/Ô/Ð/r5   N)r€   r�   r‚   rƒ   r   r  r  rh   ro   rÛ   rr   r{   rv   rä   r~   r„   r5   r3   r½	  r½	  t!  s    € € € € € ðð ð. "Ô4€Mðð ð ð
-ð -ð -ð9ð 9ð 9ð
/ð /ð /ð&ð &ð &ð,ð ,ð ,ð0ð 0ð 0ð0ð 0ð 0ð 0ð 0r5   r½	  Úpowerlognormc                   óB   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
S )Úpowernorm_genah  A power normal continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `powernorm` is:

    .. math::

        f(x, c) = c \phi(x) (\Phi(-x))^{c-1}

    where :math:`\phi` is the normal pdf, :math:`\Phi` is the normal cdf,
    :math:`x` is any real, and :math:`c > 0` [1]_.

    `powernorm` takes ``c`` as a shape parameter for :math:`c`.

    %(after_notes)s

    References
    ----------
    .. [1] NIST Engineering Statistics Handbook, Section 1.3.6.6.13,
           https://www.itl.nist.gov/div898/handbook//eda/section3/eda366d.htm

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r  re   rg   s    r3   rh   zpowernorm_gen._shape_infoÊ!  r  r5   c                 óT   — |t          |¦  «        z  t          | ¦  «        |dz
  z  z  S r  ©r·   r½   r
  s      r3   ro   zpowernorm_gen._pdfÍ!  s(   € à•˜1‘”‰~¥¨A¨2¡¤°°3±Ñ!7Ñ8Ð8r5   c                 óx   — t          j        |¦  «        t          |¦  «        z   |dz
  t          | ¦  «        z  z   S r[   rÂ	  r
  s      r3   rÛ   zpowernorm_gen._logpdfÑ!  s3   € ÝŒv�a‰yŒy�<¨™?œ?Ñ*¨a°©cµ<ÀÀÑ3CÔ3CÑ-CÑCÐCr5   c                 óT   — t          j        |                      ||¦  «        ¦  «         S rK   ra  r
  s      r3   rr   zpowernorm_gen._cdfÔ!  s#   € Ý”˜Ÿš Q¨Ñ*Ô*Ñ+Ô+Ð+Ð+r5   c                 óJ   — t          t          d|z
  d|z  ¦  «        ¦  «         S r  )rÄ   r�  r  s      r3   r{   zpowernorm_gen._ppf×!  s%   € Ý�#˜c A™g s¨Q¡wÑ/Ô/Ñ0Ô0Ð0Ð0r5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   r6  r
  s      r3   rv   zpowernorm_gen._sfÚ!  rü  r5   c                 ó(   — |t          | ¦  «        z  S rK   rÉ   r
  s      r3   rä   zpowernorm_gen._logsfÝ!  s   € Ø•<  Ñ#Ô#Ñ#Ð#r5   c                 óp   — t          t          j        t          j        |¦  «        |z  ¦  «        ¦  «         S rK   )rÄ   rM   r´   rí   r  s      r3   r~   zpowernorm_gen._isfà!  s)   € Ý�"œ&¥¤¨¡¤¨Q¡Ñ/Ô/Ñ0Ô0Ð0Ð0r5   N)r€   r�   r‚   rƒ   rh   ro   rÛ   rr   r{   rv   rä   r~   r„   r5   r3   rË	  rË	  ®!  sœ   € € € € € ðð ð6Eð Eð Eð9ð 9ð 9ðDð Dð Dð,ð ,ð ,ð1ð 1ð 1ð)ð )ð )ð$ð $ð $ð1ð 1ð 1ð 1ð 1r5   rË	  Ú	powernormc                   óD   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	dd	„Z
d
„ ZdS )Ú	rdist_gena/  An R-distributed (symmetric beta) continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `rdist` is:

    .. math::

        f(x, c) = \frac{(1-x^2)^{c/2-1}}{B(1/2, c/2)}

    for :math:`-1 \le x \le 1`, :math:`c > 0`. `rdist` is also called the
    symmetric beta distribution: if B has a `beta` distribution with
    parameters (c/2, c/2), then X = 2*B - 1 follows a R-distribution with
    parameter c.

    `rdist` takes ``c`` as a shape parameter for :math:`c`.

    This distribution includes the following distribution kernels as
    special cases::

        c = 2:  uniform
        c = 3:  `semicircular`
        c = 4:  Epanechnikov (parabolic)
        c = 6:  quartic (biweight)
        c = 8:  triweight

    %(after_notes)s

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r  re   rg   s    r3   rh   zrdist_gen._shape_info	"  r  r5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   rÛ  r
  s      r3   ro   zrdist_gen._pdf"  rV  r5   c                 ó~   — t          j        d¦  «         t                               |dz   dz  |dz  |dz  ¦  «        z   S râ  )rM   rí   rk  rÛ   r
  s      r3   rÛ   zrdist_gen._logpdf"  s7   € Ý”�q‘	”	ˆz�DŸLšL¨!¨a©%°©°A°a±C¸¸1¹Ñ=Ô=Ñ=Ð=r5   c                 óR   — t                                |dz   dz  |dz  |dz  ¦  «        S r-  rç  r
  s      r3   rr   zrdist_gen._cdf"  s(   € Ý�yŠy˜!˜a™% ™ A a¡C¨¨1©Ñ-Ô-Ð-r5   c                 óR   — t                                |dz   dz  |dz  |dz  ¦  «        S r-  rà  r
  s      r3   rv   zrdist_gen._sf"  s(   € Ý�xŠx˜˜Q™ ™	 1 Q¡3¨¨!©Ñ,Ô,Ð,r5   c                 óR   — dt                                ||dz  |dz  ¦  «        z  dz
  S râ  )rk  r{   r  s      r3   r{   zrdist_gen._ppf"  s*   € Ø•—’˜1˜a ™c 1 Q¡3Ñ'Ô'Ñ'¨!Ñ+Ð+r5   Nc                 óH   — d|                      |dz  |dz  |¦  «        z  dz
  S râ  rj  rµ  s       r3   rÖ   zrdist_gen._rvs"  s,   € Ø�<×$Ò$ Q q¡S¨!¨A©#¨tÑ4Ô4Ñ4°qÑ8Ð8r5   c                 ó†   — d|dz  z
  t          j        |dz   dz  |dz  ¦  «        z  }|t          j        d|dz  ¦  «        z  S )Nr   rR   r†   r³   r‘   rT  )rB   r_   r  Ú	numerators       r3   rÿ   zrdist_gen._munp"  sG   € Ø˜!˜a™%‘[¥B¤G¨Q°©W¸©M¸1¸s¹7Ñ$CÔ$CÑCˆ	Ø�2œ7 6¨1¨r©6Ñ2Ô2Ñ2Ð2r5   r   )r€   r�   r‚   rƒ   rh   ro   rÛ   rr   rv   r{   rÖ   rÿ   r„   r5   r3   r×	  r×	  ç!  sŸ   € € € € € ð ð  ðBEð Eð Eð*ð *ð *ð>ð >ð >ð.ð .ð .ð-ð -ð -ð,ð ,ð ,ð9ð 9ð 9ð 9ð3ð 3ð 3ð 3ð 3r5   r×	  r<  Úrdistc                   óª   ‡ — e Zd ZdZej        Zd„ Zdd„Zd„ Z	d„ Z
d„ Zd„ Zd	„ Zd
„ Zd„ Zd„ Zd„ Ze eed¬¦  «        ˆ fd„¦   «         ¦   «         Zˆ xZS )Úrayleigh_gena7  A Rayleigh continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `rayleigh` is:

    .. math::

        f(x) = x \exp(-x^2/2)

    for :math:`x \ge 0`.

    `rayleigh` is a special case of `chi` with ``df=2``.

    %(after_notes)s

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   zrayleigh_gen._shape_info?"  r£   r5   Nc                 ó<   — t                                d||¬¦  «        S )NrR   rÕ  r  rÓ   s      r3   rÖ   zrayleigh_gen._rvsB"  s   € Ý�wŠw�q˜t°,ˆwÑ?Ô?Ð?r5   c                 óP   — t          j        |                      |¦  «        ¦  «        S rK   rÛ  ©rB   rò  s     r3   ro   zrayleigh_gen._pdfE"  rž  r5   c                 ó<   — t          j        |¦  «        d|z  |z  z
  S r  r.  rç	  s     r3   rÛ   zrayleigh_gen._logpdfI"  s   € ÝŒv�a‰yŒy˜3 ™7 Q™;Ñ&Ð&r5   c                 ó8   — t          j        d|dz  z  ¦  «         S r‘  r=  rç	  s     r3   rr   zrayleigh_gen._cdfL"  s   € Ý”˜  1¡™Ñ%Ô%Ð%Ð%r5   c                 óV   — t          j        dt          j        | ¦  «        z  ¦  «        S ©Nr  )rM   rü   rt   r£  r­   s     r3   r{   zrayleigh_gen._ppfO"  s!   € ÝŒw�r�BœH a R™LœLÑ(Ñ)Ô)Ð)r5   c                 óP   — t          j        |                      |¦  «        ¦  «        S rK   r6  rç	  s     r3   rv   zrayleigh_gen._sfR"  s   € ÝŒv�d—k’k !‘n”nÑ%Ô%Ð%r5   c                 ó   — d|z  |z  S )Nrî  r„   rç	  s     r3   rä   zrayleigh_gen._logsfU"  s   € Ø�a‰x˜!‰|Ðr5   c                 óT   — t          j        dt          j        |¦  «        z  ¦  «        S rë	  )rM   rü   rí   r­   s     r3   r~   zrayleigh_gen._isfX"  s   € ÝŒw�r�BœF 1™IœI‘~Ñ&Ô&Ð&r5   c                 ó  — dt           j        z
  }t          j        t           j        dz  ¦  «        |dz  dt           j        dz
  z  t          j        t           j        ¦  «        z  |dz  z  dt           j        z  |z  d|dz  z  z
  fS )Nr   rR   rƒ  r¼  r‚  r(  r*  r+  s     r3   r   zrayleigh_gen._stats["  sp   € Ø•"”%‰iˆÝ”�œ˜a™Ñ Ô Ø�A‘Ø•2”5˜‘7‘�BœG¥B¤E™NœNÑ*¨3°©8Ñ3Ø•"”%‘˜‘˜B˜s A™v™IÑ%ð'ð 	'r5   c                 óL   — t           dz  dz   dt          j        d¦  «        z  z
  S )Nr³   r   r‘   rR   r  rg   s    r3   rï   zrayleigh_gen._entropyb"  s!   € Ý�c‰z˜A‰~ ¥B¤F¨1¡I¤I¡Ñ-Ð-r5   aú          Notes specifically for ``rayleigh.fit``: If the location is fixed with
        the `floc` parameter, this method uses an analytical formula to find
        the scale.  Otherwise, this function uses a numerical root finder on
        the first order conditions of the log-likelihood function to find the
        MLE.  Only the (optional) `loc` parameter is used as the initial guess
        for the root finder; the `scale` parameter and any other parameters
        for the optimizer are ignored.

rð   c                 óÐ  •‡— |                      dd¦  «        r t          ¦   «         j        ‰g|¢R i |¤ŽS t          | ‰||¦  «        \  Š}}ˆfd„}ˆfd„}|fˆfd„	}|�Dt	          j        ‰|z
  dk    ¦  «        rt          ddt          j        ¬	¦  «        ‚| ||¦  «        fS |                     d
¦  «        }	|	€|  	                    ‰¦  «        d         }	|€|n|}
t	          j
        t	          j        ‰¦  «        t          j         ¦  «        }t          |
|¦  «        }t          j        |
||f¬¦  «        }|j        st!          |j        ¦  «        ‚|j        }|p
 ||¦  «        }||fS )Nr  Fc                 ód   •— t          j        ‰| z
  dz  ¦  «        dt          ‰¦  «        z  z  dz  S r´  )rM   r¢  r¡  )r,   rC   s    €r3   Ú	scale_mlez#rayleigh_gen.fit.<locals>.scale_mlet"  s2   ø€ õ ”F˜D 3™J¨1Ñ,Ñ-Ô-°µS¸±Y´Y±Ñ?ÀBÑFÐFr5   c                 óÈ   •— ‰| z
  }|                      ¦   «         }|dz                        ¦   «         }d|z                        ¦   «         }||dt          ‰¦  «        z  z  |z  z
  S râ  )r¢  r¡  )r,   ræ  rY  r_  Ús3rC   s        €r3   Úloc_mlez!rayleigh_gen.fit.<locals>.loc_mley"  s\   ø€ ð ˜‘ˆBØ—’‘”ˆBØ�a‘%—’‘”ˆBØ�B‘$—’‘”ˆBØ˜˜A�c $™iœi™KÑ(¨Ñ+Ñ+Ð+r5   c                 ór   •— ‰| z
  }|                      ¦   «         |dz  d|z                        ¦   «         z  z
  S râ  )r¢  )r,   r-   ræ  rC   s      €r3   Úloc_mle_scale_fixedz-rayleigh_gen.fit.<locals>.loc_mle_scale_fixed‚"  s6   ø€ ð ˜‘ˆBØ—6’6‘8”8˜e Q™h¨!¨B©$¯ª©¬Ñ5Ñ5Ð5r5   r   Úrayleighr   rœ  r,   rà  )r0   r>   r@   r  rM   r   rH  rf   r:   r’  r  rK  rW   r   r)   r  rT   Úflagr  )rB   rC   rD   r2   ró   rô   ró	  rö	  rø	  Úloc0rF   rP   rO   r¶  r,   r-   r“  s    `              €r3   r@   zrayleigh_gen.fite"  sÇ  øø€ ð �8Š8�J Ñ&Ô&ð 	4Ø•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3Ý8¸¸tØ9=¸tñEô EÑˆˆd�Fð	Gð 	Gð 	Gð 	Gð 	Gð
	,ð 	,ð 	,ð 	,ð 	,ð ,2ð 	6ð 	6ð 	6ð 	6ð 	6ð 	6ð ÐåŒv�d˜T‘k QÒ&Ñ'Ô'ð -Ý" :°Q½b¼fÐEÑEÔEÐEà˜Y˜Y t™_œ_Ð,Ð,ð �xŠx˜‰ŒˆØˆ<à—>’> $Ñ'Ô'¨Ô*ˆDà˜ˆgˆgÐ-@ˆÝ”�bœf T™lœl­R¬V¨GÑ4Ô4ˆÝ" 3¨Ñ/Ô/ˆÝÔ" 3°¸Ð0@ÐAÑAÔAˆØŒ}ð 	+Ý  ¤Ñ*Ô*Ð*ØŒhˆØÐ(˜)˜) C™.œ.ˆØ�EˆzÐr5   r   )r€   r�   r‚   rƒ   r   r  r  rh   rÖ   ro   rÛ   rr   r{   rv   rä   r~   r   rï   rH   r	   r@   rÎ  rÏ  s   @r3   rã	  rã	  '"  s,  ø€ € € € € ðð ð* "Ô4€Mðð ð ð@ð @ð @ð @ð'ð 'ð 'ð'ð 'ð 'ð&ð &ð &ð*ð *ð *ð&ð &ð &ðð ð ð'ð 'ð 'ð'ð 'ð 'ð.ð .ð .ð ØÐ˜}ð 5.ð /ñ /ô /ð/ð /ð /ð /ñ/ô /ñ „_ð/ð /ð /ð /ð /r5   rã	  rù	  c                   óŒ   ‡ — e Zd ZdZd„ Zd„ Zˆ fd„Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Zd„ ZdZ eee¬¦  «        ˆ fd„¦   «         Zˆ xZS )Úreciprocal_gena,  A loguniform or reciprocal continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for this class is:

    .. math::

        f(x, a, b) = \frac{1}{x \log(b/a)}

    for :math:`a \le x \le b`, :math:`b > a > 0`. This class takes
    :math:`a` and :math:`b` as shape parameters.

    %(after_notes)s

    %(example)s

    This doesn't show the equal probability of ``0.01``, ``0.1`` and
    ``1``. This is best when the x-axis is log-scaled:

    >>> import numpy as np
    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots(1, 1)
    >>> ax.hist(np.log10(r))
    >>> ax.set_ylabel("Frequency")
    >>> ax.set_xlabel("Value of random variable")
    >>> ax.xaxis.set_major_locator(plt.FixedLocator([-2, -1, 0]))
    >>> ticks = ["$10^{{ {} }}$".format(i) for i in [-2, -1, 0]]
    >>> ax.set_xticklabels(ticks)  # doctest: +SKIP
    >>> plt.show()

    This random variable will be log-uniform regardless of the base chosen for
    ``a`` and ``b``. Let's specify with base ``2`` instead:

    >>> rvs = %(name)s(2**-2, 2**0).rvs(size=1000)

    Values of ``1/4``, ``1/2`` and ``1`` are equally likely with this random
    variable.  Here's the histogram:

    >>> fig, ax = plt.subplots(1, 1)
    >>> ax.hist(np.log2(rvs))
    >>> ax.set_ylabel("Frequency")
    >>> ax.set_xlabel("Value of random variable")
    >>> ax.xaxis.set_major_locator(plt.FixedLocator([-2, -1, 0]))
    >>> ticks = ["$2^{{ {} }}$".format(i) for i in [-2, -1, 0]]
    >>> ax.set_xticklabels(ticks)  # doctest: +SKIP
    >>> plt.show()

    c                 ó   — |dk    ||k    z  S r®  r„   rÕ  s      r3   r`   zreciprocal_gen._argcheck×"  ó   € Ø�A’˜!˜aš%Ñ Ð r5   c                 ó‚   — t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }||gS rd  re   re  s      r3   rh   zreciprocal_gen._shape_infoÚ"  rh  r5   c                 óè   •— t          |t          ¦  «        r|                     ¦   «         }t          ¦   «                              |t          j        |¦  «        t          j        |¦  «        f¬¦  «        S ©NrJ  ©r<   r(   r�  r>   r’  rM   rK  rc  r  s     €r3   r’  zreciprocal_gen._fitstartß"  sV   ø€ Ý�d�LÑ)Ô)ð 	$Ø—>’>Ñ#Ô#ˆDå‰wŒw× Ò  ­R¬V°D©\¬\½2¼6À$¹<¼<Ð,HÐ ÑIÔIÐIr5   c                 ó
   — ||fS rK   r„   rÕ  s      r3   r“   zreciprocal_gen._get_supportå"  r   r5   c                 óT   — t          j        |                      |||¦  «        ¦  «        S rK   rÛ  rq  s       r3   ro   zreciprocal_gen._pdfè"  rÜ  r5   c                 ó¤   — t          j        |¦  «         t          j        t          j        |¦  «        t          j        |¦  «        z
  ¦  «        z
  S rK   r.  rq  s       r3   rÛ   zreciprocal_gen._logpdfì"  s6   € Ý”�q‘	”	ˆz�BœF¥2¤6¨!¡9¤9­r¬v°a©y¬yÑ#8Ñ9Ô9Ñ9Ð9r5   c                 ó¨   — t          j        |¦  «        t          j        |¦  «        z
  t          j        |¦  «        t          j        |¦  «        z
  z  S rK   r.  rq  s       r3   rr   zreciprocal_gen._cdfï"  s7   € Ý”�q‘	”	�"œ& ™)œ)Ñ#­¬¨q©	¬	µB´F¸1±I´IÑ(=Ñ>Ð>r5   c                 ó¨   — t          j        t          j        |¦  «        |t          j        |¦  «        t          j        |¦  «        z
  z  z   ¦  «        S rK   ©rM   r´   rí   r€  s       r3   r{   zreciprocal_gen._ppfò"  s9   € ÝŒv•b”f˜Q‘i”i !¥R¤V¨A¡Y¤Yµ´¸±´Ñ%:Ñ";Ñ;Ñ<Ô<Ð<r5   c                 ó&  — dt          j        |¦  «        t          j        |¦  «        z
  z  |z  }t          j        t          j        t	          |t          j        |¦  «        z  |t          j        |¦  «        z  ¦  «        ¦  «        ¦  «        }||z  S r[   )rM   rí   r–  r´   Ú	_log_diff)rB   r_   rˆ   r‰   r·  r¸  s         r3   rÿ   zreciprocal_gen._munpõ"  sj   € Ø•"”&˜‘)”)�bœf Q™iœiÑ'Ñ(¨1Ñ,ˆÝŒW•R”V�I a­"¬&°©)¬)¡m°Qµr´v¸a±y´y±[ÑAÔAÑBÔBÑCÔCˆØ�B‰wˆr5   c                 óÒ   — dt          j        |¦  «        t          j        |¦  «        z   z  t          j        t          j        |¦  «        t          j        |¦  «        z
  ¦  «        z   S r  r.  rÕ  s      r3   rï   zreciprocal_gen._entropyú"  sF   € Ø•B”F˜1‘I”I¥¤ q¡	¤	Ñ)Ñ*­R¬VµB´F¸1±I´IÅÄÀqÁ	Ä	Ñ4IÑ-JÔ-JÑJÐJr5   z“        `loguniform`/`reciprocal` is over-parameterized. `fit` automatically
         fixes `scale` to 1 unless `fscale` is provided by the user.

rð   c                 ón   •— |                      dd¦  «        } t          ¦   «         j        |g|¢R d|i|¤ŽS )Nrô   r   )r0   r>   r@   )rB   rC   rD   r2   rô   r“  s        €r3   r@   zreciprocal_gen.fit#  sA   ø€ à—’˜( AÑ&Ô&ˆØ�u‰wŒwŒ{˜4Ð> $Ð>Ð>Ð>¨vÐ>¸Ð>Ð>Ð>r5   )r€   r�   r‚   rƒ   r`   rh   r’  r“   ro   rÛ   rr   r{   rÿ   rï   Úfit_noter	   r   r@   rÎ  rÏ  s   @r3   rý	  rý	  £"  s  ø€ € € € € ð2ð 2ðf!ð !ð !ðð ð ð
Jð Jð Jð Jð Jðð ð ð-ð -ð -ð:ð :ð :ð?ð ?ð ?ð=ð =ð =ðð ð ð
Kð Kð KðL€Hð Ð˜}°HÐ=Ñ=Ô=ð?ð ?ð ?ð ?ñ >Ô=ð?ð ?ð ?ð ?ð ?r5   rý	  Ú
loguniformÚ
reciprocalc                   ó>   — e Zd ZdZd„ Zd„ Zd
d„Zd„ Zd„ Zd„ Z	d	„ Z
dS )Úrice_gena  A Rice continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `rice` is:

    .. math::

        f(x, b) = x \exp(- \frac{x^2 + b^2}{2}) I_0(x b)

    for :math:`x >= 0`, :math:`b > 0`. :math:`I_0` is the modified Bessel
    function of order zero (`scipy.special.i0`).

    `rice` takes ``b`` as a shape parameter for :math:`b`.

    %(after_notes)s

    The Rice distribution describes the length, :math:`r`, of a 2-D vector with
    components :math:`(U+u, V+v)`, where :math:`U, V` are constant, :math:`u,
    v` are independent Gaussian random variables with standard deviation
    :math:`s`.  Let :math:`R = \sqrt{U^2 + V^2}`. Then the pdf of :math:`r` is
    ``rice.pdf(x, R/s, scale=s)``.

    %(example)s

    c                 ó   — |dk    S r®  r„   ©rB   r‰   s     r3   r`   zrice_gen._argcheck,#  r¯  r5   c                 ó@   — t          dddt          j        fd¦  «        gS )Nr‰   Fr   rd   re   rg   s    r3   rh   zrice_gen._shape_info/#  r²  r5   Nc                 óº   — |t          j        d¦  «        z  |                     d|z   ¬¦  «        z   }t          j        ||z                       d¬¦  «        ¦  «        S )NrR   )rR   r  r   rû  )rM   rü   rÒ   r¢  )rB   r‰   rÔ   rÕ   r˜  s        r3   rÖ   zrice_gen._rvs2#  sO   € à�bŒg�a‰jŒj‰L˜<×7Ò7¸TÀD¹[Ð7ÑIÔIÑIˆÝŒw˜˜!™—y’y a�yÑ(Ô(Ñ)Ô)Ð)r5   c                 óv   — t          j        t          j        |¦  «        dt          j        |¦  «        ¦  «        S r  )rt   ÚchndtrrM   rá  r‚  s      r3   rr   zrice_gen._cdf7#  s&   € ÝŒy�œ 1™œ q­"¬)°A©,¬,Ñ7Ô7Ð7r5   c           	      óv   — t          j        t          j        |dt          j        |¦  «        ¦  «        ¦  «        S r  )rM   rü   rt   Úchndtrixrá  r�  s      r3   r{   zrice_gen._ppf:#  s(   € ÝŒw•r”{ 1 a­¬°1©¬Ñ6Ô6Ñ7Ô7Ð7r5   c                 óz   — |t          j        ||z
   ||z
  z  dz  ¦  «        z  t          j        ||z  ¦  «        z  S r;  )rM   r´   rt   Úi0er‚  s      r3   ro   zrice_gen._pdf=#  s=   € ð •2”6˜A˜a™C˜& ! A¡#™, sÑ*Ñ+Ô+Ñ+­b¬f°Q°q±S©k¬kÑ9Ð9r5   c                 ó´   — |dz  }d|z   }||z  dz  }d|z  t          j        | ¦  «        z  t          j        |¦  «        z  t          j        |d|¦  «        z  S rÔ  )rM   r´   rt   rÖ  rý  )rB   r_   r‰   Únd2Ún1rz  s         r3   rÿ   zrice_gen._munpF#  s_   € Ø�‰eˆØ�‰WˆØˆq‰S�‰WˆØ�c‘
�RœV R C™[œ[Ñ(­2¬8°B©<¬<Ñ7Ý”	˜"˜a Ñ$Ô$ñ%ð 	&r5   r   )r€   r�   r‚   rƒ   r`   rh   rÖ   rr   r{   ro   rÿ   r„   r5   r3   r
  r
  #  s�   € € € € € ðð ð8ð ð ðDð Dð Dð*ð *ð *ð *ð
8ð 8ð 8ð8ð 8ð 8ð:ð :ð :ð&ð &ð &ð &ð &r5   r
  Úricec                   óŒ   — e Zd ZdZ eed¬¦  «        d„ ¦   «         Zd„ Zd„ Zd„ Z	d„ Z
ed	„ ¦   «         Zd
„ Zd„ Zd„ Zdd„Zd„ ZdS )Úirwinhall_gena\
  An Irwin-Hall (Uniform Sum) continuous random variable.

    An `Irwin-Hall <https://en.wikipedia.org/wiki/Irwin-Hall_distribution/>`_
    continuous random variable is the sum of :math:`n` independent
    standard uniform random variables [1]_ [2]_.

    %(before_notes)s

    Notes
    -----
    Applications include `Rao's Spacing Test
    <https://jammalam.faculty.pstat.ucsb.edu/html/favorite/test.htm>`_,
    a more powerful alternative to the Rayleigh test
    when the data are not unimodal, and radar [3]_.

    Conveniently, the pdf and cdf are the :math:`n`-fold convolution of
    the ones for the standard uniform distribution, which is also the
    definition of the cardinal B-splines of degree :math:`n-1`
    having knots evenly spaced from :math:`1` to :math:`n` [4]_ [5]_.

    The Bates distribution, which represents the *mean* of statistically
    independent, uniformly distributed random variables, is simply the
    Irwin-Hall distribution scaled by :math:`1/n`. For example, the frozen
    distribution ``bates = irwinhall(10, scale=1/10)`` represents the
    distribution of the mean of 10 uniformly distributed random variables.
    
    %(after_notes)s

    References
    ----------
    .. [1] P. Hall, "The distribution of means for samples of size N drawn
            from a population in which the variate takes values between 0 and 1,
            all such values being equally probable",
            Biometrika, Volume 19, Issue 3-4, December 1927, Pages 240-244,
            :doi:`10.1093/biomet/19.3-4.240`.
    .. [2] J. O. Irwin, "On the frequency distribution of the means of samples
            from a population having any law of frequency with finite moments,
            with special reference to Pearson's Type II,
            Biometrika, Volume 19, Issue 3-4, December 1927, Pages 225-239,
            :doi:`0.1093/biomet/19.3-4.225`.
    .. [3] K. Buchanan, T. Adeyemi, C. Flores-Molina, S. Wheeland and D. Overturf, 
            "Sidelobe behavior and bandwidth characteristics
            of distributed antenna arrays,"
            2018 United States National Committee of
            URSI National Radio Science Meeting (USNC-URSI NRSM),
            Boulder, CO, USA, 2018, pp. 1-2.
            https://www.usnc-ursi-archive.org/nrsm/2018/papers/B15-9.pdf.
    .. [4] Amos Ron, "Lecture 1: Cardinal B-splines and convolution operators", p. 1
            https://pages.cs.wisc.edu/~deboor/887/lec1new.pdf.
    .. [5] Trefethen, N. (2012, July). B-splines and convolution. Chebfun. 
            Retrieved April 30, 2024, from http://www.chebfun.org/examples/approx/BSplineConv.html.

    %(example)s
    zÞ        Raises a ``NotImplementedError`` for the Irwin-Hall distribution because
        the generic `fit` implementation is unreliable and no custom implementation
        is available. Consider using `scipy.stats.fit`.

rð   c                 ó$   — d}t          |¦  «        ‚)Nz’The generic `fit` implementation is unreliable for this distribution, and no custom implementation is available. Consider using `scipy.stats.fit`.)r�	  )rB   rC   rD   r2   Ú	fit_notess        r3   r@   zirwinhall_gen.fitˆ#  s   € ð
9ˆ	õ " )Ñ,Ô,Ð,r5   c                 óX   — |dk    t          |¦  «        z  t          j        |¦  «        z  S r®  )r   rM   Ú	isrealobjr^   s     r3   r`   zirwinhall_gen._argcheck’#  s$   € Ø�A’� Q™œÑ'­"¬,°q©/¬/Ñ9Ð9r5   c                 ó
   — d|fS r®  r„   r^   s     r3   r“   zirwinhall_gen._get_support•#  r   r5   c                 ó@   — t          dddt          j        fd¦  «        gS rc   re   rg   s    r3   rh   zirwinhall_gen._shape_info˜#  ri   r5   c                 ó^   — d„ } t          j        |t           j        g¬¦  «        ||¦  «        S )Nc                 ól   — t          j        || z   |d¬¦  «        t          j        || z   |d¬¦  «        z  S )NT)Úexact)rt   Ú	stirling2r„  )r  r_   s     r3   Úvmunpz"irwinhall_gen._munp.<locals>.vmunpž#  s<   € Ý”L  5¡¨!°4Ð8Ñ8Ô8Ý”g˜a ™g q°Ð5Ñ5Ô5ñ6ð 7r5   rR  ©rM   rL  rV  )rB   r  r_   r-
  s       r3   rÿ   zirwinhall_gen._munp›#  s8   € ð	7ð 	7ð 	7ð
 8�rŒ|˜E­2¬:¨,Ð7Ñ7Ô7¸¸qÑAÔAÐAr5   c                 óX   — t          j        | dz   ¦  «        }t          j        |¦  «        S r[   )rM   rM  r   Úbasis_element)r_   r˜  s     r3   Ú	_cardbsplzirwinhall_gen._cardbspl¥#  s$   € åŒI�a˜‘c‰NŒNˆÝÔ$ QÑ'Ô'Ð'r5   c                 ód   ‡ — ˆ fd„} t          j        |t           j        g¬¦  «        ||¦  «        S )Nc                 ó@   •—  ‰                      |¦  «        | ¦  «        S rK   )r1
  ©rn   r_   rB   s     €r3   Úvpdfz irwinhall_gen._pdf.<locals>.vpdf«#  s   ø€ Ø$�4—>’> !Ñ$Ô$ QÑ'Ô'Ð'r5   rR  r.
  )rB   rn   r_   r5
  s   `   r3   ro   zirwinhall_gen._pdfª#  sA   ø€ ð	(ð 	(ð 	(ð 	(ð 	(à6�rŒ|˜D­"¬*¨Ð6Ñ6Ô6°q¸!Ñ<Ô<Ð<r5   c                 ód   ‡ — ˆ fd„} t          j        |t           j        g¬¦  «        ||¦  «        S )Nc                 ód   •—  ‰                      |¦  «                             ¦   «         | ¦  «        S rK   ©r1
  Úantiderivativer4
  s     €r3   Úvcdfz irwinhall_gen._cdf.<locals>.vcdf°#  s+   ø€ Ø5�4—>’> !Ñ$Ô$×3Ò3Ñ5Ô5°aÑ8Ô8Ð8r5   rR  r.
  )rB   rn   r_   r:
  s   `   r3   rr   zirwinhall_gen._cdf¯#  sA   ø€ ð	9ð 	9ð 	9ð 	9ð 	9à6�rŒ|˜D­"¬*¨Ð6Ñ6Ô6°q¸!Ñ<Ô<Ð<r5   c                 ód   ‡ — ˆ fd„} t          j        |t           j        g¬¦  «        ||¦  «        S )Nc                 ój   •—  ‰                      |¦  «                             ¦   «         || z
  ¦  «        S rK   r8
  r4
  s     €r3   Úvsfzirwinhall_gen._sf.<locals>.vsfµ#  s/   ø€ Ø5�4—>’> !Ñ$Ô$×3Ò3Ñ5Ô5°a¸±cÑ:Ô:Ð:r5   rR  r.
  )rB   rn   r_   r=
  s   `   r3   rv   zirwinhall_gen._sf´#  sA   ø€ ð	;ð 	;ð 	;ð 	;ð 	;à5�rŒ|˜C­¬¨Ð5Ñ5Ô5°a¸Ñ;Ô;Ð;r5   Nc                 ó@   — t           dd„¦   «         } ||||¬¦  «        S )Nc                 óÄ   — t          j        | ¦  «                             t          ¦  «        } |€| fn| g|¢R }|                     |¬¦  «                             d¬¦  «        S )Nr  r   rû  )rM   r  rn  rÈ  r  r¢  )r_   rÔ   rÕ   Úusizes       r3   Ú_rvs1z!irwinhall_gen._rvs.<locals>._rvs1º#  s\   € å”˜‘”×"Ò"¥3Ñ'Ô'ˆAØ ˜L�Q�D�D¨q¨j°4¨j¨jˆEØ×'Ò'¨UÐ'Ñ3Ô3×7Ò7¸QÐ7Ñ?Ô?Ð?r5   rÕ  r   )r   )rB   r_   rÔ   rÕ   rD   rA
  s         r3   rÖ   zirwinhall_gen._rvs¹#  s>   € Ý	#ð	@ð 	@ð 	@ñ 
$Ô	#ð	@ð ˆu�Q˜T°Ð=Ñ=Ô=Ð=r5   c                 ó&   — |dz  |dz  ddd|z  z  fS )NrR   r½  r   r¬  rC  r„   r^   s     r3   r   zirwinhall_gen._statsÁ#  s#   € ð �‰s�A�b‘D˜!˜R  1¡™XÐ%Ð%r5   r   )r€   r�   r‚   rƒ   r
   r   r@   r`   r“   rh   rÿ   rƒ  r1
  ro   rr   rv   rÖ   r   r„   r5   r3   r"
  r"
  P#  s  € € € € € ð5ð 5ðn  Ð ð 6?ð @ñ @ô @ð-ð -ñ	@ô @ð-ð:ð :ð :ðð ð ðCð Cð CðBð Bð Bð ð(ð (ñ „\ð(ð=ð =ð =ð
=ð =ð =ð
<ð <ð <ð
>ð >ð >ð >ð&ð &ð &ð &ð &r5   r"
  Ú	irwinhallc                   ó8   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd	d„Z	dS )
Úrecipinvgauss_gena­  A reciprocal inverse Gaussian continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `recipinvgauss` is:

    .. math::

        f(x, \mu) = \frac{1}{\sqrt{2\pi x}}
                    \exp\left(\frac{-(1-\mu x)^2}{2\mu^2x}\right)

    for :math:`x \ge 0`.

    `recipinvgauss` takes ``mu`` as a shape parameter for :math:`\mu`.

    %(after_notes)s

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS rQ  re   rg   s    r3   rh   zrecipinvgauss_gen._shape_infoç#  r¤  r5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   rÛ  rX  s      r3   ro   zrecipinvgauss_gen._pdfê#  s"   € õ Œv�d—l’l 1 bÑ)Ô)Ñ*Ô*Ð*r5   c                 óL   — t          |dk    ||fd„ t          j         ¬¦  «        S )Nr   c                 ó‚   — d|| z  z
  dz   d| z  |dz  z  z  dt          j        dt           j        z  | z  ¦  «        z  z
  S )Nr   r³   rR   r‘   rì   )rn   r@  s     r3   rå  z+recipinvgauss_gen._logpdf.<locals>.<lambda>ñ#  sH   € ¨1¨r°!©t©8°c©/Ð)9¸Q¸q¹SÀÀSÁ¹[Ñ)IØ+.­r¬v°a½¼±g¸a±iÑ/@Ô/@Ñ+@ñ*A€ r5   rÿ  r  rX  s      r3   rÛ   zrecipinvgauss_gen._logpdfï#  s8   € Ý˜!˜aš% ! R ðBð Bå%'¤V Gð-ñ -ô -ð 	-r5   c                 óÎ   — d|z  |z
  }d|z  |z   }dt          j        |¦  «        z  }t          | |z  ¦  «        t          j        d|z  ¦  «        t          | |z  ¦  «        z  z
  S ©Nr†   r³   ©rM   rü   r½   r´   ©rB   rn   r@  r7	  r9	  Úisqxs         r3   rr   zrecipinvgauss_gen._cdfõ#  se   € Ø�2‰v˜‰zˆØ�2‰v˜‰zˆØ•2”7˜1‘:”:‰~ˆÝ˜$˜˜t™Ñ$Ô$¥r¤v¨c°"©f¡~¤~µiÀÀÀdÁ
Ñ6KÔ6KÑ'KÑKÐKr5   c                 óÌ   — d|z  |z
  }d|z  |z   }dt          j        |¦  «        z  }t          ||z  ¦  «        t          j        d|z  ¦  «        t          | |z  ¦  «        z  z   S rK
  rL
  rM
  s         r3   rv   zrecipinvgauss_gen._sfû#  sc   € Ø�2‰v˜‰zˆØ�2‰v˜‰zˆØ•2”7˜1‘:”:‰~ˆÝ˜˜d™Ñ#Ô#¥b¤f¨S°©V¡n¤nµYÀ¸uÀT¹zÑ5JÔ5JÑ&JÑJÐJr5   Nc                 ó8   — d|                      |d|¬¦  «        z  S rS  rT  rV  s       r3   rÖ   zrecipinvgauss_gen._rvs$  s"   € Ø�<×$Ò$ R¨°4Ð$Ñ8Ô8Ñ8Ð8r5   r   )
r€   r�   r‚   rƒ   rh   ro   rÛ   rr   rv   rÖ   r„   r5   r3   rE
  rE
  Ð#  s†   € € € € € ðð ð,Fð Fð Fð+ð +ð +ð
-ð -ð -ðLð Lð LðKð Kð Kð9ð 9ð 9ð 9ð 9ð 9r5   rE
  Úrecipinvgaussc                   óD   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zdd„Z	d	„ Z
d
„ ZdS )Úsemicircular_gena  A semicircular continuous random variable.

    %(before_notes)s

    See Also
    --------
    rdist

    Notes
    -----
    The probability density function for `semicircular` is:

    .. math::

        f(x) = \frac{2}{\pi} \sqrt{1-x^2}

    for :math:`-1 \le x \le 1`.

    The distribution is a special case of `rdist` with `c = 3`.

    %(after_notes)s

    References
    ----------
    .. [1] "Wigner semicircle distribution",
           https://en.wikipedia.org/wiki/Wigner_semicircle_distribution

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   zsemicircular_gen._shape_info'$  r£   r5   c                 óV   — dt           j        z  t          j        d||z  z
  ¦  «        z  S rÔ  r*  r¦   s     r3   ro   zsemicircular_gen._pdf*$  s#   € Ø•2”5‰y�œ  1 Q¡3¡™œÑ'Ð'r5   c                 ó|   — t          j        dt           j        z  ¦  «        dt          j        | |z  ¦  «        z  z   S r´  rÐ  r¦   s     r3   rÛ   zsemicircular_gen._logpdf-$  s.   € ÝŒv�a�œ‘g‰Œ ¥R¤X¨q¨b°©d¡^¤^Ñ!3Ñ3Ð3r5   c                 óŒ   — ddt           j        z  |t          j        d||z  z
  ¦  «        z  t          j        |¦  «        z   z  z   S )Nr‘   r†   r   )rM   rî   rü   r&  r¦   s     r3   rr   zsemicircular_gen._cdf0$  s:   € Ø�3•r”u‘9˜a¥¤¨¨!¨A©#©¡¤Ñ.µ´¸1±´Ñ=Ñ>Ñ>Ð>r5   c                 ó8   — t                                |d¦  «        S ©Nrƒ  )rá	  r{   r­   s     r3   r{   zsemicircular_gen._ppf3$  s   € Ý�zŠz˜!˜QÑÔÐr5   Nc                 óÆ   — t          j        |                     |¬¦  «        ¦  «        }t          j        t           j        |                     |¬¦  «        z  ¦  «        }||z  S r  )rM   rü   r  r  rî   )rB   rÔ   rÕ   rò  rˆ   s        r3   rÖ   zsemicircular_gen._rvs6$  sT   € õ ŒG�L×(Ò(¨dÐ(Ñ3Ô3Ñ4Ô4ˆÝŒF•2”5˜<×/Ò/°TÐ/Ñ:Ô:Ñ:Ñ;Ô;ˆØ�1‰uˆr5   c                 ó   — dS )N)r   rž  r   r<  r„   rg   s    r3   r   zsemicircular_gen._stats=$  r0  r5   c                 ó   — dS )NgzCÏ‘ ¡ä?r„   rg   s    r3   rï   zsemicircular_gen._entropy@$  s   € Ø%Ð%r5   r   )r€   r�   r‚   rƒ   rh   ro   rÛ   rr   r{   rÖ   r   rï   r„   r5   r3   rS
  rS
  $  s›   € € € € € ðð ð<ð ð ð(ð (ð (ð4ð 4ð 4ð?ð ?ð ?ð ð  ð  ðð ð ð ð ð  ð  ð&ð &ð &ð &ð &r5   rS
  Úsemicircularc                   ó>   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zdd„Z	d	„ Z
d
S )Úskewcauchy_genaò  A skewed Cauchy random variable.

    %(before_notes)s

    See Also
    --------
    cauchy : Cauchy distribution

    Notes
    -----

    The probability density function for `skewcauchy` is:

    .. math::

        f(x) = \frac{1}{\pi \left(\frac{x^2}{\left(a\, \text{sign}(x) + 1
                                                   \right)^2} + 1 \right)}

    for a real number :math:`x` and skewness parameter :math:`-1 < a < 1`.

    When :math:`a=0`, the distribution reduces to the usual Cauchy
    distribution.

    %(after_notes)s

    References
    ----------
    .. [1] "Skewed generalized *t* distribution", Wikipedia
       https://en.wikipedia.org/wiki/Skewed_generalized_t_distribution#Skewed_Cauchy_distribution

    %(example)s

    c                 ó2   — t          j        |¦  «        dk     S r[   )rM   r
  r  s     r3   r`   zskewcauchy_gen._argchecki$  s   € ÝŒv�a‰yŒy˜1Š}Ðr5   c                 ó(   — t          dddd¦  «        gS )Nrˆ   F)r<  r†   r  ©r   rg   s    r3   rh   zskewcauchy_gen._shape_infol$  s   € Ý˜3  {°NÑCÔCÐDÐDr5   c                 ón   — dt           j        |dz  |t          j        |¦  «        z  dz   dz  z  dz   z  z  S r-  )rM   rî   rN   r
  s      r3   ro   zskewcauchy_gen._pdfo$  s8   € Ø•B”E˜Q ™T Q­¬°©¬¡^°aÑ%7¸!Ñ$;Ñ;¸aÑ?Ñ@ÑAÐAr5   c                 ó  — t          j        |dk    d|z
  dz  d|z
  t           j        z  t          j        |d|z
  z  ¦  «        z  z   d|z
  dz  d|z   t           j        z  t          j        |d|z   z  ¦  «        z  z   ¦  «        S ©Nr   r   rR   )rM   rO  rî   rˆ  r
  s      r3   rr   zskewcauchy_gen._cdfr$  s�   € ÝŒx˜˜QšØ˜Q™ !™ q¨1¡uµ´¡o½¼	À!ÀqÈ1ÁuÁ+Ñ8NÔ8NÑ&NÑNØ˜Q™ !™ q¨1¡uµ´¡o½¼	À!ÀqÈ1ÁuÁ+Ñ8NÔ8NÑ&NÑNñPô Pð 	Pr5   c           
      ó2  — ||                       d|¦  «        k     }t          j        |t          j        t          j        d|z
  z  |d|z
  dz  z
  z  ¦  «        d|z
  z  t          j        t          j        d|z   z  |d|z
  dz  z
  z  ¦  «        d|z   z  ¦  «        S re
  )rr   rM   rO  rŒ  rî   )rB   rn   rˆ   rô  s       r3   r{   zskewcauchy_gen._ppfw$  s“   € Ø�—	’	˜!˜Q‘”ÒˆÝŒx˜Ýœ�rœu¨¨A©™°!°q¸1±uÀ±k±/ÑBÑCÔCÀqÈ1ÁuÑMÝœ�rœu¨¨A©™°!°q¸1±uÀ±k±/ÑBÑCÔCÀqÈ1ÁuÑMñOô Oð 	Or5   rA  c                 ó^   — t           j        t           j        t           j        t           j        fS rK   r�  )rB   rˆ   r  s      r3   r   zskewcauchy_gen._stats}$  r‘  r5   c                 ó    — t          |t          ¦  «        r|                     ¦   «         }t          j        |g d¢¦  «        \  }}}d|||z
  dz  fS )Nr•  r…   rR   r™  )rB   rC   r›  rœ  r�  s        r3   r’  zskewcauchy_gen._fitstart€$  sU   € õ �d�LÑ)Ô)ð 	$Ø—>’>Ñ#Ô#ˆDÝœ d¨L¨L¨LÑ9Ô9‰ˆˆS�#Ø�C˜# ™) Q™Ð&Ð&r5   NrL  )r€   r�   r‚   rƒ   r`   rh   ro   rr   r{   r   r’  r„   r5   r3   r_
  r_
  G$  s™   € € € € € ð ð  ðBð ð ðEð Eð EðBð Bð BðPð Pð Pð
Oð Oð Oð.ð .ð .ð .ð'ð 'ð 'ð 'ð 'r5   r_
  Ú
skewcauchyc                   ó¨   ‡ — e Zd ZdZd„ Zd„ Zd„ Zd„ Zˆ fd„Zd„ Z	d„ Z
d	„ Zdd„Zdd„Zed„ ¦   «         Zd„ Z eed¬¦  «        ˆ fd„¦   «         Zˆ xZS )Úskewnorm_genaf  A skew-normal random variable.

    %(before_notes)s

    Notes
    -----
    The pdf is::

        skewnorm.pdf(x, a) = 2 * norm.pdf(x) * norm.cdf(a*x)

    `skewnorm` takes a real number :math:`a` as a skewness parameter
    When ``a = 0`` the distribution is identical to a normal distribution
    (`norm`). `rvs` implements the method of [1]_.

    %(after_notes)s

    %(example)s

    References
    ----------
    .. [1] A. Azzalini and A. Capitanio (1999). Statistical applications of
        the multivariate skew-normal distribution. J. Roy. Statist. Soc.,
        B 61, 579-602. :arxiv:`0911.2093`

    c                 ó*   — t          j        |¦  «        S rK   rd  r  s     r3   r`   zskewnorm_gen._argcheck§$  re  r5   c                 óV   — t          ddt          j         t          j        fd¦  «        gS )Nrˆ   Fr  re   rg   s    r3   rh   zskewnorm_gen._shape_infoª$  rh  r5   c                 ó8   — t          |dk    ||fd„ d„ ¬¦  «        S )Nr   c                 ó    — t          | ¦  «        S rK   rØ   ©rn   rˆ   s     r3   rå  z#skewnorm_gen._pdf.<locals>.<lambda>¯$  s   € ­°1©¬€ r5   c                 óL   — dt          | ¦  «        z  t          || z  ¦  «        z  S r;  rÎ	  rp
  s     r3   rå  z#skewnorm_gen._pdf.<locals>.<lambda>°$  s   € ˜B�y¨™|œ|™O­I°a¸±c©N¬NÑ:€ r5   rè  rê  r
  s      r3   ro   zskewnorm_gen._pdf­$  s2   € ÝØ�ŠF�Q˜�FÐ5Ð5Ø:Ð:ð
ñ 
ô 
ð 	
r5   c                 ó8   — t          |dk    ||fd„ d„ ¬¦  «        S )Nr   c                 ó    — t          | ¦  «        S rK   rÚ   rp
  s     r3   rå  z&skewnorm_gen._logpdf.<locals>.<lambda>µ$  s   € ­°a©¬€ r5   c                 óp   — t          j        d¦  «        t          | ¦  «        z   t          || z  ¦  «        z   S r  rÂ	  rp
  s     r3   rå  z&skewnorm_gen._logpdf.<locals>.<lambda>¶$  s*   € �BœF 1™IœI¥l°1¡o¤oÑ5µlÀ1ÀQÁ3Ñ6GÔ6GÑG€ r5   rè  rê  r
  s      r3   rÛ   zskewnorm_gen._logpdf³$  s2   € ÝØ�ŠF�Q˜�FÐ8Ð8ØGÐGð
ñ 
ô 
ð 	
r5   c                 ó6  •— t          j        |¦  «        }t          j        |dd|¦  «        }t          j        ||j        ¦  «        }|dk     |dk    z  }t          ¦   «                              ||         ||         ¦  «        ||<   t          j        |dd¦  «        S )Nr…   r†   g�íµ ÷Æ°>r   r   )	rM   r¦  rk   Ú_skewnorm_cdfr	  rw  r>   rr   r6	  )rB   rn   rˆ   rš   Úi_small_cdfr“  s        €r3   rr   zskewnorm_gen._cdf¹$  s…   ø€ ÝŒM˜!ÑÔˆÝÔ  3¨¨QÑ/Ô/ˆåŒO˜A˜sœyÑ)Ô)ˆà˜T’z a¨!¢eÑ,ˆÝ ™7œ7Ÿ<š<¨¨+¬¸¸+¼ÑGÔGˆˆKÑÝŒw�s˜A˜qÑ!Ô!Ð!r5   c                 ó0   — t          j        |dd|¦  «        S ©Nr…   r†   )rk   Ú_skewnorm_ppfr
  s      r3   r{   zskewnorm_gen._ppfÃ$  ó   € ÝÔ   C¨¨aÑ0Ô0Ð0r5   c                 ó2   — |                       | | ¦  «        S rK   rA  r
  s      r3   rv   zskewnorm_gen._sfÆ$  s   € ð �yŠy˜!˜˜a˜RÑ Ô Ð r5   c                 ó0   — t          j        |dd|¦  «        S ry
  )rk   Ú_skewnorm_isfr
  s      r3   r~   zskewnorm_gen._isfË$  r{
  r5   Nc                 ó  — |                      |¬¦  «        }|                      |¬¦  «        }|t          j        d|dz  z   ¦  «        z  }||z  |t          j        d|dz  z
  ¦  «        z  z   }t          j        |dk    || ¦  «        S )Nr  r   rR   r   )ÚnormalrM   rü   rO  )rB   rˆ   rÔ   rÕ   Úu0rÉ  rÌ  rØ  s           r3   rÖ   zskewnorm_gen._rvsÎ$  s‰   € Ø× Ò  dÐ Ñ+Ô+ˆØ×Ò TÐÑ*Ô*ˆØ�bŒg�a˜!˜Q™$‘hÑÔÑˆØˆr‰T�A•b”g˜a ! Q¡$™hÑ'Ô'Ñ'Ñ'ˆÝŒx˜˜aš  b SÑ)Ô)Ð)r5   rA  c                 ó†  — g d¢}t          j        dt           j        z  ¦  «        |z  t          j        d|dz  z   ¦  «        z  }d|v r||d<   d|v rd|dz  z
  |d<   d|v r6dt           j        z
  dz  |t          j        d|dz  z
  ¦  «        z  d	z  z  |d<   d
|v r'dt           j        d	z
  z  |dz  d|dz  z
  dz  z  z  |d	<   |S )Nr3  rR   r   rÊ  r   rÉ  r  r   rƒ  r  r  )rB   rˆ   r  r-  Úconsts        r3   r   zskewnorm_gen._statsÕ$  sã   € Ø)Ð)Ð)ˆÝ”˜�"œ%™Ñ Ô  1Ñ$¥R¤W¨Q°°A±©XÑ%6Ô%6Ñ6ˆà�'ˆ>ˆ>ØˆF�1‰IØ�'ˆ>ˆ>Ø˜E 1™H™ˆF�1‰IØ�'ˆ>ˆ>Ø�bœe™) Q™¨5µ´¸¸UÀA¹X¹Ñ1FÔ1FÑ+FÈÑ*JÑJˆF�1‰IØ�'ˆ>ˆ>Ø�BœE A™I™¨5°!©8°Q¸À¹±\ÀAÑ4EÑ+EÑFˆF�1‰Iàˆr5   c                 óJ  — t          dg¦  «        t          ddg¦  «        t          g d¢¦  «        t          g d¢¦  «        t          g d¢¦  «        t          g d¢¦  «        t          g d¢¦  «        t          g d	¢¦  «        t          g d
¢¦  «        t          g d¢¦  «        dœ
}|S )Nr   rƒ  r¼  )rÈ  iöÿÿÿrƒ  )éi   i—ÿÿÿé?   iñÿÿÿ)i±  iûÿÿin  iäýÿÿr…
  )é›(  iS¼ÿÿi6Q  iþÅÿÿi�  iOüÿÿ)iß iBàûÿi�/ iÌúÿiÉo iàþÿr‡
  )éî iƒÔ·ÿiáç� i«Yeÿi{Hx i±óÄÿi“§ i!ðýÿ)	i!Ïi¨×…úiì‡€iø†‘ïiV ùiX'‹õiƒliˆ‘çþrˆ
  )
is_'i§áìŠl   </õ1 lýÿÿÿdy˜( l   J8²D lýÿÿÿ.~ l   ¬-Rx iìW¢i[©iß0òý)
r   rƒ  rC  rÆ  r  r¥  é   rÈ  é   é   r   )rB   Úskewnorm_odd_momentss     r3   Ú_skewnorm_odd_momentsz"skewnorm_gen._skewnorm_odd_momentsê$  sê   € õ ˜1˜#‰ŒÝ˜1˜b˜'Ñ"Ô"Ý˜,˜,˜,Ñ'Ô'ÝÐ.Ð.Ð.Ñ/Ô/ÝÐ7Ð7Ð7Ñ8Ô8ÝÐEÐEÐEÑFÔFÝð #ð #ð #ñ $ô $åð 8ð 8ð 8ñ 9ô 9åð %ð %ð %ñ &ô &õ ð 2ð 2ð 2ñ 3ô 3ð 
ð  
Ðð$ $Ð#r5   c                 ó  — |dz  rV|dk    rt          d¦  «        ‚|t          j        d|dz  z   ¦  «        z  }| | j        |         |dz  ¦  «        z  t          z  S t          j        |dz   dz  ¦  «        d|dz  z  z  t          z  S )Nr   r‹
  zKskewnorm noncentral moments not implemented for odd orders greater than 19.rR   )r�	  rM   rü   r�
  r&   rt   rÖ  r%   )rB   r  rˆ   rè  s       r3   rÿ   zskewnorm_gen._munp %  s¥   € Ø�1‰9ð 	EØ�rŠzˆzÝ)ð +5ñ 6ô 6ð 6ð
 •b”g˜a ! Q¡$™hÑ'Ô'Ñ'ˆEØÐ=˜DÔ6°uÔ=¸eÀQ¹hÑGÔGÑGÝ%ñ&ð 'õ ”8˜U Q™Y¨™MÑ*Ô*¨Q°°q±©\Ñ9½HÑDÐDr5   aÕ          If ``method='mm'``, parameters fixed by the user are respected, and the
        remaining parameters are used to match distribution and sample moments
        where possible. For example, if the user fixes the location with
        ``floc``, the parameters will only match the distribution skewness and
        variance to the sample skewness and variance; no attempt will be made
        to match the means or minimize a norm of the errors.
        Note that the maximum possible skewness magnitude of a
        `scipy.stats.skewnorm` distribution is approximately 0.9952717; if the
        magnitude of the data's sample skewness exceeds this, the returned
        shape parameter ``a`` will be infinite.
        

rð   c           	      óº  •— |                      dd¦  «        r t          ¦   «         j        |g|¢R i |¤ŽS t          |t          ¦  «        rJ|                     ¦   «         dk    r|                     ¦   «         }n t          ¦   «         j        |g|¢R i |¤ŽS t          | |||¦  «        \  }}}}|                     dd¦  «         	                    ¦   «         }d„ }d„ }	|dk    rd	\  }
}}nEt          |¦  «        r|d         nd }
|                      d
d ¦  «        }|                      dd ¦  «        }|€Ó|
€Ñt          j        |¦  «        }|dk    rt          j        |dd¦  «        }n" |d¦  «        }t          j        || |¦  «        } |	|¦  «        }t          j        d¬¦  «        5  t          j        t          j        |dz  d|dz  z
  ¦  «        ¦  «        t          j        |¦  «        z  }
d d d ¦  «         n# 1 swxY w Y   n#|�|n|
}
|
t          j        d|
dz  z   ¦  «        z  }|€D|€Bt          j        |¦  «        }t          j        |dd|dz  z  t          j        z  z
  z  ¦  «        }n|�|}|€A|€?t          j        |¦  «        }|||z  t          j        dt          j        z  ¦  «        z  z
  }n|�|}|dk    r|
||fS  t          ¦   «         j        ||
f||dœ|¤ŽS )Nr  Fr   r/   r8   c                 ó®   — dt           j        z
  dz  | t          j        dt           j        z  ¦  «        z  dz  dd| dz  z  t           j        z  z
  dz  z  z  S )Nr   rR   rƒ  r   r¼  r*  ©rÌ  s    r3   Úskew_dz skewnorm_gen.fit.<locals>.skew_d1%  sX   € Ø•b”e‘G˜Q‘; 1¥r¤w¨qµ2´5©yÑ'9Ô'9Ñ#9¸AÑ"=Ø%&¨¨1¨a©4©µ"´%©Ñ%7¸3Ñ$?ñ#@ñ Að Ar5   c                 óÔ   — t          j        | ¦  «        dz  }t          j        | ¦  «        t          j        t           j        dz  |z  |dt           j        z
  dz  dz  z   z  ¦  «        z  S )NrK  rR   r   )rM   r
  rN   rü   rî   )r  Ús_23s     r3   Úd_skewz skewnorm_gen.fit.<locals>.d_skew4%  s]   € Ý”6˜$‘<”< #Ñ&ˆDÝ”7˜4‘=”=¥2¤7Ý”�a‘˜$‘ $¨1­r¬u©9°a©-¸3Ñ)?Ñ"?Ñ@ñ$ô $ñ ð r5   r9   r  r,   r-   g®Gáz®ï¿g®Gáz®ï?r   r5  r6  rR   r  )r0   r>   r@   r<   r(   r=   r�  r  r:   r;   r¡  rð  r  rM   r6	  r8  rü   r7  rN   r¤  rî   rû   )rB   rC   rD   r2   r—  ró   rô   r/   r’
  r•
  rˆ   r,   r-   r  Ús_maxrÌ  rÉ  rÊ  r“  s                     €r3   r@   zskewnorm_gen.fit%  sl  ø€ ð �8Š8�J Ñ&Ô&ð 	4Ø•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3Ý�d�LÑ)Ô)ð 	8Ø× Ò Ñ"Ô" aÒ'Ð'Ø—~’~Ñ'Ô'��à"•u‘w”w”{ 4Ð7¨$Ð7Ð7Ð7°$Ð7Ð7Ð7õ "=¸TÀ4Ø=AÀ4ñ"Iô "IÑˆˆb�$˜à—’˜( EÑ*Ô*×0Ò0Ñ2Ô2ˆð	Að 	Að 	Að	ð 	ð 	ð �TŠ>ˆ>Ø,‰MˆAˆs�E�Eå˜t™9œ9Ð.��Q”�¨$ˆAØ—(’(˜5 $Ñ'Ô'ˆCØ—H’H˜W dÑ+Ô+ˆEàˆ:˜!˜)õ ”
˜4Ñ Ô ˆAØ˜Šˆõ ”G˜A˜u dÑ+Ô+��à˜˜q™	œ	�Ý”G˜A ˜v uÑ-Ô-�Ø��q‘	”	ˆAÝ” HÐ-Ñ-Ô-ð Bð BÝ”G�BœI a¨¡d¨Q¨q°!©t©VÑ5Ô5Ñ6Ô6µr´w¸q±z´zÑA�ðBð Bð Bñ Bô Bð Bð Bð Bð Bð Bð Bøøøð Bð Bð Bð Bøð �n��¨!ˆAØ•B”G˜A  1¡™HÑ%Ô%Ñ%ˆAàˆ>˜e˜mÝ”�t‘”ˆAÝ”G˜A  Q q¨!¡t¡V­B¬E¡\Ñ!1Ñ2Ñ3Ô3ˆEˆEØÐØˆEàˆ<˜C˜KÝ”˜‘”ˆAØ�e˜A‘g�bœg a­¬¡gÑ.Ô.Ñ.Ñ.ˆCˆCØÐØˆCà�TŠ>ˆ>Ø�c˜5�=Ð ð •5‘7”7”;˜t QÐE¨C°uÐEÐEÀÐEÐEÐEs   Æ"AG4Ç4G8Ç;G8r   rL  )r€   r�   r‚   rƒ   r`   rh   ro   rÛ   rr   r{   rv   r~   rÖ   r   r   r�
  rÿ   r	   r   r@   rÎ  rÏ  s   @r3   rk
  rk
  �$  sV  ø€ € € € € ðð ð2ð ð ðKð Kð Kð
ð 
ð 
ð
ð 
ð 
ð"ð "ð "ð "ð "ð1ð 1ð 1ð!ð !ð !ð
1ð 1ð 1ð*ð *ð *ð *ðð ð ð ð* ð$ð $ñ „_ð$ð*Eð Eð Eð( Ð˜}ð 5ð ñ ô ðFFð FFð FFð FFñô ðFFð FFð FFð FFð FFr5   rk
  Úskewnormc                   ó<   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	S )
Útrapezoid_gena›  A trapezoidal continuous random variable.

    %(before_notes)s

    Notes
    -----
    The trapezoidal distribution can be represented with an up-sloping line
    from ``loc`` to ``(loc + c*scale)``, then constant to ``(loc + d*scale)``
    and then downsloping from ``(loc + d*scale)`` to ``(loc+scale)``.  This
    defines the trapezoid base from ``loc`` to ``(loc+scale)`` and the flat
    top from ``c`` to ``d`` proportional to the position along the base
    with ``0 <= c <= d <= 1``.  When ``c=d``, this is equivalent to `triang`
    with the same values for `loc`, `scale` and `c`.
    The method of [1]_ is used for computing moments.

    `trapezoid` takes :math:`c` and :math:`d` as shape parameters.

    %(after_notes)s

    The standard form is in the range [0, 1] with c the mode.
    The location parameter shifts the start to `loc`.
    The scale parameter changes the width from 1 to `scale`.

    %(example)s

    References
    ----------
    .. [1] Kacker, R.N. and Lawrence, J.F. (2007). Trapezoidal and triangular
       distributions for Type B evaluation of standard uncertainty.
       Metrologia 44, 117-127. :doi:`10.1088/0026-1394/44/2/003`


    c                 óF   — |dk    |dk    z  |dk    z  |dk    z  ||k    z  S rž	  r„   ©rB   r  rÌ  s      r3   r`   ztrapezoid_gen._argcheckŽ%  s0   € Ø�Q’˜1 š6Ñ" a¨1¢fÑ-°°a²Ñ8¸AÀºFÑCÐCr5   c                 óR   — t          dddd¦  «        }t          dddd¦  «        }||gS )Nr  F©r   r†   ©TTrÌ  rb
  r   s      r3   rh   ztrapezoid_gen._shape_info‘%  s1   € Ý˜˜U H¨lÑ;Ô;ˆÝ˜˜U H¨lÑ;Ô;ˆØ�Bˆxˆr5   c                 óz   — d||z
  dz   z  }t          ||k     ||k    ||k    z  ||k    gd„ d„ d„ g||||f¦  «        S )NrR   r   c                 ó   — || z  |z  S rK   r„   ©rn   r  rÌ  r  s       r3   rå  z$trapezoid_gen._pdf.<locals>.<lambda>œ%  s   € ¨q°1©u°q©y€ r5   c                 ó   — |S rK   r„   r¡
  s       r3   rå  z$trapezoid_gen._pdf.<locals>.<lambda>�%  s   € ¨q€ r5   c                 ó   — |d| z
  z  d|z
  z  S r[   r„   r¡
  s       r3   rå  z$trapezoid_gen._pdf.<locals>.<lambda>ž%  s   € ¨q°A°a±C©y¸A¸a¹CÑ/@€ r5   ©r   )rB   rn   r  rÌ  r  s        r3   ro   ztrapezoid_gen._pdf–%  sn   € Ø��1‘�Q‘‰Kˆå˜A šEØ !šV¨¨QªÑ/Ø šEð#ð 9Ð8Ø0Ð0Ø@Ð@ðBð ˜q ! Q˜<ñ)ô )ð 	)r5   c                 ób   — t          ||k     ||k    ||k    z  ||k    gd„ d„ d„ g|||f¦  «        S )Nc                 ó$   — | dz  |z  ||z
  dz   z  S râ  r„   ©rn   r  rÌ  s      r3   rå  z$trapezoid_gen._cdf.<locals>.<lambda>¥%  s   € ¨A¨q©D°1©H¸¸!¹¸A¹Ñ,>€ r5   c                 ó*   — |d| |z
  z  z   ||z
  dz   z  S râ  r„   r§
  s      r3   rå  z$trapezoid_gen._cdf.<locals>.<lambda>¦%  s   € ¨Q°°a¸±c±©]¸qÀ¹sÀ1¹uÑ,E€ r5   c                 ó6   — dd| z
  dz  ||z
  dz   z  d|z
  z  z
  S r-  r„   r§
  s      r3   rå  z$trapezoid_gen._cdf.<locals>.<lambda>§%  s3   € ¨A°°!±¸©zØ23°A±#°a±%ñ09Ø<=¸a¹Cñ0Añ -B€ r5   r¤
  r3  s       r3   rr   ztrapezoid_gen._cdf¡%  sa   € Ý˜A šEØ !šV¨¨QªÑ/Ø šEð#ð ?Ð>ØEÐEðBð BðCð ˜q !˜9ñ&ô &ð 	&r5   c                 ób  — |                       |||¦  «        |                       |||¦  «        }}||k     ||k    ||k    g}t          j        ||z  d|z   |z
  z  ¦  «        d|z  d|z   |z
  z  d|z  z   dt          j        d|z
  ||z
  dz   z  d|z
  z  ¦  «        z
  g}t          j        ||¦  «        S rÏ  )rr   rM   rü   Úselect)rB   rz   r  rÌ  ÚqcÚqdrU  r)	  s           r3   r{   ztrapezoid_gen._ppf«%  sÆ   € Ø—’˜1˜a Ñ#Ô# T§Y¢Y¨q°!°QÑ%7Ô%7ˆBˆØ˜’F˜A šG Q¨¢VÐ,ˆÝ”g˜a !™e q¨1¡u¨q¡yÑ1Ñ2Ô2Ø˜A‘g  Q¡¨¡Ñ+¨c°A©gÑ5Ø�"œ' 1 q¡5¨Q°©U°Q©YÑ"7¸1¸q¹5Ñ"AÑBÔBÑBðDˆ
õ Œy˜ :Ñ.Ô.Ð.r5   c                 ó¶   ‡— |‰dz   z  }t          |dk    d|k     |dk     z  |dk    gd„ ˆfd„ˆfd„g|g¦  «        }dd|z   |z
  z  ||z
  z  ‰dz   ‰dz   z  z  }|S )	Nr   r…   r†   c                 ó   — dS r  r„   r‘
  s    r3   rå  z%trapezoid_gen._munp.<locals>.<lambda>Å%  s   € �s€ r5   c                 óh   •— t          j        ‰dz   t          j        | ¦  «        z  ¦  «        | dz
  z  S rz  )rM   r  rí   ©rÌ  r_   s    €r3   rå  z%trapezoid_gen._munp.<locals>.<lambda>Æ%  s+   ø€ •r”x  1¡­¬¨q©	¬	Ñ 1Ñ2Ô2°a¸±eÑ<€ r5   c                 ó   •— ‰dz   S r  r„   r±
  s    €r3   rå  z%trapezoid_gen._munp.<locals>.<lambda>Ç%  s   ø€ �q˜‘s€ r5   r³   rR   r¤
  )rB   r_   r  rÌ  Úab_termÚdc_termrB  s    `     r3   rÿ   ztrapezoid_gen._munp³%  s™   ø€ ð �a˜‘c‘(ˆÝØ�#ŠX˜˜aš A¨¢GÑ,¨a°3ªhÐ7Øˆ]Ø<Ð<Ð<Ð<Øˆ]ˆ]ˆ]ðð ˆCñô ˆð �S˜‘U˜1‘W‰o ¨7Ñ!2Ñ3¸¸!¹ÀÀ!Á±}ÑEˆØˆ
r5   c                 óf   — dd|z
  |z   z  d|z   |z
  z  t          j        dd|z   |z
  z  ¦  «        z   S r�   r.  r›
  s      r3   rï   ztrapezoid_gen._entropyÌ%  s>   € ð �c˜!‘e˜A‘g‰ # a¡%¨¡'Ñ*­R¬V°C¸3¸q¹5À¹7±OÑ-DÔ-DÑDÐDr5   N)r€   r�   r‚   rƒ   r`   rh   ro   rr   r{   rÿ   rï   r„   r5   r3   r™
  r™
  l%  s�   € € € € € ð ð  ðBDð Dð Dðð ð ð
	)ð 	)ð 	)ð&ð &ð &ð/ð /ð /ðð ð ð2Eð Eð Eð Eð Er5   r™
  zS`trapz` is deprecated in favour of `trapezoid` and will be removed in SciPy 1.16.0.c                   ó   — e Zd ZdZd„ ZdS )Ú	trapz_genz‰

    .. deprecated:: 1.14.0
        `trapz` is deprecated and will be removed in SciPy 1.16.
        Plese use `trapezoid` instead!
    c                 ó^   — t          j        t          t          d¬¦  «          | j        |i |¤ŽS ©NrR   r  )r  r  ÚdeprmsgÚDeprecationWarningÚfreeze)rB   rD   r2   s      r3   Ú__call__ztrapz_gen.__call__ä%  s1   € ÝŒ•gÕ1¸aÐ@Ñ@Ô@Ð@ØˆtŒ{˜DÐ) DÐ)Ð)Ð)r5   N)r€   r�   r‚   rƒ   r½
  r„   r5   r3   r·
  r·
  Û%  s-   € € € € € ðð ð*ð *ð *ð *ð *r5   r·
  Ú	trapezoidÚtrapz)rš   ÚentropyÚexpectr@   Úintervalrk  Úlogcdfr³  Úlogsfrû   rH  r  Úpdfre  r×  r�  rð  Ústdr¤  c                   ó   — e Zd Zd„ Zd„ ZdS )Ú_DeprecationWrapperc                 óV   — d|› d|› d�| _         t          t          |¦  «        | _        d S )Nz`trapz.z'` is deprecated in favour of trapezoid.zt. Please replace all uses of the distribution class `trapz` with `trapezoid`. `trapz` will be removed in SciPy 1.16.)rV   Úgetattrr¾
  r/   )rB   r/   s     r3   rM  z_DeprecationWrapper.__init__ö%  sE   € ðX˜fð Xð XÈVð Xð Xð XˆŒõ �i¨Ñ0Ô0ˆŒˆˆr5   c                 ó^   — t          j        | j        t          d¬¦  «          | j        |i |¤ŽS r¹
  )r  r  rV   r»
  r/   )rB   rD   Úkwargss      r3   r½
  z_DeprecationWrapper.__call__ü%  s3   € ÝŒ�d”hÕ 2¸qÐAÑAÔAÐAØˆtŒ{˜DÐ+ FÐ+Ð+Ð+r5   N)r€   r�   r‚   rM  r½
  r„   r5   r3   rÈ
  rÈ
  õ%  s2   € € € € € ð1ð 1ð 1ð,ð ,ð ,ð ,ð ,r5   rÈ
  c                   óD   — e Zd ZdZdd„Zd„ Zd„ Zd„ Zd„ Zd„ Z	d	„ Z
d
„ ZdS )Ú
triang_gena5  A triangular continuous random variable.

    %(before_notes)s

    Notes
    -----
    The triangular distribution can be represented with an up-sloping line from
    ``loc`` to ``(loc + c*scale)`` and then downsloping for ``(loc + c*scale)``
    to ``(loc + scale)``.

    `triang` takes ``c`` as a shape parameter for :math:`0 \le c \le 1`.

    %(after_notes)s

    The standard form is in the range [0, 1] with c the mode.
    The location parameter shifts the start to `loc`.
    The scale parameter changes the width from 1 to `scale`.

    %(example)s

    Nc                 ó2   — |                      d|d|¦  «        S rž	  )Ú
triangularrµ  s       r3   rÖ   ztriang_gen._rvs&  s   € Ø×&Ò& q¨!¨Q°Ñ5Ô5Ð5r5   c                 ó   — |dk    |dk    z  S rž	  r„   r}  s     r3   r`   ztriang_gen._argcheck&  s   € Ø�Q’˜1 š6Ñ"Ð"r5   c                 ó(   — t          dddd¦  «        gS )Nr  Fr�
  rž
  rb
  rg   s    r3   rh   ztriang_gen._shape_info!&  s   € Ý˜3  x°Ñ>Ô>Ð?Ð?r5   c                 ór   — t          |dk    ||k     ||k    |dk    z  |dk    gd„ d„ d„ d„ g||f¦  «        }|S )Nr   r   c                 ó   — dd| z  z
  S r  r„   rn  s     r3   rå  z!triang_gen._pdf.<locals>.<lambda>.&  s   €  a¨!¨a©%¡i€ r5   c                 ó   — d| z  |z  S r  r„   rn  s     r3   rå  z!triang_gen._pdf.<locals>.<lambda>/&  ó   €  a¨!¡e¨a¡i€ r5   c                 ó   — dd| z
  z  d|z
  z  S râ  r„   rn  s     r3   rå  z!triang_gen._pdf.<locals>.<lambda>0&  s   €  a¨1¨q©5¡k°Q¸±UÑ&;€ r5   c                 ó   — d| z  S r  r„   rn  s     r3   rå  z!triang_gen._pdf.<locals>.<lambda>1&  ó
   €  a¨!¡e€ r5   r¤
  ©rB   rn   r  rò  s       r3   ro   ztriang_gen._pdf$&  sk   € õ ˜˜ašØ˜QšØ˜qš& Q¨!¢VÑ,Ø˜ašð!ð 0Ð/Ø/Ð/Ø;Ð;Ø+Ð+ð-ð ˜A˜ñ ô  ˆð ˆr5   c                 ór   — t          |dk    ||k     ||k    |dk    z  |dk    gd„ d„ d„ d„ g||f¦  «        }|S )Nr   r   c                 ó   — d| z  | | z  z
  S r  r„   rn  s     r3   rå  z!triang_gen._cdf.<locals>.<lambda>:&  s   €  a¨¡c¨A¨a©C¡i€ r5   c                 ó   — | | z  |z  S rK   r„   rn  s     r3   rå  z!triang_gen._cdf.<locals>.<lambda>;&  rÖ
  r5   c                 ó*   — | | z  d| z  z
  |z   |dz
  z  S râ  r„   rn  s     r3   rå  z!triang_gen._cdf.<locals>.<lambda><&  s   €  q¨¡s¨Q¨q©S¡y°1¡}¸¸1¹Ñ&=€ r5   c                 ó   — | | z  S rK   r„   rn  s     r3   rå  z!triang_gen._cdf.<locals>.<lambda>=&  rÙ
  r5   r¤
  rÚ
  s       r3   rr   ztriang_gen._cdf5&  si   € Ý˜˜ašØ˜QšØ˜qš& Q¨!¢VÑ,Ø˜ašð!ð 0Ð/Ø/Ð/Ø=Ð=Ø+Ð+ð-ð ˜A˜ñ ô  ˆð ˆr5   c           
      óœ   — t          j        ||k     t          j        ||z  ¦  «        dt          j        d|z
  d|z
  z  ¦  «        z
  ¦  «        S r[   )rM   rO  rü   r  s      r3   r{   ztriang_gen._ppfA&  sA   € ÝŒx˜˜Aš�rœw q¨1¡u™~œ~¨qµ´¸!¸A¹#À!ÀAÁ#¹Ñ1GÔ1GÑ/GÑHÔHÐHr5   c           	      óÄ   — |dz   dz  d|z
  ||z  z   dz  t          j        d¦  «        d|z  dz
  z  |dz   z  |dz
  z  dt          j        d|z
  ||z  z   d¦  «        z  z  dfS )	Nr†   rD  é   rR   r   rC  r¼  g333333ã¿)rM   rü   r¾  r}  s     r3   r   ztriang_gen._statsD&  sy   € Ø�3‘˜‘Ø�Q‘�q˜‘s‘˜B‘Ý”˜‘
”
˜A˜a™C ™EÑ" A a¡CÑ(¨!¨A©#Ñ.°!µB´H¸cÀ!¹eÀAÀaÁC¹iÈ#Ñ4NÔ4NÑ2NÑOØðð 	r5   c                 ó0   — dt          j        d¦  «        z
  S r­  r.  r}  s     r3   rï   ztriang_gen._entropyJ&  s   € Ø•2”6˜!‘9”9‰}Ðr5   r   )r€   r�   r‚   rƒ   rÖ   r`   rh   ro   rr   r{   r   rï   r„   r5   r3   rÎ
  rÎ
  &  s¡   € € € € € ðð ð*6ð 6ð 6ð 6ð#ð #ð #ð@ð @ð @ðð ð ð"
ð 
ð 
ðIð Ið Iðð ð ðð ð ð ð r5   rÎ
  Útriangc                   óX   ‡ — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zˆ fd
„Zd„ Zˆ xZS )Útruncexpon_genad  A truncated exponential continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `truncexpon` is:

    .. math::

        f(x, b) = \frac{\exp(-x)}{1 - \exp(-b)}

    for :math:`0 <= x <= b`.

    `truncexpon` takes ``b`` as a shape parameter for :math:`b`.

    %(after_notes)s

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r€  re   rg   s    r3   rh   ztruncexpon_gen._shape_infog&  r  r5   c                 ó   — | j         |fS rK   rñ  r
  s     r3   r“   ztruncexpon_gen._get_supportj&  ó   € ØŒv�qˆyÐr5   c                 óZ   — t          j        | ¦  «        t          j        | ¦  «         z  S rK   rŠ  r‚  s      r3   ro   ztruncexpon_gen._pdfm&  s#   € åŒv�q�b‰zŒz�BœH a R™LœL˜=Ñ)Ð)r5   c                 óZ   — | t          j        t          j        | ¦  «         ¦  «        z
  S rK   r’  r‚  s      r3   rÛ   ztruncexpon_gen._logpdfq&  s%   € Øˆr•B”F�BœH a R™LœL˜=Ñ)Ô)Ñ)Ð)r5   c                 óX   — t          j        | ¦  «        t          j        | ¦  «        z  S rK   r=  r‚  s      r3   rr   ztruncexpon_gen._cdft&  s!   € ÝŒx˜˜‰|Œ|�BœH a R™LœLÑ(Ð(r5   c                 óX   — t          j        |t          j        | ¦  «        z  ¦  «         S rK   )rt   r£  r  r�  s      r3   r{   ztruncexpon_gen._ppfw&  s#   € Ý”˜�2œ8 Q B™<œ<™Ñ(Ô(Ð(Ð(r5   c                 ó„   — t          j        | ¦  «        t          j        | ¦  «        z
  t          j        | ¦  «        z  S rK   rŠ  r‚  s      r3   rv   ztruncexpon_gen._sfz&  s0   € Ý”˜�r‘
”
�RœV Q B™ZœZÑ'­¬°1°"©¬Ñ5Ð5r5   c                 ó„   — t          j        t          j        | ¦  «        |t          j        | ¦  «        z  z
  ¦  «         S rK   )rM   rí   r´   rt   r  r�  s      r3   r~   ztruncexpon_gen._isf}&  s3   € Ý”•r”v˜q˜b‘z”z A­¬°!°©¬Ñ$4Ñ4Ñ5Ô5Ð5Ð5r5   c                 óR  •— |dk    r5d|dz   t          j        | ¦  «        z  z
  t          j        | ¦  «         z  S |dk    rDddd||z  d|z  z   dz   z  t          j        | ¦  «        z  z
  z  t          j        | ¦  «         z  S t	          ¦   «                              ||¦  «        S r  )rM   r´   rt   r  r>   rÿ   )rB   r_   r‰   r“  s      €r3   rÿ   ztruncexpon_gen._munp€&  s¤   ø€ ð �Š6ˆ6Ø�q˜‘s�BœF A 2™JœJÑ&Ñ&­"¬(°A°2©,¬,¨Ñ7Ð7Ø�!ŠVˆVØ�a˜˜Q˜q™S  1¡™W Q™Y™­¬°¨r©
¬
Ñ2Ñ2Ñ3µb´hÀ¸r±l´l°]ÑCÐCõ ‘7”7—=’=  AÑ&Ô&Ð&r5   c                 ó|   — t          j        |¦  «        }t          j        |dz
  ¦  «        d||dz
  z  z   d|z
  z  z   S r…  r	
  )rB   r‰   ÚeBs      r3   rï   ztruncexpon_gen._entropy‹&  s;   € ÝŒV�A‰YŒYˆÝŒv�b˜‘d‰|Œ|˜Q˜r 1 S¡5™z™\¨C°©FÑ3Ñ3Ð3r5   )r€   r�   r‚   rƒ   rh   r“   ro   rÛ   rr   r{   rv   r~   rÿ   rï   rÎ  rÏ  s   @r3   ræ
  ræ
  Q&  sÌ   ø€ € € € € ðð ð*Eð Eð Eðð ð ð*ð *ð *ð*ð *ð *ð)ð )ð )ð)ð )ð )ð6ð 6ð 6ð6ð 6ð 6ð	'ð 	'ð 	'ð 	'ð 	'ð4ð 4ð 4ð 4ð 4ð 4ð 4r5   ræ
  Ú
truncexponc                 ó2   — t          j        | |gd¬¦  «        S )Nr   rû  )rt   r«  ©Úlog_pÚlog_qs     r3   Ú_log_sumrø
  ”&  s   € ÝŒ<˜ ˜¨QÐ/Ñ/Ô/Ð/r5   c                 óR   — t          j        | |t          j        dz  z   gd¬¦  «        S )Nù              ð?r   rû  )rt   r«  rM   rî   rõ
  s     r3   r
  r
  ™&  s&   € ÝŒ<˜ ¥b¤e¨B¡h¡Ð/°aÐ8Ñ8Ô8Ð8r5   c                 óÜ  ‡— t          j        | |¦  «        \  } }|dk    }| dk    }||z   }d„ Šˆfd„}d„ }t          j        | t           j        t           j        ¬¦  «        }| |         j        r ‰| |         ||         ¦  «        ||<   | |         j        r || |         ||         ¦  «        ||<   | |         j        r || |         ||         ¦  «        ||<   t          j        |¦  «        S )z3Log of Gaussian probability mass within an intervalr   c                 óV   — t          t          |¦  «        t          | ¦  «        ¦  «        S rK   )r
  rÀ   r«  s     r3   Úmass_case_leftz'_log_gauss_mass.<locals>.mass_case_left§&  s   € Ý� a™œ­,°q©/¬/Ñ:Ô:Ð:r5   c                 ó    •—  ‰| |  ¦  «        S rK   r„   )rˆ   r‰   rý
  s     €r3   Úmass_case_rightz(_log_gauss_mass.<locals>.mass_case_rightª&  s   ø€ Øˆ~˜q˜b 1 "Ñ%Ô%Ð%r5   c                 óh   — t          j        t          | ¦  «         t          | ¦  «        z
  ¦  «        S rK   )rt   r£  r½   r«  s     r3   Úmass_case_centralz*_log_gauss_mass.<locals>.mass_case_central­&  s)   € õ Œx� 1™œ˜­	°1°"©¬Ñ5Ñ6Ô6Ð6r5   )rA  rÌ  )rM   rï  rÎ  r  Ú
complex128rÔ   r–  )	rˆ   r‰   Ú	case_leftÚ
case_rightÚcase_centralrÿ
  r  ró  rý
  s	           @r3   Ú_log_gauss_massr  �&  s$  ø€ åÔ˜q !Ñ$Ô$�D€A€qð �Q’€IØ�Q’€JØ Ñ+Ð,€Lð;ð ;ð ;ð&ð &ð &ð &ð &ð7ð 7ð 7õ Œ,�q¥R¤Vµ2´=Ð
AÑ
AÔ
A€CØˆ„|Ôð DØ'˜¨¨)¬°a¸	´lÑCÔCˆˆI‰Øˆ„}Ôð HØ)˜/¨!¨J¬-¸¸:¼ÑGÔGˆˆJ‰Øˆ„Ôð PØ-Ð-¨a°¬o¸qÀ¼ÑOÔOˆˆLÑÝŒ7�3‰<Œ<Ðr5   c                   óx   ‡ — e Zd ZdZd„ Zd„ Zˆ fd„Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Zd„ Zd„ Zd„ Zd„ Zd„ Zdd„Zˆ xZS )Útruncnorm_genaw
  A truncated normal continuous random variable.

    %(before_notes)s

    Notes
    -----
    This distribution is the normal distribution centered on ``loc`` (default
    0), with standard deviation ``scale`` (default 1), and truncated at ``a``
    and ``b`` *standard deviations* from ``loc``. For arbitrary ``loc`` and
    ``scale``, ``a`` and ``b`` are *not* the abscissae at which the shifted
    and scaled distribution is truncated.

    .. note::
        If ``a_trunc`` and ``b_trunc`` are the abscissae at which we wish
        to truncate the distribution (as opposed to the number of standard
        deviations from ``loc``), then we can calculate the distribution
        parameters ``a`` and ``b`` as follows::

            a, b = (a_trunc - loc) / scale, (b_trunc - loc) / scale

        This is a common point of confusion. For additional clarification,
        please see the example below.

    %(example)s

    In the examples above, ``loc=0`` and ``scale=1``, so the plot is truncated
    at ``a`` on the left and ``b`` on the right. However, suppose we were to
    produce the same histogram with ``loc = 1`` and ``scale=0.5``.

    >>> loc, scale = 1, 0.5
    >>> rv = truncnorm(a, b, loc=loc, scale=scale)
    >>> x = np.linspace(truncnorm.ppf(0.01, a, b),
    ...                 truncnorm.ppf(0.99, a, b), 100)
    >>> r = rv.rvs(size=1000)

    >>> fig, ax = plt.subplots(1, 1)
    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
    >>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
    >>> ax.set_xlim(a, b)
    >>> ax.legend(loc='best', frameon=False)
    >>> plt.show()

    Note that the distribution is no longer appears to be truncated at
    abscissae ``a`` and ``b``. That is because the *standard* normal
    distribution is first truncated at ``a`` and ``b``, *then* the resulting
    distribution is scaled by ``scale`` and shifted by ``loc``. If we instead
    want the shifted and scaled distribution to be truncated at ``a`` and
    ``b``, we need to transform these values before passing them as the
    distribution parameters.

    >>> a_transformed, b_transformed = (a - loc) / scale, (b - loc) / scale
    >>> rv = truncnorm(a_transformed, b_transformed, loc=loc, scale=scale)
    >>> x = np.linspace(truncnorm.ppf(0.01, a, b),
    ...                 truncnorm.ppf(0.99, a, b), 100)
    >>> r = rv.rvs(size=10000)

    >>> fig, ax = plt.subplots(1, 1)
    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
    >>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
    >>> ax.set_xlim(a-0.1, b+0.1)
    >>> ax.legend(loc='best', frameon=False)
    >>> plt.show()
    c                 ó   — ||k     S rK   r„   rÕ  s      r3   r`   ztruncnorm_gen._argcheck'  s   € Ø�1Šuˆr5   c                 ó®   — t          ddt          j         t          j        fd¦  «        }t          ddt          j         t          j        fd¦  «        }||gS )Nrˆ   Frd   r‰   )FTre   re  s      r3   rh   ztruncnorm_gen._shape_info	'  sG   € Ý˜˜U¥b¤f W­b¬fÐ$5°}ÑEÔEˆÝ˜˜U¥b¤f W­b¬fÐ$5°}ÑEÔEˆØ�Bˆxˆr5   c                 óè   •— t          |t          ¦  «        r|                     ¦   «         }t          ¦   «                              |t          j        |¦  «        t          j        |¦  «        f¬¦  «        S r
  r
  r  s     €r3   r’  ztruncnorm_gen._fitstart'  sV   ø€ å�d�LÑ)Ô)ð 	$Ø—>’>Ñ#Ô#ˆDÝ‰wŒw× Ò  ­R¬V°D©\¬\½2¼6À$¹<¼<Ð,HÐ ÑIÔIÐIr5   c                 ó
   — ||fS rK   r„   rÕ  s      r3   r“   ztruncnorm_gen._get_support'  r   r5   c                 óT   — t          j        |                      |||¦  «        ¦  «        S rK   rÛ  rq  s       r3   ro   ztruncnorm_gen._pdf'  r  r5   c                 óB   — t          |¦  «        t          ||¦  «        z
  S rK   )rº   r  rq  s       r3   rÛ   ztruncnorm_gen._logpdf'  s   € Ý˜A‰Œ¥°°AÑ!6Ô!6Ñ6Ð6r5   c                 óT   — t          j        |                      |||¦  «        ¦  «        S rK   r¶  rq  s       r3   rr   ztruncnorm_gen._cdf'  r  r5   c           
      óv  — t          j        |||¦  «        \  }}}t          j        t          ||¦  «        t          ||¦  «        z
  ¦  «        }|dk    }t          j        |¦  «        rQt          j        t          j        |                      ||         ||         ||         ¦  «        ¦  «         ¦  «        ||<   |S ©Ngš™™™™™¹¿)rM   rï  rø   r  r   r£  r´   rä   )rB   rn   rˆ   r‰   rÃ
  rô  s         r3   rà   ztruncnorm_gen._logcdf '  sŸ   € ÝÔ% a¨¨AÑ.Ô.‰ˆˆ1ˆaÝ”�O¨A¨qÑ1Ô1µOÀAÀqÑ4IÔ4IÑIÑJÔJˆØ�TŠMˆÝŒ6�!‰9Œ9ð 	IÝœ¥"¤&¨¯ª°Q°q´T¸1¸Q¼4ÀÀ1ÄÑ)FÔ)FÑ"GÔ"GÐ!GÑHÔHˆF�1‰IØˆr5   c                 óT   — t          j        |                      |||¦  «        ¦  «        S rK   r6  rq  s       r3   rv   ztruncnorm_gen._sf('  r7  r5   c           
      óv  — t          j        |||¦  «        \  }}}t          j        t          ||¦  «        t          ||¦  «        z
  ¦  «        }|dk    }t          j        |¦  «        rQt          j        t          j        |                      ||         ||         ||         ¦  «        ¦  «         ¦  «        ||<   |S r  )rM   rï  rø   r  r   r£  r´   rà   )rB   rn   rˆ   r‰   rÄ
  rô  s         r3   rä   ztruncnorm_gen._logsf+'  sŸ   € ÝÔ% a¨¨AÑ.Ô.‰ˆˆ1ˆaÝ”
�?¨1¨aÑ0Ô0µ?À1ÀaÑ3HÔ3HÑHÑIÔIˆØ�DŠLˆÝŒ6�!‰9Œ9ð 	IÝ”x¥¤¨¯ª°Q°q´T¸1¸Q¼4ÀÀ1ÄÑ(FÔ(FÑ!GÔ!GÐ GÑHÔHˆE�!‰HØˆr5   c                 ó2  — t          |¦  «        }t          |¦  «        }||z
  }t          j        t          j        dt          j        z  t          j        z  ¦  «        |z  ¦  «        }|t          |¦  «        z  |t          |¦  «        z  z
  d|z  z  }||z   }|S r  )r½   rM   rí   rü   rî   r  r·   )	rB   rˆ   r‰   r+  r,  ÚZr  ÚDræ  s	            r3   rï   ztruncnorm_gen._entropy3'  sƒ   € Ý�a‰LŒLˆÝ�a‰LŒLˆØ�‰EˆÝŒF•2”7˜1�rœu™9¥r¤tÑ+Ñ,Ô,¨qÑ0Ñ1Ô1ˆØ•˜1‘”Ñ ¥I¨a¡L¤LÑ 0Ñ0°Q¸±UÑ;ˆØ�‰EˆØˆr5   c                 ó,  — t          j        |||¦  «        \  }}}|dk     }| }d„ }d„ }t          j        |¦  «        }||         }	||         }
|	j        r ||	||         ||         ¦  «        ||<   |
j        r ||
||         ||         ¦  «        ||<   |S )Nr   c                 óª   — t          t          |¦  «        t          j        | ¦  «        t	          ||¦  «        z   ¦  «        }t          j        |¦  «        S rK   )rø
  rÀ   rM   rí   r  rt   Ú	ndtri_exp©rz   rˆ   r‰   Ú	log_Phi_xs       r3   Úppf_leftz$truncnorm_gen._ppf.<locals>.ppf_leftB'  sE   € Ý ¥¨a¡¤Ý!#¤¨¡¤­_¸QÀÑ-BÔ-BÑ!BñDô DˆIå”< 	Ñ*Ô*Ð*r5   c                 ó°   — t          t          | ¦  «        t          j        |  ¦  «        t	          ||¦  «        z   ¦  «        }t          j        |¦  «         S rK   )rø
  rÀ   rM   r£  r  rt   r  r  s       r3   Ú	ppf_rightz%truncnorm_gen._ppf.<locals>.ppf_rightG'  sN   € Ý ¥¨q¨bÑ!1Ô!1Ý!#¤¨1¨"¡¤µÀÀ1Ñ0EÔ0EÑ!EñGô GˆIå”L Ñ+Ô+Ð+Ð+r5   ©rM   rï  Ú
empty_likerÔ   )rB   rz   rˆ   r‰   r  r  r  r  ró  Úq_leftÚq_rights              r3   r{   ztruncnorm_gen._ppf<'  sÆ   € ÝÔ% a¨¨AÑ.Ô.‰ˆˆ1ˆaà˜’Eˆ	Ø�Zˆ
ð	+ð 	+ð 	+ð
	,ð 	,ð 	,õ
 Œm˜AÑÔˆà�9”ˆØ�J”-ˆàŒ;ð 	JØ%˜X f¨a°	¬l¸A¸i¼LÑIÔIˆC�	‰NØŒ<ð 	OØ'˜i¨°°:´ÀÀ*ÄÑNÔNˆC�
‰Oàˆ
r5   c                 ó,  — t          j        |||¦  «        \  }}}|dk     }| }d„ }d„ }t          j        |¦  «        }||         }	||         }
|	j        r ||	||         ||         ¦  «        ||<   |
j        r ||
||         ||         ¦  «        ||<   |S )Nr   c                 óÎ   — t          t          |¦  «        t          j        | ¦  «        t	          ||¦  «        z   ¦  «        }t          j        t          j        |¦  «        ¦  «        S rK   )r
  rÀ   rM   rí   r  rt   r  r–  r  s       r3   Úisf_leftz$truncnorm_gen._isf.<locals>.isf_left_'  sO   € Ý!¥,¨q¡/¤/Ý"$¤&¨¡)¤)­o¸aÀÑ.CÔ.CÑ"CñEô EˆIå”<¥¤¨	Ñ 2Ô 2Ñ3Ô3Ð3r5   c                 óÔ   — t          t          | ¦  «        t          j        |  ¦  «        t	          ||¦  «        z   ¦  «        }t          j        t          j        |¦  «        ¦  «         S rK   )r
  rÀ   rM   r£  r  rt   r  r–  r  s       r3   Ú	isf_rightz%truncnorm_gen._isf.<locals>.isf_rightd'  sX   € Ý!¥,°¨rÑ"2Ô"2Ý"$¤(¨A¨2¡,¤,µÀÀAÑ1FÔ1FÑ"FñHô HˆIå”L¥¤¨Ñ!3Ô!3Ñ4Ô4Ð4Ð4r5   r  )rB   rz   rˆ   r‰   r  r  r%  r'  ró  r!  r"  s              r3   r~   ztruncnorm_gen._isfX'  sÆ   € åÔ% a¨¨AÑ.Ô.‰ˆˆ1ˆaà˜’Eˆ	Ø�Zˆ
ð	4ð 	4ð 	4ð
	5ð 	5ð 	5õ
 Œm˜AÑÔˆà�9”ˆØ�J”-ˆàŒ;ð 	JØ%˜X f¨a°	¬l¸A¸i¼LÑIÔIˆC�	‰NØŒ<ð 	OØ'˜i¨°°:´ÀÀ*ÄÑNÔNˆC�
‰Oàˆ
r5   c                 ó®   ‡ — ˆ fd„}t          |dk    ||k    z  ||k    z  |||ft          j        |t          j        g¬¦  «        t          j        ¦  «        S )Nc                 óT  •‡	— ‰
                      t          j        ||g¦  «        ||¦  «        \  }}|| g}ddg}t          d| dz   ¦  «        D ]TŠ	t	          ||||ggˆ	fd„d¬¦  «        }t          j        |¦  «        ‰	dz
  |d         z  z   }|                     |¦  «         ŒU|d         S )zƒ
            Returns n-th moment. Defined only if n >= 0.
            Function cannot broadcast due to the loop over n
            r   r   c                 ó   •— | |‰dz
  z  z  S r[   r„   )rn   ri  r  s     €r3   rå  z:truncnorm_gen._munp.<locals>.n_th_moment.<locals>.<lambda>„'  s   ø€ ¨q°1°q¸±s±8©|€ r5   rÿ  r  r¼  )ro   rM   rø   rþ  r   r¢  rÞ  )r_   rˆ   r‰   ÚpAÚpBÚprobsr  rÑ  Úmkr  rB   s            @€r3   Ún_th_momentz(truncnorm_gen._munp.<locals>.n_th_momentv'  sÍ   øø€ ð
 —Y’Y�rœz¨1¨a¨&Ñ1Ô1°1°aÑ8Ô8‰FˆB�Ø˜"˜�IˆEØ˜!�fˆGÝ˜1˜a ™c‘]”]ð #ð #�õ
 " %¨%°!°Q°¨Ø";Ð";Ð";Ð";ÀqðJñ Jô J�å”V˜D‘\”\ Q q¡S¨G°B¬KÑ$7Ñ7�Ø—’˜rÑ"Ô"Ð"Ð"Ø˜2”;Ðr5   r   rR  r  )rB   r_   rˆ   r‰   r/  s   `    r3   rÿ   ztruncnorm_gen._munpu'  sk   ø€ ð	ð 	ð 	ð 	ð 	õ& ˜1 š6 a¨1¢fÑ-°°a²Ñ8¸1¸aÀ¸)Ýœ, {½B¼J¸<ÐHÑHÔHÝœ&ñ"ô "ð 	"r5   r  c                 ó®   — |                       t          j        ||g¦  «        ||¦  «        \  }}d„ }t          j        |d¬¦  «        } ||||||¦  «        S )Nc                 ó^  — ||z
  }|}|| g}t          ||| |ggd„ d¬¦  «        }dt          j        |¦  «        z   }	t          ||| |z
  ||z
  ggd„ d¬¦  «        }dt          j        |¦  «        z   }
t          ||| |ggd„ d¬¦  «        }d|z  t          j        |¦  «        z   }t          ||| |ggd„ d¬¦  «        }d	|	z  t          j        |¦  «        z   }||d
|	z  d|dz  z  z   z  z   }|t          j        |
d¦  «        z  }||d|z  d	|z  d|	z  |dz  z
  z  z   z  z   }||
dz  z  d	z
  }||
||fS )Nc                 ó   — | |z  S rK   r„   rh  s     r3   rå  zGtruncnorm_gen._stats.<locals>._truncnorm_stats_scalar.<locals>.<lambda>•'  s
   € À1ÀQÁ3€ r5   r   rÿ  r   c                 ó   — | |z  S rK   r„   rh  s     r3   rå  zGtruncnorm_gen._stats.<locals>._truncnorm_stats_scalar.<locals>.<lambda>˜'  s
   € ÈÈ1É€ r5   c                 ó   — | |dz  z  S r  r„   rh  s     r3   rå  zGtruncnorm_gen._stats.<locals>._truncnorm_stats_scalar.<locals>.<lambda>�'  ó   € À1ÀQÈÁTÁ6€ r5   rR   c                 ó   — | |dz  z  S rY
  r„   rh  s     r3   rå  zGtruncnorm_gen._stats.<locals>._truncnorm_stats_scalar.<locals>.<lambda> '  r5  r5   rƒ  rÆ  r¼  rÇ  )r   rM   r¢  r¾  )rˆ   r‰   r+  r,  r  rú  r@  r-  rÑ  rû  rA  rü  Úm4Úmu3rB  Úmu4rC  s                    r3   Ú_truncnorm_stats_scalarz5truncnorm_gen._stats.<locals>._truncnorm_stats_scalar�'  sœ  € Ø�b‘ˆBØˆBà˜"˜�IˆEÝ˜e e¨a°¨V _Ð6FÐ6FØ()ð+ñ +ô +ˆDà•R”V˜D‘\”\Ñ!ˆBÝ˜e e¨a°©d°A°b±D¨\Ð%:Ð<LÐ<LØ()ð+ñ +ô +ˆDð •b”f˜T‘l”lÑ"ˆCÝ˜e e¨a°¨V _Ð6IÐ6IØ()ð+ñ +ô +ˆDà�2‘�œ˜t™œÑ$ˆBÝ˜e e¨a°¨V _Ð6IÐ6IØ()ð+ñ +ô +ˆDà�2‘�œ˜t™œÑ$ˆBà�r˜R ™U Q r¨1¡u¡W™_Ñ-Ñ-ˆCØ•r”x  SÑ)Ô)Ñ)ˆBØ�r˜2˜b™5 1 R¡4¨¨2©°°A±©Ñ#6Ñ6Ñ7Ñ7ˆCØ�s˜A‘v‘ Ñ!ˆBØ�s˜B �?Ð"r5   )r  )Úexcluded)rÅ
  rM   r[  rL  )rB   rˆ   r‰   r  r+  r,  r:  Ú_truncnorm_statss           r3   r   ztruncnorm_gen._stats�'  sp   € Ø—’�"œ( A q 6Ñ*Ô*¨A¨qÑ1Ô1‰ˆˆBð	#ð 	#ð 	#õ4 œ<Ð(?Ø1=ð?ñ ?ô ?ÐàÐ  1 b¨"¨gÑ6Ô6Ð6r5   r  )r€   r�   r‚   rƒ   r`   rh   r’  r“   ro   rÛ   rr   rà   rv   rä   rï   r{   r~   rÿ   r   rÎ  rÏ  s   @r3   r  r  Å&  s  ø€ € € € € ð>ð >ð@ð ð ðð ð ð
Jð Jð Jð Jð Jðð ð ð-ð -ð -ð7ð 7ð 7ð-ð -ð -ðð ð ð,ð ,ð ,ðð ð ðð ð ðð ð ð8ð ð ð:"ð "ð "ð07ð 7ð 7ð 7ð 7ð 7ð 7ð 7r5   r  Ú	truncnorm)rŠ   rŸ   c                   ó¨   ‡ — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Zd„ Zd„ Zd„ Zd„ Zd„ Ze ee¦  «        ˆ fd„¦   «         ¦   «         Zˆ xZS )Útruncpareto_genac  An upper truncated Pareto continuous random variable.

    %(before_notes)s

    See Also
    --------
    pareto : Pareto distribution

    Notes
    -----
    The probability density function for `truncpareto` is:

    .. math::

        f(x, b, c) = \frac{b}{1 - c^{-b}} \frac{1}{x^{b+1}}

    for :math:`b > 0`, :math:`c > 1` and :math:`1 \le x \le c`.

    `truncpareto` takes `b` and `c` as shape parameters for :math:`b` and
    :math:`c`.

    Notice that the upper truncation value :math:`c` is defined in
    standardized form so that random values of an unscaled, unshifted variable
    are within the range ``[1, c]``.
    If ``u_r`` is the upper bound to a scaled and/or shifted variable,
    then ``c = (u_r - loc) / scale``. In other words, the support of the
    distribution becomes ``(scale + loc) <= x <= (c*scale + loc)`` when
    `scale` and/or `loc` are provided.

    %(after_notes)s

    References
    ----------
    .. [1] Burroughs, S. M., and Tebbens S. F.
        "Upper-truncated power laws in natural systems."
        Pure and Applied Geophysics 158.4 (2001): 741-757.

    %(example)s

    c                 ó‚   — t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }||gS )Nr‰   Fr…   r  r  r†   re   )rB   rg  r!  s      r3   rh   ztruncpareto_gen._shape_infoÜ'  s=   € Ý˜˜U S­"¬& M°>ÑBÔBˆÝ˜˜U S­"¬& M°>ÑBÔBˆØ�Bˆxˆr5   c                 ó   — |dk    |dk    z  S ry
  r„   ©rB   r‰   r  s      r3   r`   ztruncpareto_gen._argchecká'  s   € Ø�B’˜1˜rš6Ñ"Ð"r5   c                 ó   — | j         |fS rK   rñ  rB  s      r3   r“   ztruncpareto_gen._get_supportä'  ré
  r5   c                 ó2   — |||dz    z  z  dd||z  z  z
  z  S r[   r„   ©rB   rn   r‰   r  s       r3   ro   ztruncpareto_gen._pdfç'  s'   € Ø�1˜˜!™�f‘9‰}  A a¨¡d¡F¡
Ñ+Ð+r5   c           	      óÜ   — t          j        |¦  «        t          j        t          j        | t          j        |¦  «        z  ¦  «         ¦  «        z
  |dz   t          j        |¦  «        z  z
  S r[   )rM   rí   r  rE  s       r3   rÛ   ztruncpareto_gen._logpdfê'  sO   € ÝŒv�a‰yŒy�2œ6¥2¤8¨Q¨B­r¬v°a©y¬y©LÑ#9Ô#9Ð"9Ñ:Ô:Ñ:¸aÀ¹cÅ2Ä6È!Á9Ä9¹_ÑLÐLr5   c                 ó,   — d|| z  z
  dd||z  z  z
  z  S r[   r„   rE  s       r3   rr   ztruncpareto_gen._cdfí'  s#   € Ø�A˜�r‘E‘	˜a ! A q¡D¡&™jÑ)Ð)r5   c                 ój   — t          j        || z   ¦  «        t          j        d||z  z  ¦  «        z
  S rÿ  r9  rE  s       r3   rà   ztruncpareto_gen._logcdfð'  s1   € ÝŒx˜˜Q˜B™˜ÑÔ¥"¤(¨2¨a°©d©7Ñ"3Ô"3Ñ3Ð3r5   c                 óF   — t          ddd||z  z  z
  |z  z
  d|z  ¦  «        S ©Nr   r¼  rþ  ©rB   rz   r‰   r  s       r3   r{   ztruncpareto_gen._ppfó'  s+   € Ý�1˜˜A˜a ™d™F™
 A‘~Ñ% r¨!¡tÑ,Ô,Ð,r5   c                 ó8   — || z  d||z  z  z
  dd||z  z  z
  z  S r[   r„   rE  s       r3   rv   ztruncpareto_gen._sfö'  s+   € Ø�A�2‘˜˜!˜Q™$™‘ 1 q¨¨A©¡v¡:Ñ.Ð.r5   c                 óz   — t          j        || z  d||z  z  z
  ¦  «        t          j        d||z  z  ¦  «        z
  S rJ  r¥  rE  s       r3   rä   ztruncpareto_gen._logsfù'  s;   € ÝŒv�a˜!˜‘e˜a  1¡™f‘nÑ%Ô%­¬°°A°q±D±Ñ(9Ô(9Ñ9Ð9r5   c                 óR   — t          d||z  z  dd||z  z  z
  |z  z   d|z  ¦  «        S rJ  rþ  rK  s       r3   r~   ztruncpareto_gen._isfü'  s3   € Ý�1�Q˜‘T‘6˜Q  1 a¡4¡™Z¨™NÑ*¨B¨q©DÑ1Ô1Ð1r5   c                 ó˜   — t          j        |dd||z  z  z
  z  ¦  «        |dz   t          j        |¦  «        ||z  dz
  z  d|z  z
  z  z    S r[   r.  rB  s      r3   rï   ztruncpareto_gen._entropyÿ'  sX   € Ý”˜˜1˜q  A¡™v™:™Ñ'Ô'Ø�a‘C�"œ& ™)œ) Q¨¡T¨A¡XÑ.°°1±Ñ4Ñ5ñ6ð 7ð 	7r5   c                 ó²   — ||k                          ¦   «         r#|t          j        |¦  «        z  dd||z  z  z
  z  S |||z
  z  ||z  ||z  z
  z  ||z  dz
  z  S r[   )rú   rM   rí   )rB   r_   r‰   r  s       r3   rÿ   ztruncpareto_gen._munp(  se   € Ø�ŠF�<Š<‰>Œ>ð 	:Ø•R”V˜A‘Y”Y‘; ! a¨¨1©¡f¡*Ñ-Ð-à˜˜!™‘9  1¡ q¨!¡t¡Ñ,°°1±°q±Ñ9Ð9r5   c                 óÆ   — t          |t          ¦  «        r|                     ¦   «         }t                               |¦  «        \  }}}t          |¦  «        |z
  |z  }||||fS rK   )r<   r(   r�  r[	  r@   rc  )rB   rC   r‰   r,   r-   r  s         r3   r’  ztruncpareto_gen._fitstart	(  s]   € Ý�d�LÑ)Ô)ð 	$Ø—>’>Ñ#Ô#ˆDÝŸ
š
 4Ñ(Ô(‰ˆˆ3�Ý�‰YŒY˜‰_˜eÑ#ˆØ�!�S˜%ÐÐr5   c                 ó|  •‡ ‡‡‡ ‡!‡"‡#‡$‡%— |                      dd¦  «        r t          ¦   «         j        ‰g|¢R i |¤ŽS d„ Š#d„ Š"ˆˆ"ˆ#fd„Šˆ%fd„Š ˆ$ˆ%fd„}ˆ$fd„Š!dˆˆˆ ˆ!ˆ"fd	„	}d
„ }ˆ&ˆ fd„}t          ‰ ‰||¦  «        }|\  Š}	}
}}‰                     ¦   «         ‰                     ¦   «         cŠ$Š%t          j        ‰$t          j         ¦  «        }|	�|
�|�|�t          d¦  «        ‚|
�€|�€|�€ |	�€$ˆˆ ˆ!ˆ"fd„}t          j        ‰$t          j         ¦  «        }|}d}|dz
  }|t          j         k    rd ||¦  «         ||¦  «        z  dk    rI|dz  }|t          j
        d|¦  «        z
  }|t          j         k    r ||¦  «         ||¦  «        z  dk    °I|t          j         k    s |‰g|¢R i |¤ŽS t          |||f¬¦  «        }|j        s |‰g|¢R i |¤ŽS |j        dz
  }|dz
  }d}|t          j         k    rd ||¦  «         ||¦  «        z  dk    rI|dz  }|t          j
        d|¦  «        z
  }|t          j         k    r ||¦  «         ||¦  «        z  dk    °I|t          j         k    s |‰g|¢R i |¤ŽS t          |||f¬¦  «        }|j        s |‰g|¢R i |¤ŽS |j        } ‰!|¦  «        } ‰ ||¦  «        } ‰|||¦  «        }‰|z
  |z  }t	          d ‰#|¦  «        z  d ‰"|¦  «        dz
  z  ¦  «        }||k     s |‰g|¢R i |¤ŽS �n|}|dz
  }d}|t          j         k    rX |||	¦  «         |||	¦  «        z  dk    r;|dz  }|d|z  z
  }|t          j         k    r |||	¦  «         |||	¦  «        z  dk    °;|t          j         k    s |‰g|¢R i |¤ŽS t          ||	f||f¬¦  «        }|j        s |‰g|¢R i |¤ŽS |j        } ‰!|¦  «        } ‰ ||¦  «        }|	}�nD|�|n ||
|¦  «        }|p
 ‰!|¦  «        }|
p ‰ ||¦  «        }|�-‰                     ¦   «         |z
  dk     rt          dd|¬¦  «        ‚|
r>|�<|r:‰                     ¦   «         |
|z  |z   k    rt          dd ‰ ||¦  «        ¬¦  «        ‚|	€¦‰|z
  |z  } ‰#|¦  «        }t          j        |¦  «        }d|z  |k     s |‰g|¢R i |¤ŽS d|z  d||z
  z  z   }t          j        d|z  d¦  «        }	 t          |||f||f¬¦  «        }|j        s |‰g|¢R i |¤ŽS |j        }n# t          $ r |}Y nw xY w|	}||z   ‰$k     sC|r!t          j        |t          j         ¦  «        }n  ‰!|¦  «        }t          j        |d¦  «        }||z  |z   ‰%k    s+ ‰ ||¦  «        }t          j        |t          j        ¦  «        }t          j        ‰                      ||¦  «        ¦  «        r|dk    s |‰g|¢R i |¤ŽS ||||f}|€B|€@ |‰g|¢R i |¤Ž}‰                      |‰¦  «        }‰                      |‰¦  «        }||k     r|S |S )Nr  Fc                 óN   — t          j        t          j        | ¦  «        ¦  «        S rK   )rM   rû   rí   r¶   s    r3   Úlog_meanz%truncpareto_gen.fit.<locals>.log_mean(  s   € Ý”7�2œ6 !™9œ9Ñ%Ô%Ð%r5   c                 ó6   — dt          j        d| z  ¦  «        z  S r[   )rM   rû   r¶   s    r3   Ú	harm_meanz&truncpareto_gen.fit.<locals>.harm_mean(  s   € Ø•R”W˜Q˜q™S‘\”\‘>Ð!r5   c                 ó®   •— ‰|z
  |z  } ‰|¦  «        } ‰	|¦  «        }|dz
  |z  }d|dz
  |dd| z  z
  |z  t          j        | ¦  «        z  z
  z  z
  |z  S r[   r.  )
r  r,   r-   r  Úharm_mÚlog_mÚquotrC   rV  rT  s
          €€€r3   Úget_bz"truncpareto_gen.fit.<locals>.get_b(  sq   ø€ Ø�c‘˜5Ñ ˆAØ�Y˜q‘\”\ˆFØ�H˜Q‘K”KˆEØ˜1‘H˜eÑ#ˆDØ˜˜a™ D¨A°°!±©G°VÑ+;½B¼FÀ1¹I¼IÑ+EÑ$EÑFÑFÈÑMÐMr5   c                 ó   •— ‰| z
  |z  S rK   r„   )r,   r-   Úmxs     €r3   Úget_cz"truncpareto_gen.fit.<locals>.get_c#(  s   ø€ Ø˜‘H˜eÑ#Ð#r5   c                 ó>   •— |r‰|z
  }|S | r| ‰z  ‰z
  | dz
  z  }|S d S r[   r„   )r  rô   r,   rZ  r]  s      €€r3   Úget_locz$truncpareto_gen.fit.<locals>.get_loc&(  sF   ø€ Øð Ø˜6‘k�Ø�
Øð Ø˜"‘u˜r‘z B¨¡FÑ+�Ø�
ðð r5   c                 ó   •— ‰| z
  S rK   r„   )r,   rZ  s    €r3   r£	  z&truncpareto_gen.fit.<locals>.get_scale.(  s   ø€ Ø˜‘8ˆOr5   c                 óÂ   •—  ‰	| ¦  «        } ‰| |¦  «        }|€ ‰|| |¦  «        n|} ‰
‰| z
  |z  ¦  «        }dd|dz
  ||dz   z  |z
  z  z   dd|dz   z  z
  z  |z  z
  S r[   r„   )r,   rä  r-   r  r‰   rX  rC   r[  r^  r£	  rV  s         €€€€€r3   rÿ  z$truncpareto_gen.fit.<locals>.dL_dLoc4(  s’   ø€ ð �I˜c‘N”NˆEØ��c˜5Ñ!Ô!ˆAØ(*¨
���a˜˜eÑ$Ô$Ð$¸ˆAØ�Y  s¡
¨EÑ1Ñ2Ô2ˆFØ˜˜Q ™U Q¨¨1©¡X°¡\Ñ2Ñ2°q¸1¸aÀ¹c¹7±{ÑCÀfÑLÑLÐLr5   c                 óN   — | t          j        | |z  d| |z  z
  z  ¦  «        |z  z
  S r[   r9  )r‰   ÚlogcÚlogms      r3   ÚdL_dBz"truncpareto_gen.fit.<locals>.dL_dB=(  s/   € ð •r”x  $¡¨!¨a°©f©*Ñ 5Ñ6Ô6¸Ñ=Ñ=Ð=r5   c                 óL   •—  t          t          ‰¦  «        j        | g|¢R i |¤ŽS rK   )r>   r?  r@   )rC   rD   rÌ
  r“  rB   s      €€r3   Úfallbackz%truncpareto_gen.fit.<locals>.fallbackC(  s0   ø€ à3•5�¨$Ñ/Ô/Ô3°DÐJ¸4ÐJÐJÐJÀ6ÐJÐJÐJr5   z2All parameters fixed.There is nothing to optimize.c                 ó    •—  ‰| ¦  «        } ‰| |¦  «        } ‰‰| z
  |z  ¦  «        }dd|dz
  z  z   t          j        |¦  «        z  |z  dz
  S r[   r.  )r,   r-   r  rX  rC   r^  r£	  rV  s       €€€€r3   Úcond_bz#truncpareto_gen.fit.<locals>.cond_bT(  sb   ø€ à%˜I c™NœN�EØ˜˜c 5Ñ)Ô)�AØ&˜Y¨¨s©
°EÑ'9Ñ:Ô:�FØ  1 Q¡3¡™K­2¬6°!©9¬9Ñ4°vÑ=ÀÑAÐAr5   r   r   r³   rà  gü©ñÒMbP?rR   Útruncparetorœ  rK   )r0   r>   r@   r  rK  rc  rM   r  rf   r÷   r¾  r)   r  r  rH  rí   rú   r`   r  )'rB   rC   rD   r2   r`  rÿ  rf  rh  r  rš  r  ró   rô   Úmn_infrj  rP   rô  rO   r¶  r,   r-   r  r‰   Ústd_dataÚ
up_bound_bre  rd  Úparams_overrideÚparams_superÚnllf_overrideÚ
nllf_superr[  r^  r£	  rV  rT  rZ  r]  r“  s'   ``                             @@@@@@@€r3   r@   ztruncpareto_gen.fit(  se	  øøøøøøøøøø€ ð �8Š8�J Ñ&Ô&ð 	4Ø•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3ð	&ð 	&ð 	&ð	"ð 	"ð 	"ð	Nð 	Nð 	Nð 	Nð 	Nð 	Nð 	Nð	$ð 	$ð 	$ð 	$ð 	$ð	ð 	ð 	ð 	ð 	ð 	ð	ð 	ð 	ð 	ð 	ð	Mð 	Mð 	Mð 	Mð 	Mð 	Mð 	Mð 	Mð 	Mð 	Mð	>ð 	>ð 	>ð	Kð 	Kð 	Kð 	Kð 	Kð 	Kõ 1°°t¸TÀ4ÑHÔHˆ
Ø%/Ñ"ˆˆb�"�d˜FØ—’‘”˜TŸXšX™ZœZˆˆˆBÝ”˜b¥2¤6 'Ñ*Ô*ˆàˆNØ�NØÐ$ØÐ&Ýð =ñ >ô >ð >à‰Z˜D™L¨V©^Ø‰zðBð Bð Bð Bð Bð Bð Bð Bõ œ b­2¬6¨'Ñ2Ô2�Ø�Ø�Ø !™�Ø¥"¤& Ò(Ð(Ø"˜F 6™NœN¨6¨6°&©>¬>Ñ9¸QÒ>Ð>Ø˜‘F�AØ#¥b¤h¨r°1¡o¤oÑ5�Fð ¥"¤& Ò(Ð(Ø"˜F 6™NœN¨6¨6°&©>¬>Ñ9¸QÒ>Ð>ð ¥¤ Ò'Ð'Ø#˜8 DÐ8¨4Ð8Ð8Ð8°4Ð8Ð8Ð8Ý! &°6¸6Ð2BÐCÑCÔC�Ø”}ð 9Ø#˜8 DÐ8¨4Ð8Ð8Ð8°4Ð8Ð8Ð8ð œ D™�Ø !™�Ø�Ø¥"¤& Ò(Ð(Ø#˜G F™OœO¨G¨G°F©O¬OÑ;¸qÒ@Ð@Ø˜‘F�AØ#¥b¤h¨r°1¡o¤oÑ5�Fð ¥"¤& Ò(Ð(Ø#˜G F™OœO¨G¨G°F©O¬OÑ;¸qÒ@Ð@ð ¥¤ Ò'Ð'Ø#˜8 DÐ8¨4Ð8Ð8Ð8°4Ð8Ð8Ð8Ý! '°F¸FÐ3CÐDÑDÔD�Ø”}ð 9Ø#˜8 DÐ8¨4Ð8Ð8Ð8°4Ð8Ð8Ð8Ø”h�Ø!˜	 #™œ�Ø�E˜#˜uÑ%Ô%�Ø�E˜!˜S %Ñ(Ô(�à  3™J¨Ñ-�å   8 8¨HÑ#5Ô#5Ñ!5Ø!" I I¨hÑ$7Ô$7¸Ñ$9Ñ!:ñ<ô <�
à˜Jš˜Ø#˜8 DÐ8¨4Ð8Ð8Ð8°4Ð8Ð8Ð8ñ 'ð
  �Ø !™�Ø�à¥¤ Ò'Ð'Ø#˜G F¨BÑ/Ô/Ø%˜g f¨bÑ1Ô1ñ2Ø56ò7ð 7à˜‘F�AØ# a¨¡d™]�Fð	 ¥¤ Ò'Ð'Ø#˜G F¨BÑ/Ô/Ø%˜g f¨bÑ1Ô1ñ2Ø56ò7ð 7ð ¥¤ Ò'Ð'Ø#˜8 DÐ8¨4Ð8Ð8Ð8°4Ð8Ð8Ð8Ý! '¨B¨5Ø+1°6Ð*:ð<ñ <ô <�à”}ð 9Ø#˜8 DÐ8¨4Ð8Ð8Ð8°4Ð8Ð8Ð8Ø”h�Ø!˜	 #™œ�Ø�E˜#˜uÑ%Ô%�Ø�‘ð Ð*�$�$°°¸¸FÑ0CÔ0CˆCØÐ,˜i˜i¨™nœnˆEØÐ'�e�e˜C Ñ'Ô'ˆAð Ð D§H¢H¡J¤J°Ñ$5¸Ò$9Ð$9Ý" =¸ÀÐCÑCÔCÐCð ð @�tÐ'¨VÐ'Ø—8’8‘:”:  6¡	¨DÑ 0Ò0Ð0Ý& }¸AØ-2¨U°3¸Ñ->Ô->ð@ñ @ô @ð @ð ˆzØ  3™J¨Ñ-�Ø�x Ñ)Ô)�Ý”v˜a‘y”y�à˜$™ š˜Ø#˜8 DÐ8¨4Ð8Ð8Ð8°4Ð8Ð8Ð8à˜4™ ! T¨D¡[¡/Ñ1�Ýœ a¨¡f¨aÑ0Ô0�ðÝ% e¨d°D¨\Ø/5°vÐ.>ð@ñ @ô @�Cð œ=ð =Ø'˜x¨Ð<¨tÐ<Ð<Ð<°tÐ<Ð<Ð<Øœ�A�AøÝ!ð ð ð Ø�A�A�Aðøøøð �ð �c‘	˜RÒÐØð /Ý”l 3­¬¨Ñ0Ô0��à!˜	 #™œ�Ýœ U¨AÑ.Ô.�Ø�%‘˜‘˜rÒ!Ð!Ø��c˜5Ñ!Ô!ˆAÝ”˜Q¥¤Ñ'Ô'ˆAå”�t—~’~ a¨Ñ+Ô+Ñ,Ô,ð 	1°%¸!²)°)Ø�8˜DÐ0 4Ð0Ð0Ð0¨4Ð0Ð0Ð0à˜Q  UÐ*ˆØˆ<˜F˜Nð
 $˜8 DÐ8¨4Ð8Ð8Ð8°4Ð8Ð8ˆLØ ŸIšI o°tÑ<Ô<ˆMØŸš <°Ñ6Ô6ˆJØ˜MÒ)Ð)Ø#Ð#àÐs   Ó0(T! ÔT! Ô!T0Ô/T0)r€   r�   r‚   rƒ   rh   r`   r“   ro   rÛ   rr   rà   r{   rv   rä   r~   rï   rÿ   r’  rH   r   r   r@   rÎ  rÏ  s   @r3   r?  r?  ²'  sC  ø€ € € € € ð'ð 'ðRð ð ð
#ð #ð #ðð ð ð,ð ,ð ,ðMð Mð Mð*ð *ð *ð4ð 4ð 4ð-ð -ð -ð/ð /ð /ð:ð :ð :ð2ð 2ð 2ð7ð 7ð 7ð:ð :ð :ð ð  ð  ð ØÐ˜MÑ*Ô*ðZð Zð Zð Zñ +Ô*ñ „_ðZð Zð Zð Zð Zr5   r?  rk  c                   ó<   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	S )
Útukeylambda_gena*  A Tukey-Lamdba continuous random variable.

    %(before_notes)s

    Notes
    -----
    A flexible distribution, able to represent and interpolate between the
    following distributions:

    - Cauchy                (:math:`lambda = -1`)
    - logistic              (:math:`lambda = 0`)
    - approx Normal         (:math:`lambda = 0.14`)
    - uniform from -1 to 1  (:math:`lambda = 1`)

    `tukeylambda` takes a real number :math:`lambda` (denoted ``lam``
    in the implementation) as a shape parameter.

    %(after_notes)s

    %(example)s

    c                 ó*   — t          j        |¦  «        S rK   rd  ©rB   Úlams     r3   r`   ztukeylambda_gen._argcheck	)  s   € ÝŒ{˜3ÑÔÐr5   c                 óV   — t          ddt          j         t          j        fd¦  «        gS )Nrw  Fr  re   rg   s    r3   rh   ztukeylambda_gen._shape_info)  s$   € Ý˜5 %­2¬6¨'µ2´6Ð):¸NÑKÔKÐLÐLr5   c                 óP  — t          j        t          j        ||¦  «        ¦  «        }||dz
  z  t          j        d|z
  ¦  «        |dz
  z  z   }dt          j        |¦  «        z  }t          j        |dk    t          |¦  «        dt          j        |¦  «        z  k     z  |d¦  «        S )Nr†   r   r   r…   )rM   rø   rt   ÚtklmbdarO  r
  )rB   rn   rw  ÚFxr   s        r3   ro   ztukeylambda_gen._pdf)  s�   € ÝŒZ�œ
 1 cÑ*Ô*Ñ+Ô+ˆØ�#�c‘'‰]�bœj¨¨2©Ñ.Ô.°#°c±'Ñ:Ñ:ˆØ•”˜B‘”ÑˆÝŒx˜ š¥c¨!¡f¤f¨sµ2´:¸c±?´?Ñ/BÒ&BÑCÀRÈÑMÔMÐMr5   c                 ó,   — t          j        ||¦  «        S rK   )rt   rz  )rB   rn   rw  s      r3   rr   ztukeylambda_gen._cdf)  s   € ÝŒz˜!˜SÑ!Ô!Ð!r5   c                 óZ   — t          j        ||¦  «        t          j        | |¦  «        z
  S rK   )rt   rx  rv  )rB   rz   rw  s      r3   r{   ztukeylambda_gen._ppf)  s'   € ÝŒy˜˜CÑ Ô ¥2¤;°¨r°3Ñ#7Ô#7Ñ7Ð7r5   c                 óB   — dt          |¦  «        dt          |¦  «        fS r®  )Ú_tlvarÚ_tlkurtrv  s     r3   r   ztukeylambda_gen._stats)  s   € Ø•&˜‘+”+˜q¥'¨#¡,¤,Ð.Ð.r5   c                 óF   ‡— ˆfd„}t          j        |dd¦  «        d         S )Nc                 ó|   •— t          j        t          | ‰dz
  ¦  «        t          d| z
  ‰dz
  ¦  «        z   ¦  «        S r[   )rM   rí   r�  )rñ  rw  s    €r3   Úintegz'tukeylambda_gen._entropy.<locals>.integ)  s4   ø€ Ý”6�#˜a  Q¡™-œ-­¨A¨a©C°°Q±©¬Ñ7Ñ8Ô8Ð8r5   r   r   )r   ra  )rB   rw  rƒ  s    ` r3   rï   ztukeylambda_gen._entropy)  s5   ø€ ð	9ð 	9ð 	9ð 	9ð 	9åŒ~˜e Q¨Ñ*Ô*¨1Ô-Ð-r5   N)r€   r�   r‚   rƒ   r`   rh   ro   rr   r{   r   rï   r„   r5   r3   rt  rt  ò(  s�   € € € € € ðð ð, ð  ð  ðMð Mð MðNð Nð Nð"ð "ð "ð8ð 8ð 8ð/ð /ð /ð.ð .ð .ð .ð .r5   rt  Útukeylambdac                   ó   — e Zd Zd„ ZdS )ÚFitUniformFixedScaleDataErrorc                 ó"   — d|› d|› d�| _         d S )Nz Invalid values in `data`.  Maximum likelihood estimation with the uniform distribution and fixed scale requires that np.ptp(data) <= fscale, but np.ptp(data) = z and fscale = r  rJ  )rB   r±	  rô   s      r3   rM  z&FitUniformFixedScaleDataError.__init__()  s3   € ð"à:=ð"ð "ð ð"ð "ð "ð 	Œ	ˆ	ˆ	r5   N)r€   r�   r‚   rM  r„   r5   r3   r†  r†  ')  s#   € € € € € ð
ð 
ð 
ð 
ð 
r5   r†  c                   óT   — e Zd ZdZd„ Zdd„Zd„ Zd„ Zd„ Zd„ Z	d	„ Z
ed
„ ¦   «         ZdS )Úuniform_gena  A uniform continuous random variable.

    In the standard form, the distribution is uniform on ``[0, 1]``. Using
    the parameters ``loc`` and ``scale``, one obtains the uniform distribution
    on ``[loc, loc + scale]``.

    %(before_notes)s

    %(example)s

    c                 ó   — g S rK   r„   rg   s    r3   rh   zuniform_gen._shape_info=)  r£   r5   Nc                 ó0   — |                      dd|¦  «        S ry
  )r  rÓ   s      r3   rÖ   zuniform_gen._rvs@)  s   € Ø×#Ò# C¨¨dÑ3Ô3Ð3r5   c                 ó   — d||k    z  S r  r„   r¦   s     r3   ro   zuniform_gen._pdfC)  s   € Ø�A˜’F‰|Ðr5   c                 ó   — |S rK   r„   r¦   s     r3   rr   zuniform_gen._cdfF)  ó   € Øˆr5   c                 ó   — |S rK   r„   r­   s     r3   r{   zuniform_gen._ppfI)  rŽ  r5   c                 ó   — dS )N)r‘   gUUUUUUµ?r   g333333ó¿r„   rg   s    r3   r   zuniform_gen._statsL)  s   € Ø#Ð#r5   c                 ó   — dS r  r„   rg   s    r3   rï   zuniform_gen._entropyO)  rG  r5   c                 ó,  — t          |¦  «        dk    rt          d¦  «        ‚|                     dd¦  «        }|                     dd¦  «        }t          |¦  «         |�|�t	          d¦  «        ‚t          j        |¦  «        }t          j        |¦  «                             ¦   «         st	          d¦  «        ‚|€r|€)| 	                    ¦   «         }t          j
        |¦  «        }n‘|}|                     ¦   «         |z
  }| 	                    ¦   «         |k     rt          d|||z   ¬	¦  «        ‚nJt          j
        |¦  «        }||k    rt          ||¬
¦  «        ‚| 	                    ¦   «         d||z
  z  z
  }|}t          |¦  «        t          |¦  «        fS )a’	  
        Maximum likelihood estimate for the location and scale parameters.

        `uniform.fit` uses only the following parameters.  Because exact
        formulas are used, the parameters related to optimization that are
        available in the `fit` method of other distributions are ignored
        here.  The only positional argument accepted is `data`.

        Parameters
        ----------
        data : array_like
            Data to use in calculating the maximum likelihood estimate.
        floc : float, optional
            Hold the location parameter fixed to the specified value.
        fscale : float, optional
            Hold the scale parameter fixed to the specified value.

        Returns
        -------
        loc, scale : float
            Maximum likelihood estimates for the location and scale.

        Notes
        -----
        An error is raised if `floc` is given and any values in `data` are
        less than `floc`, or if `fscale` is given and `fscale` is less
        than ``data.max() - data.min()``.  An error is also raised if both
        `floc` and `fscale` are given.

        Examples
        --------
        >>> import numpy as np
        >>> from scipy.stats import uniform

        We'll fit the uniform distribution to `x`:

        >>> x = np.array([2, 2.5, 3.1, 9.5, 13.0])

        For a uniform distribution MLE, the location is the minimum of the
        data, and the scale is the maximum minus the minimum.

        >>> loc, scale = uniform.fit(x)
        >>> loc
        2.0
        >>> scale
        11.0

        If we know the data comes from a uniform distribution where the support
        starts at 0, we can use `floc=0`:

        >>> loc, scale = uniform.fit(x, floc=0)
        >>> loc
        0.0
        >>> scale
        13.0

        Alternatively, if we know the length of the support is 12, we can use
        `fscale=12`:

        >>> loc, scale = uniform.fit(x, fscale=12)
        >>> loc
        1.5
        >>> scale
        12.0

        In that last example, the support interval is [1.5, 13.5].  This
        solution is not unique.  For example, the distribution with ``loc=2``
        and ``scale=12`` has the same likelihood as the one above.  When
        `fscale` is given and it is larger than ``data.max() - data.min()``,
        the parameters returned by the `fit` method center the support over
        the interval ``[data.min(), data.max()]``.

        r   rI  ró   Nrô   rõ   rö   r  rœ  )r±	  rô   r‘   )r¡  r1   r0   r4   r÷   rM   rø   rù   rú   rK  r±	  rc  rH  r†  rL  )	rB   rC   rD   r2   ró   rô   r,   r-   r±	  s	            r3   r@   zuniform_gen.fitR)  s�  € õV ˆt‰9Œ9�qŠ=ˆ=ÝÐ1Ñ2Ô2Ð2à�xŠx˜ Ñ%Ô%ˆØ—’˜( DÑ)Ô)ˆå$ TÑ*Ô*Ð*àÐ Ð 2åð )ñ *ô *ð *õ Œz˜$ÑÔˆåŒ{˜4Ñ Ô ×$Ò$Ñ&Ô&ð 	EÝÐCÑDÔDÐDð> ˆ>àˆ|à—h’h‘j”j�Ýœ˜t™œ��ð �ØŸš™
œ
 SÑ(�Ø—8’8‘:”: Ò#Ð#Ý& y¸À3ÈÁ;ÐOÑOÔOÐOð $õ ”&˜‘,”,ˆCØ�VŠ|ˆ|Ý3¸ÀFÐKÑKÔKÐKð —(’(‘*”*˜s F¨S¡LÑ1Ñ1ˆCØˆEõ �S‰zŒz�5 ™<œ<Ð'Ð'r5   r   )r€   r�   r‚   rƒ   rh   rÖ   ro   rr   r{   r   rï   rH   r@   r„   r5   r3   r‰  r‰  1)  s¬   € € € € € ð
ð 
ðð ð ð4ð 4ð 4ð 4ðð ð ðð ð ðð ð ð$ð $ð $ðð ð ð ðR(ð R(ñ „_ðR(ð R(ð R(r5   r‰  r  c                   óì   ‡ — e Zd ZdZd„ Zd„ Zdd„Z ee¦  «        ˆ fd„¦   «         Z	d„ Z
d„ Zd	„ Zd
„ Zd„ Z eed¬¦  «        	 	 dˆ fd„	¦   «         Ze eed¬¦  «        ˆ fd„¦   «         ¦   «         Zˆ xZS )Úvonmises_genaU  A Von Mises continuous random variable.

    %(before_notes)s

    See Also
    --------
    scipy.stats.vonmises_fisher : Von-Mises Fisher distribution on a
                                  hypersphere

    Notes
    -----
    The probability density function for `vonmises` and `vonmises_line` is:

    .. math::

        f(x, \kappa) = \frac{ \exp(\kappa \cos(x)) }{ 2 \pi I_0(\kappa) }

    for :math:`-\pi \le x \le \pi`, :math:`\kappa \ge 0`. :math:`I_0` is the
    modified Bessel function of order zero (`scipy.special.i0`).

    `vonmises` is a circular distribution which does not restrict the
    distribution to a fixed interval. Currently, there is no circular
    distribution framework in SciPy. The ``cdf`` is implemented such that
    ``cdf(x + 2*np.pi) == cdf(x) + 1``.

    `vonmises_line` is the same distribution, defined on :math:`[-\pi, \pi]`
    on the real line. This is a regular (i.e. non-circular) distribution.

    Note about distribution parameters: `vonmises` and `vonmises_line` take
    ``kappa`` as a shape parameter (concentration) and ``loc`` as the location
    (circular mean). A ``scale`` parameter is accepted but does not have any
    effect.

    Examples
    --------
    Import the necessary modules.

    >>> import numpy as np
    >>> import matplotlib.pyplot as plt
    >>> from scipy.stats import vonmises

    Define distribution parameters.

    >>> loc = 0.5 * np.pi  # circular mean
    >>> kappa = 1  # concentration

    Compute the probability density at ``x=0`` via the ``pdf`` method.

    >>> vonmises.pdf(0, loc=loc, kappa=kappa)
    0.12570826359722018

    Verify that the percentile function ``ppf`` inverts the cumulative
    distribution function ``cdf`` up to floating point accuracy.

    >>> x = 1
    >>> cdf_value = vonmises.cdf(x, loc=loc, kappa=kappa)
    >>> ppf_value = vonmises.ppf(cdf_value, loc=loc, kappa=kappa)
    >>> x, cdf_value, ppf_value
    (1, 0.31489339900904967, 1.0000000000000004)

    Draw 1000 random variates by calling the ``rvs`` method.

    >>> sample_size = 1000
    >>> sample = vonmises(loc=loc, kappa=kappa).rvs(sample_size)

    Plot the von Mises density on a Cartesian and polar grid to emphasize
    that it is a circular distribution.

    >>> fig = plt.figure(figsize=(12, 6))
    >>> left = plt.subplot(121)
    >>> right = plt.subplot(122, projection='polar')
    >>> x = np.linspace(-np.pi, np.pi, 500)
    >>> vonmises_pdf = vonmises.pdf(x, loc=loc, kappa=kappa)
    >>> ticks = [0, 0.15, 0.3]

    The left image contains the Cartesian plot.

    >>> left.plot(x, vonmises_pdf)
    >>> left.set_yticks(ticks)
    >>> number_of_bins = int(np.sqrt(sample_size))
    >>> left.hist(sample, density=True, bins=number_of_bins)
    >>> left.set_title("Cartesian plot")
    >>> left.set_xlim(-np.pi, np.pi)
    >>> left.grid(True)

    The right image contains the polar plot.

    >>> right.plot(x, vonmises_pdf, label="PDF")
    >>> right.set_yticks(ticks)
    >>> right.hist(sample, density=True, bins=number_of_bins,
    ...            label="Histogram")
    >>> right.set_title("Polar plot")
    >>> right.legend(bbox_to_anchor=(0.15, 1.06))

    c                 ó@   — t          dddt          j        fd¦  «        gS )NrL  Fr   rd   re   rg   s    r3   rh   zvonmises_gen._shape_infoK*  s   € Ý˜7 E¨A­r¬v¨;¸ÑFÔFÐGÐGr5   c                 ó   — |dk    S r®  r„   r\  s     r3   r`   zvonmises_gen._argcheckN*  s   € Ø˜ŠzÐr5   Nc                 ó2   — |                      d||¬¦  «        S )Nr…   r  )Úvonmises)rB   rL  rÔ   rÕ   s       r3   rÖ   zvonmises_gen._rvsQ*  s   € Ø×$Ò$ S¨%°dÐ$Ñ;Ô;Ð;r5   c                 ó®   •—  t          ¦   «         j        |i |¤Ž}t          j        |t          j        z   dt          j        z  ¦  «        t          j        z
  S r  )r>   r×  rM   Úmodrî   )rB   rD   r2   r×  r“  s       €r3   r×  zvonmises_gen.rvsT*  sB   ø€ à�e‰gŒgŒk˜4Ð( 4Ð(Ð(ˆÝŒv�c�BœE‘k 1¥R¤U¡7Ñ+Ô+­b¬eÑ3Ð3r5   c                 óž   — t          j        |t          j        |¦  «        z  ¦  «        dt           j        z  t          j        |¦  «        z  z  S r  )rM   r´   rt   Úcosm1rî   r
  rN  s      r3   ro   zvonmises_gen._pdfY*  s9   € õ
 Œv�e�BœH Q™KœKÑ'Ñ(Ô(¨A­b¬e©GµB´F¸5±M´MÑ,AÑBÐBr5   c                 óÂ   — |t          j        |¦  «        z  t          j        dt          j        z  ¦  «        z
  t          j        t          j        |¦  «        ¦  «        z
  S r  )rt   rœ  rM   rí   rî   r
  rN  s      r3   rÛ   zvonmises_gen._logpdf`*  s?   € à•r”x ‘{”{Ñ"¥R¤V¨A­b¬e©G¡_¤_Ñ4µr´v½b¼fÀU¹m¼mÑ7LÔ7LÑLÐLr5   c                 ó,   — t          j        ||¦  «        S rK   )r   Úvon_mises_cdfrN  s      r3   rr   zvonmises_gen._cdfd*  s   € ÝÔ# E¨1Ñ-Ô-Ð-r5   c                 ó   — dS r/  r„   r\  s     r3   Ú_stats_skipzvonmises_gen._stats_skipg*  r0  r5   c                 óÐ   — | t          j        |¦  «        z  t          j        |¦  «        z  t          j        dt          j        z  t          j        |¦  «        z  ¦  «        z   |z   S r  )rt   Úi1er
  rM   rí   rî   r\  s     r3   rï   zvonmises_gen._entropyj*  sU   € ð ��œ ™œÑ&­¬°©¬Ñ6Ý”�q�2œ5‘y¥2¤6¨%¡=¤=Ñ0Ñ1Ô1ñ2Ø49ñ:ð 	;r5   z¢        The default limits of integration are endpoints of the interval
        of width ``2*pi`` centered at `loc` (e.g. ``[-pi, pi]`` when
        ``loc=0``).

rð   r„   r   r   Fc           	      ó’   •— t           j         t           j        }
}	|€||	z   }|€||
z   } t          ¦   «         j        |||||||fi |¤ŽS rK   )rM   rî   r>   rÁ
  )rB   r[  rD   r,   r-   ÚlbÚubÚconditionalr2   r¤  r£  r“  s              €r3   rÁ
  zvonmises_gen.expectv*  sk   ø€ õ ”%��œˆBˆàˆ:Ø�r‘ˆBØˆ:Ø�r‘ˆBà�u‰wŒwŒ~˜d D¨#Ø# R¨¨[ðBð BØ<@ðBð Bð 	Br5   a          Fit data is assumed to represent angles and will be wrapped onto the
        unit circle. `f0` and `fscale` are ignored; the returned shape is
        always the maximum likelihood estimate and the scale is always
        1. Initial guesses are ignored.

c                 ó  •— |                      dd¦  «        r t          ¦   «         j        |g|¢R i |¤ŽS t          | |||¦  «        \  }}}}| j        t
          j         k    r t          ¦   «         j        |g|¢R i |¤ŽS t          j        |dt
          j        z  ¦  «        }d„ }d„ }|�|n
 ||¦  «        }	|�|n |||	¦  «        }
t          j        |	t
          j        z   dt
          j        z  ¦  «        t
          j        z
  }	|
|	dfS )Nr  FrR   c                 ó*   — t          j        | ¦  «        S rK   )rð  Úcircmean)rC   s    r3   Úfind_muz!vonmises_gen.fit.<locals>.find_mu™*  s   € Ý”> $Ñ'Ô'Ð'r5   c                 óx  ‡— t          j        t          j        || z
  ¦  «        ¦  «        t          | ¦  «        z  Š‰dk    rdS ‰dk    rUˆfd„}‰d‰z
  z  d‰z   z  }d|z  } ||¦  «        dk    r|S  ||¦  «        dk    r|S t	          |d||f¬¦  «        }|j        S t          j        t          ¦  «        j        S )Nr   g €à7yÃACr   c                 ó\   •— t          j        | ¦  «        t          j        | ¦  «        z  ‰z
  S rK   )rt   r£  r
  )rL  rò  s    €r3   Úsolve_for_kappaz=vonmises_gen.fit.<locals>.find_kappa.<locals>.solve_for_kappa¯*  s#   ø€ Ýœ6 %™=œ=­¬°©¬Ñ6¸Ñ:Ð:r5   rR   rù  )r/   r  )	rM   r¢  r  r¡  r)   r  râ  rL  rã  )rC   r,   r®  Úlower_boundÚupper_boundÚroot_resrò  s         @r3   Ú
find_kappaz$vonmises_gen.fit.<locals>.find_kappaœ*  s÷   ø€ õ ”•r”v˜c D™jÑ)Ô)Ñ*Ô*­3¨t©9¬9Ñ4ˆAð �AŠvˆvð �tØ�Q’�ð;ð ;ð ;ð ;ð ;ð    1¡™g q¨¡s™m�Ø ™m�ð #�? ;Ñ/Ô/°1Ò4Ð4Ø&Ð&Ø$�_ [Ñ1Ô1°QÒ6Ð6Ø&Ð&å*¨?À8Ø4?ÀÐ3Mð Oñ  Oô  O�Hà#œ=Ð(õ ”x¥‘”Ô+Ð+r5   r   )r0   r>   r@   r  rˆ   rM   rî   rš  )rB   rC   rD   r2   rú  ró   rô   r«  r²  r,   rw  r“  s              €r3   r@   zvonmises_gen.fit†*  s5  ø€ ð �8Š8�J Ñ&Ô&ð 	4Ø•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3å%@ÀÀtØAEÀtñ&Mô &MÑ"ˆˆf�d˜FàŒ6•b”e�VÒÐà•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3õ Œv�d˜A¥¤™IÑ&Ô&ˆð	(ð 	(ð 	(ð6	,ð 6	,ð 6	,ðr Ð&ˆdˆd¨G¨G°D©M¬Mˆà Ð,��°*°*¸TÀ3Ñ2GÔ2GˆåŒf�S�2œ5‘[ !¥b¤e¡)Ñ,Ô,­r¬uÑ4ˆØ�c˜1ˆ}Ðr5   r   )Nr„   r   r   NNF)r€   r�   r‚   rƒ   rh   r`   rÖ   r   r   r×  ro   rÛ   rr   r¡  rï   r	   rÁ
  rH   r@   rÎ  rÏ  s   @r3   r”  r”  ë)  s�  ø€ € € € € ð^ð ^ð~Hð Hð Hðð ð ð<ð <ð <ð <ð Ð˜MÑ*Ô*ð4ð 4ð 4ð 4ñ +Ô*ð4ðCð Cð CðMð Mð Mð.ð .ð .ð ð  ð  ð
;ð 
;ð 
;ð Ð˜}ð 5ð ñ ô ð FJØ ð
Bð 
Bð 
Bð 
Bð 
Bñ	ô ð
Bð ØÐ˜}ð 5/ð 0ñ 0ô 0ð
Nð Nð Nð Nñ0ô 0ñ „_ðNð Nð Nð Nð Nr5   r”  r˜  Úvonmises_linec                   ój   — e Zd ZdZej        Zd„ Zdd„Zd„ Z	d„ Z
d„ Zd„ Zd	„ Zd
„ Zd„ Zd„ Zd„ Zd„ ZdS )ro  aX  A Wald continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `wald` is:

    .. math::

        f(x) = \frac{1}{\sqrt{2\pi x^3}} \exp(- \frac{ (x-1)^2 }{ 2x })

    for :math:`x >= 0`.

    `wald` is a special case of `invgauss` with ``mu=1``.

    %(after_notes)s

    %(example)s
    c                 ó   — g S rK   r„   rg   s    r3   rh   zwald_gen._shape_infoø*  r£   r5   Nc                 ó2   — |                      dd|¬¦  «        S rS  rT  rÓ   s      r3   rÖ   zwald_gen._rvsû*  s   € Ø× Ò   c°Ð Ñ5Ô5Ð5r5   c                 ó8   — t                                |d¦  «        S r  )rn  ro   r¦   s     r3   ro   zwald_gen._pdfþ*  s   € å�}Š}˜Q Ñ$Ô$Ð$r5   c                 ó8   — t                                |d¦  «        S r  )rn  rr   r¦   s     r3   rr   zwald_gen._cdf+  ó   € Ý�}Š}˜Q Ñ$Ô$Ð$r5   c                 ó8   — t                                |d¦  «        S r  )rn  rv   r¦   s     r3   rv   zwald_gen._sf+  s   € Ý�|Š|˜A˜sÑ#Ô#Ð#r5   c                 ó8   — t                                |d¦  «        S r  )rn  r{   r¦   s     r3   r{   zwald_gen._ppf+  r¹  r5   c                 ó8   — t                                |d¦  «        S r  )rn  r~   r¦   s     r3   r~   zwald_gen._isf+  r¹  r5   c                 ó8   — t                                |d¦  «        S r  )rn  rÛ   r¦   s     r3   rÛ   zwald_gen._logpdf+  ó   € Ý×Ò  3Ñ'Ô'Ð'r5   c                 ó8   — t                                |d¦  «        S r  )rn  rà   r¦   s     r3   rà   zwald_gen._logcdf+  r¾  r5   c                 ó8   — t                                |d¦  «        S r  )rn  rä   r¦   s     r3   rä   zwald_gen._logsf+  s   € Ý�Š˜q #Ñ&Ô&Ð&r5   c                 ó   — dS )N)r†   r†   rD  rY  r„   rg   s    r3   r   zwald_gen._stats+  s   € Ø"Ð"r5   c                 ó6   — t                                d¦  «        S r  )rn  rï   rg   s    r3   rï   zwald_gen._entropy+  s   € Ý× Ò  Ñ%Ô%Ð%r5   r   )r€   r�   r‚   rƒ   r   r  r  rh   rÖ   ro   rr   rv   r{   r~   rÛ   rà   rä   r   rï   r„   r5   r3   ro  ro  á*  sá   € € € € € ðð ð( "Ô4€Mðð ð ð6ð 6ð 6ð 6ð%ð %ð %ð%ð %ð %ð$ð $ð $ð%ð %ð %ð%ð %ð %ð(ð (ð (ð(ð (ð (ð'ð 'ð 'ð#ð #ð #ð&ð &ð &ð &ð &r5   ro  rU  c                   ó<   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	S )
Úwrapcauchy_gena  A wrapped Cauchy continuous random variable.

    %(before_notes)s

    Notes
    -----
    The probability density function for `wrapcauchy` is:

    .. math::

        f(x, c) = \frac{1-c^2}{2\pi (1+c^2 - 2c \cos(x))}

    for :math:`0 \le x \le 2\pi`, :math:`0 < c < 1`.

    `wrapcauchy` takes ``c`` as a shape parameter for :math:`c`.

    %(after_notes)s

    %(example)s

    c                 ó   — |dk    |dk     z  S rž	  r„   r}  s     r3   r`   zwrapcauchy_gen._argcheck7+  rÿ	  r5   c                 ó(   — t          dddd¦  «        gS )Nr  F)r   r   r  rb
  rg   s    r3   rh   zwrapcauchy_gen._shape_info:+  s   € Ý˜3  v¨~Ñ>Ô>Ð?Ð?r5   c                 óz   — d||z  z
  dt           j        z  d||z  z   d|z  t          j        |¦  «        z  z
  z  z  S rÉ  rí  r
  s      r3   ro   zwrapcauchy_gen._pdf=+  s=   € à�A�a‘C‘˜!�BœE™' 1 Q q¡S¡5¨¨1©­R¬V°A©Y¬Y©Ñ#6Ñ7Ñ8Ð8r5   c                 ój   — d„ }d„ }d|z   d|z
  z  }t          |t          j        k     ||f||¬¦  «        S )Nc                 óz   — dt           j        z  t          j        |t          j        | dz  ¦  «        z  ¦  «        z  S r-  ©rM   rî   rˆ  rŒ  ©rn   Úcrs     r3   r™  zwrapcauchy_gen._cdf.<locals>.f1C+  s-   € à•R”U‘7�RœY r­"¬&°°1±©+¬+¡~Ñ6Ô6Ñ6Ð6r5   c           	      ó    — ddt           j        z  t          j        |t          j        dt           j        z  | z
  dz  ¦  «        z  ¦  «        z  z
  S r-  rÊ  rË  s     r3   ré  zwrapcauchy_gen._cdf.<locals>.f2G+  s?   € à�q�œ‘w¥¤¨2­b¬f°a½¼±gÀ±kÀ1±_Ñ.EÔ.EÑ+EÑ!FÔ!FÑFÑFÐFr5   r   r0  )r   rM   rî   )rB   rn   r  r™  ré  rÌ  s         r3   rr   zwrapcauchy_gen._cdfA+  sW   € ð	7ð 	7ð 	7ð	Gð 	Gð 	Gð �!‰e�a˜!‘e‰_ˆÝ˜!�bœeš) a¨ W°°rÐ:Ñ:Ô:Ð:r5   c           
      óV  — d|z
  d|z   z  }dt          j        |t          j        t           j        |z  ¦  «        z  ¦  «        z  }dt           j        z  dt          j        |t          j        t           j        d|z
  z  ¦  «        z  ¦  «        z  z
  }t          j        |dk     ||¦  «        S )Nr†   rR   r   r‘   )rM   rˆ  rŒ  rî   rO  )rB   rz   r  rB  ÚrcqÚrcmqs         r3   r{   zwrapcauchy_gen._ppfN+  sŠ   € Ø�1‰u�s˜1‘u‰oˆØ•”	˜#�bœf¥R¤U¨1¡W™oœoÑ-Ñ.Ô.Ñ.ˆØ•”‰w�q�œ 3¥r¤v­b¬e°Q°q±S©kÑ':Ô':Ñ#:Ñ;Ô;Ñ;Ñ;ˆÝŒx˜˜Eš	 3¨Ñ-Ô-Ð-r5   c                 óV   — t          j        dt           j        z  d||z  z
  z  ¦  «        S râ  rì   r}  s     r3   rï   zwrapcauchy_gen._entropyT+  s$   € ÝŒv�a�œ‘g˜q  1¡™u‘oÑ&Ô&Ð&r5   c                 óÆ   — t          |t          ¦  «        r|                     ¦   «         }dt          j        |¦  «        t          j        |¦  «        dt          j        z  z  fS r­  )r<   r(   r�  rM   rK  r±	  rî   )rB   rC   s     r3   r’  zwrapcauchy_gen._fitstartW+  sM   € õ �d�LÑ)Ô)ð 	$Ø—>’>Ñ#Ô#ˆDØ•B”F˜4‘L”L¥"¤&¨¡,¤,°µ"´%±Ñ"8Ð8Ð8r5   N)r€   r�   r‚   rƒ   r`   rh   ro   rr   r{   rï   r’  r„   r5   r3   rÄ  rÄ  !+  sŠ   € € € € € ðð ð*!ð !ð !ð@ð @ð @ð9ð 9ð 9ð;ð ;ð ;ð.ð .ð .ð'ð 'ð 'ð9ð 9ð 9ð 9ð 9r5   rÄ  Ú
wrapcauchyc                   óP   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
„ Zdd„ZdS )Úgennorm_gena0  A generalized normal continuous random variable.

    %(before_notes)s

    See Also
    --------
    laplace : Laplace distribution
    norm : normal distribution

    Notes
    -----
    The probability density function for `gennorm` is [1]_:

    .. math::

        f(x, \beta) = \frac{\beta}{2 \Gamma(1/\beta)} \exp(-|x|^\beta),

    where :math:`x` is a real number, :math:`\beta > 0` and
    :math:`\Gamma` is the gamma function (`scipy.special.gamma`).

    `gennorm` takes ``beta`` as a shape parameter for :math:`\beta`.
    For :math:`\beta = 1`, it is identical to a Laplace distribution.
    For :math:`\beta = 2`, it is identical to a normal distribution
    (with ``scale=1/sqrt(2)``).

    References
    ----------

    .. [1] "Generalized normal distribution, Version 1",
           https://en.wikipedia.org/wiki/Generalized_normal_distribution#Version_1

    .. [2] Nardon, Martina, and Paolo Pianca. "Simulation techniques for
           generalized Gaussian densities." Journal of Statistical
           Computation and Simulation 79.11 (2009): 1317-1329

    .. [3] Wicklin, Rick. "Simulate data from a generalized Gaussian
           distribution" in The DO Loop blog, September 21, 2016,
           https://blogs.sas.com/content/iml/2016/09/21/simulate-generalized-gaussian-sas.html

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS ©Nrk  Fr   r  re   rg   s    r3   rh   zgennorm_gen._shape_infoŽ+  ó   € Ý˜6 5¨1­b¬f¨+°~ÑFÔFÐGÐGr5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   rÛ  ©rB   rn   rk  s      r3   ro   zgennorm_gen._pdf‘+  s    € ÝŒv�d—l’l 1 dÑ+Ô+Ñ,Ô,Ð,r5   c                 ó†   — t          j        d|z  ¦  «        t          j        d|z  ¦  «        z
  t	          |¦  «        |z  z
  S r�   )rM   rí   rt   rÃ  r
  rÚ  s      r3   rÛ   zgennorm_gen._logpdf”+  s8   € ÝŒv�c˜$‘hÑÔ¥"¤*¨S°©XÑ"6Ô"6Ñ6½¸Q¹¼À¹ÑEÐEr5   c                 ó’   — dt          j        |¦  «        z  }d|z   |t          j        d|z  t	          |¦  «        |z  ¦  «        z  z
  S r�   )rM   rN   rt   r²  r
  ©rB   rn   rk  r  s       r3   rr   zgennorm_gen._cdf—+  sB   € Ø•"”'˜!‘*”*Ñˆà�a‘˜1�rœ|¨C°©Hµc¸!±f´f¸d±lÑCÔCÑCÑCÐCr5   c                 óŠ   — t          j        |dz
  ¦  «        }|t          j        d|z  d|z   d|z  |z  z
  ¦  «        d|z  z  z  S )Nr‘   r†   r³   )rM   rN   rt   rº  rÝ  s       r3   r{   zgennorm_gen._ppfœ+  sJ   € ÝŒG�A˜‘GÑÔˆà•2”? 3 t¡8¨c°A©g¸¸Q¹¸q¹Ñ-@ÑAÔAÀCÈÁHÑMÑMÐMr5   c                 ó0   — |                       | |¦  «        S rK   rA  rÚ  s      r3   rv   zgennorm_gen._sf¡+  s   € Ø�yŠy˜!˜˜TÑ"Ô"Ð"r5   c                 ó0   — |                       ||¦  «         S rK   rW  rÚ  s      r3   r~   zgennorm_gen._isf¤+  s   € Ø—	’	˜!˜TÑ"Ô"Ð"Ð"r5   c                 ó¼   — t          j        d|z  d|z  d|z  g¦  «        \  }}}dt          j        ||z
  ¦  «        dt          j        ||z   d|z  z
  ¦  «        dz
  fS )Nr†   rD  rü  r…   r³   )rt   rÃ  rM   r´   )rB   rk  Úc1Úc3Úc5s        r3   r   zgennorm_gen._stats§+  sa   € Ý”Z  T¡¨3¨t©8°S¸±XÐ >Ñ?Ô?‰
ˆˆB�Ø•2”6˜"˜r™'‘?”? B­¬¨r°B©w¸¸R¹Ñ/?Ñ(@Ô(@À2Ñ(EÐEÐEr5   c                 ól   — d|z  t          j        d|z  ¦  «        z
  t          j        d|z  ¦  «        z   S rX  r<  ©rB   rk  s     r3   rï   zgennorm_gen._entropy«+  s2   € Ø�D‰y�2œ6 " t¡)Ñ,Ô,Ñ,­r¬z¸"¸t¹)Ñ/DÔ/DÑDÐDr5   Nc                 óÈ   — |                      d|z  |¬¦  «        }|d|z  z  }t          j        |¦  «        }|                     |j        ¬¦  «        dk     }||          ||<   |S )Nr   r  r‘   )rÖ  rM   rø   Úrandomrw  )rB   rk  rÔ   rÕ   r–  ri  rV	  s          r3   rÖ   zgennorm_gen._rvs®+  sk   € ð ×Ò˜q ™v¨DÐÑ1Ô1ˆØ�!�D‘&‰MˆåŒJ�q‰MŒMˆØ×"Ò"¨¬Ð"Ñ0Ô0°3Ò6ˆØ�T”7�(ˆˆ$‰Øˆr5   r   )r€   r�   r‚   rƒ   rh   ro   rÛ   rr   r{   rv   r~   r   rï   rÖ   r„   r5   r3   rÕ  rÕ  c+  sÌ   € € € € € ð)ð )ðTHð Hð Hð-ð -ð -ðFð Fð FðDð Dð Dð
Nð Nð Nð
#ð #ð #ð#ð #ð #ðFð Fð FðEð Eð Eð	ð 	ð 	ð 	ð 	ð 	r5   rÕ  Úgennormc                   óB   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zd
S )Úhalfgennorm_genaµ  The upper half of a generalized normal continuous random variable.

    %(before_notes)s

    See Also
    --------
    gennorm : generalized normal distribution
    expon : exponential distribution
    halfnorm : half normal distribution

    Notes
    -----
    The probability density function for `halfgennorm` is:

    .. math::

        f(x, \beta) = \frac{\beta}{\Gamma(1/\beta)} \exp(-|x|^\beta)

    for :math:`x, \beta > 0`. :math:`\Gamma` is the gamma function
    (`scipy.special.gamma`).

    `halfgennorm` takes ``beta`` as a shape parameter for :math:`\beta`.
    For :math:`\beta = 1`, it is identical to an exponential distribution.
    For :math:`\beta = 2`, it is identical to a half normal distribution
    (with ``scale=1/sqrt(2)``).

    References
    ----------

    .. [1] "Generalized normal distribution, Version 1",
           https://en.wikipedia.org/wiki/Generalized_normal_distribution#Version_1

    %(example)s

    c                 ó@   — t          dddt          j        fd¦  «        gS r×  re   rg   s    r3   rh   zhalfgennorm_gen._shape_infoá+  rØ  r5   c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   rÛ  rÚ  s      r3   ro   zhalfgennorm_gen._pdfä+  s"   € õ Œv�d—l’l 1 dÑ+Ô+Ñ,Ô,Ð,r5   c                 óf   — t          j        |¦  «        t          j        d|z  ¦  «        z
  ||z  z
  S r  r<  rÚ  s      r3   rÛ   zhalfgennorm_gen._logpdfê+  s,   € ÝŒv�d‰|Œ|�bœj¨¨T©Ñ2Ô2Ñ2°Q¸±WÑ<Ð<r5   c                 ó8   — t          j        d|z  ||z  ¦  «        S r  r®  rÚ  s      r3   rr   zhalfgennorm_gen._cdfí+  s   € ÝŒ{˜3˜t™8 Q¨¡WÑ-Ô-Ð-r5   c                 ó>   — t          j        d|z  |¦  «        d|z  z  S r  rÝ  rÚ  s      r3   r{   zhalfgennorm_gen._ppfð+  s!   € ÝŒ~˜c $™h¨Ñ*Ô*¨S°©XÑ6Ð6r5   c                 ó8   — t          j        d|z  ||z  ¦  «        S r  r±  rÚ  s      r3   rv   zhalfgennorm_gen._sfó+  s   € ÝŒ|˜C ™H a¨¡gÑ.Ô.Ð.r5   c                 ó>   — t          j        d|z  |¦  «        d|z  z  S r  rì  rÚ  s      r3   r~   zhalfgennorm_gen._isfö+  s!   € ÝŒ˜s 4™x¨Ñ+Ô+¨c°$©hÑ7Ð7r5   c                 óf   — d|z  t          j        |¦  «        z
  t          j        d|z  ¦  «        z   S r  r<  ræ  s     r3   rï   zhalfgennorm_gen._entropyù+  s,   € Ø�4‰x�"œ& ™,œ,Ñ&­¬°C¸±HÑ)=Ô)=Ñ=Ð=r5   Nr’  r„   r5   r3   rë  rë  ½+  sš   € € € € € ð"ð "ðFHð Hð Hð-ð -ð -ð=ð =ð =ð.ð .ð .ð7ð 7ð 7ð/ð /ð /ð8ð 8ð 8ð>ð >ð >ð >ð >r5   rë  Úhalfgennormc                   óL   ‡ — e Zd ZdZd„ Zd„ Zˆ fd„Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zˆ xZS )
Úcrystalball_gena¹  
    Crystalball distribution

    %(before_notes)s

    Notes
    -----
    The probability density function for `crystalball` is:

    .. math::

        f(x, \beta, m) =  \begin{cases}
                            N \exp(-x^2 / 2),  &\text{for } x > -\beta\\
                            N A (B - x)^{-m}  &\text{for } x \le -\beta
                          \end{cases}

    where :math:`A = (m / |\beta|)^m  \exp(-\beta^2 / 2)`,
    :math:`B = m/|\beta| - |\beta|` and :math:`N` is a normalisation constant.

    `crystalball` takes :math:`\beta > 0` and :math:`m > 1` as shape
    parameters.  :math:`\beta` defines the point where the pdf changes
    from a power-law to a Gaussian distribution.  :math:`m` is the power
    of the power-law tail.

    %(after_notes)s

    .. versionadded:: 0.19.0

    References
    ----------
    .. [1] "Crystal Ball Function",
           https://en.wikipedia.org/wiki/Crystal_Ball_function

    %(example)s
    c                 ó   — |dk    |dk    z  S )z@
        Shape parameter bounds are m > 1 and beta > 0.
        r   r   r„   )rB   rk  rÊ  s      r3   r`   zcrystalball_gen._argcheck$,  s   € ð �A’˜$ š(Ñ#Ð#r5   c                 ó‚   — t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }||gS )Nrk  Fr   r  rÊ  r   re   )rB   ÚibetaÚims      r3   rh   zcrystalball_gen._shape_info*,  s>   € Ý˜6 5¨1­b¬f¨+°~ÑFÔFˆÝ˜˜U Q­¬ K°Ñ@Ô@ˆØ�rˆ{Ðr5   c                 óJ   •— t          ¦   «                              |d¬¦  «        S )N)r   r¼  rJ  r  r  s     €r3   r’  zcrystalball_gen._fitstart/,  s    ø€ å‰wŒw× Ò  ¨HÐ Ñ5Ô5Ð5r5   c                 óÎ   — d||z  |dz
  z  t          j        |dz   dz  ¦  «        z  t          t          |¦  «        z  z   z  }d„ }d„ }|t	          || k    |||f||¬¦  «        z  S )a`  
        Return PDF of the crystalball function.

                                            --
                                           | exp(-x**2 / 2),  for x > -beta
        crystalball.pdf(x, beta, m) =  N * |
                                           | A * (B - x)**(-m), for x <= -beta
                                            --
        r†   r   rR   r³   c                 ó8   — t          j        | dz   dz  ¦  «        S r  r9  ©rn   rk  rÊ  s      r3   Úrhsz!crystalball_gen._pdf.<locals>.rhs@,  s   € Ý”6˜1˜a™4˜% !™)Ñ$Ô$Ð$r5   c                 ój   — ||z  |z  t          j        |dz   dz  ¦  «        z  ||z  |z
  | z
  | z  z  S r²   r9  rþ  s      r3   Úlhsz!crystalball_gen._pdf.<locals>.lhsC,  sG   € Ø�t‘V˜a‘K¥"¤&¨$°©'¨°C©Ñ"8Ô"8Ñ8Ø�t‘V˜d‘] QÑ&¨1¨"Ñ-ñ.ð /r5   r0  ©rM   r´   rµ   r½   r   ©rB   rn   rk  rÊ  r®  rÿ  r  s          r3   ro   zcrystalball_gen._pdf3,  s�   € ð �1�T‘6˜Q˜q™S‘>¥B¤F¨D°!©G¨8°c©>Ñ$:Ô$:Ñ:Ý¥¨4¡¤Ñ0ñ1ñ 2ˆð	%ð 	%ð 	%ð	/ð 	/ð 	/ð •:˜a 4 %ši¨!¨T°1¨¸ÀÐEÑEÔEÑEÐEr5   c                 óò   — d||z  |dz
  z  t          j        |dz   dz  ¦  «        z  t          t          |¦  «        z  z   z  }d„ }d„ }t          j        |¦  «        t          || k    |||f||¬¦  «        z   S )zH
        Return the log of the PDF of the crystalball function.
        r†   r   rR   r³   c                 ó   — | dz   dz  S r  r„   rþ  s      r3   rÿ  z$crystalball_gen._logpdf.<locals>.rhsP,  s   € Ø�q‘D�5˜‘7ˆNr5   c                 óŠ   — |t          j        ||z  ¦  «        z  |dz  dz  z
  |t          j        ||z  |z
  | z
  ¦  «        z  z
  S r  r.  rþ  s      r3   r  z$crystalball_gen._logpdf.<locals>.lhsS,  sG   € Ø•R”V˜A˜d™F‘^”^Ñ# d¨A¡g¨a¡iÑ/°!µB´F¸1¸T¹6ÀD¹=È1Ñ;LÑ4MÔ4MÑ2MÑMÐMr5   r0  )rM   r´   rµ   r½   rí   r   r  s          r3   rÛ   zcrystalball_gen._logpdfI,  s›   € ð �1�T‘6˜Q˜q™S‘>¥B¤F¨D°!©G¨8°c©>Ñ$:Ô$:Ñ:Ý¥¨4¡¤Ñ0ñ1ñ 2ˆð	ð 	ð 	ð	Nð 	Nð 	Nõ Œv�a‰yŒy�: a¨4¨%¢i°!°T¸1°ÀÈÐMÑMÔMÑMÐMr5   c                 óÎ   — d||z  |dz
  z  t          j        |dz   dz  ¦  «        z  t          t          |¦  «        z  z   z  }d„ }d„ }|t	          || k    |||f||¬¦  «        z  S )z8
        Return CDF of the crystalball function
        r†   r   rR   r³   c                 ó¢   — ||z  t          j        |dz   dz  ¦  «        z  |dz
  z  t          t          | ¦  «        t          | ¦  «        z
  z  z   S ©NrR   r³   r   ©rM   r´   rµ   r½   rþ  s      r3   rÿ  z!crystalball_gen._cdf.<locals>.rhs_,  sT   € Ø�t‘V�rœv t¨Q¡w h°¡nÑ5Ô5Ñ5¸¸1¹Ñ=Ý¥9¨Q¡<¤<µ)¸T¸EÑ2BÔ2BÑ#BÑCñDð Er5   c                 ó|   — ||z  |z  t          j        |dz   dz  ¦  «        z  ||z  |z
  | z
  | dz   z  z  |dz
  z  S r	  r9  rþ  s      r3   r  z!crystalball_gen._cdf.<locals>.lhsc,  sW   € Ø�t‘V˜a‘K¥"¤&¨$°©'¨°C©Ñ"8Ô"8Ñ8Ø�t‘V˜d‘] QÑ&¨1¨"¨Q©$Ñ/ñ0Ø34°Q±3ñ8ð 9r5   r0  r  r  s          r3   rr   zcrystalball_gen._cdfX,  s“   € ð �1�T‘6˜Q˜q™S‘>¥B¤F¨D°!©G¨8°c©>Ñ$:Ô$:Ñ:Ý¥¨4¡¤Ñ0ñ1ñ 2ˆð	Eð 	Eð 	Eð	9ð 	9ð 	9ð •:˜a 4 %ši¨!¨T°1¨¸ÀÐEÑEÔEÑEÐEr5   c                 ó  — d||z  |dz
  z  t          j        |dz   dz  ¦  «        z  t          t          |¦  «        z  z   z  }|||z  z  t          j        |dz   dz  ¦  «        z  |dz
  z  }d„ }d„ }t	          ||k     |||f||¬¦  «        S )Nr†   r   rR   r³   c                 óâ   — t          j        |dz   dz  ¦  «        }||z  |z  |dz
  z  }d|t          t          |¦  «        z  z   z  }||z  |z
  |dz
  ||z  | z  z  |z  | z  |z  dd|z
  z  z  z
  S râ  r
  ©rñ  rk  rÊ  Úeb2r  r®  s         r3   Úppf_lessz&crystalball_gen._ppf.<locals>.ppf_lessn,  s”   € Ý”&˜$ ™'˜ !™Ñ$Ô$ˆCØ�4‘˜3‘ ! A¡#Ñ&ˆAØ�1•{¥Y¨t¡_¤_Ñ4Ñ4Ñ5ˆAØ�d‘F˜T‘MØ˜!‘e˜a ™f¨¨™^Ñ+¨CÑ/°Ñ1°!Ñ3°q¸!¸A¹#±wÑ?ñ@ð Ar5   c                 óð   — t          j        |dz   dz  ¦  «        }||z  |z  |dz
  z  }d|t          t          |¦  «        z  z   z  }t	          t          | ¦  «        dt          z  | |z  |z
  z  z   ¦  «        S râ  )rM   r´   rµ   r½   rÄ   r  s         r3   Úppf_greaterz)crystalball_gen._ppf.<locals>.ppf_greateru,  sy   € Ý”&˜$ ™'˜ !™Ñ$Ô$ˆCØ�4‘˜3‘ ! A¡#Ñ&ˆAØ�1•{¥Y¨t¡_¤_Ñ4Ñ4Ñ5ˆAÝ�Y¨ uÑ-Ô-°µ;±ÀÀ1ÁÀqÁÑ0IÑIÑJÔJÐJr5   r0  r  )rB   rñ  rk  rÊ  r®  Úpbetar  r  s           r3   r{   zcrystalball_gen._ppfi,  s¼   € Ø�1�T‘6˜Q˜q™S‘>¥B¤F¨D°!©G¨8°c©>Ñ$:Ô$:Ñ:Ý¥¨4¡¤Ñ0ñ1ñ 2ˆà�Q�t‘V‘�rœv t¨Q¡w h¨q¡jÑ1Ô1Ñ1°Q¸±UÑ;ˆð	Að 	Að 	Að	Kð 	Kð 	Kõ ˜!˜eš) a¨¨q \°XÀ+ÐNÑNÔNÐNr5   c           	      ó  — d||z  |dz
  z  t          j        |dz   dz  ¦  «        z  t          t          |¦  «        z  z   z  }d„ }|t	          |dz   |k     |||ft          j        |t           j        g¬¦  «        t           j        ¦  «        z  S )zR
        Returns the n-th non-central moment of the crystalball function.
        r†   r   rR   r³   c                 óè  — ||z  |z  t          j        |dz   dz  ¦  «        z  }||z  |z
  }d| dz
  dz  z  t          j        | dz   dz  ¦  «        z  dd| z  t          j        | dz   dz  |dz  dz  ¦  «        z  z   z  }t          j        |j        ¦  «        }t          | dz   ¦  «        D ]B}|t          j        | |¦  «        || |z
  z  z  d|z  z  ||z
  dz
  z  ||z  | |z   dz   z  z  z  }ŒC||z  |z   S )zƒ
            Returns n-th moment. Defined only if n+1 < m
            Function cannot broadcast due to the loop over n
            rR   r³   r   r†   r¼  )	rM   r´   rt   rÖ  r¯  r§  rw  rþ  Úbinom)r_   rk  rÊ  r+  r,  rÿ  r  r  s           r3   r/  z*crystalball_gen._munp.<locals>.n_th_moment„,  s   € ð
 �4‘˜!‘�bœf d¨A¡g X°¡^Ñ4Ô4Ñ4ˆAØ�$‘˜‘ˆAØ˜˜!™˜S‘y‘>¥B¤H¨a°©c°1©WÑ$5Ô$5Ñ5Ø˜2 ™'¥B¤K°°1±°a±¸¸q¹À1¹Ñ$EÔ$EÑEÑEñGˆCå”(˜3œ9Ñ%Ô%ˆCÝ˜1˜q™5‘\”\ð 0ð 0�Ø�œ  A™œ¨¨Q¨q©S©Ñ1°R¸!±GÑ;¸qÀ1¹uÀq¹yÑIØ˜4™ A 2¨¡6¨A¡:Ñ.ñ/ñ 0��à�s‘7˜S‘=Ð r5   rR  )rM   r´   rµ   r½   r   rL  rV  rf   )rB   r_   rk  rÊ  r®  r/  s         r3   rÿ   zcrystalball_gen._munp},  sŸ   € ð �1�T‘6˜Q˜q™S‘>¥B¤F¨D°!©G¨8°c©>Ñ$:Ô$:Ñ:Ý¥¨4¡¤Ñ0ñ1ñ 2ˆð	!ð 	!ð 	!ð •:˜a !™e aši¨!¨T°1¨Ý œl¨;ÅÄ
¸|ÐLÑLÔLÝ œfñ&ô &ñ &ð 	&r5   )r€   r�   r‚   rƒ   r`   rh   r’  ro   rÛ   rr   r{   rÿ   rÎ  rÏ  s   @r3   rö  rö   ,  s¸   ø€ € € € € ð"ð "ðF$ð $ð $ðð ð ð
6ð 6ð 6ð 6ð 6ðFð Fð Fð,Nð Nð NðFð Fð Fð"Oð Oð Oð(&ð &ð &ð &ð &ð &ð &r5   rö  ÚcrystalballzA Crystalball Function)rŠ   Úlongnamec                 ó>   — t          j        d| dz  dz  ¦  «        dz  S )aµ  
    Utility function for the argus distribution used in the pdf, sf and
    moment calculation.
    Note that for all x > 0:
    gammainc(1.5, x**2/2) = 2 * (_norm_cdf(x) - x * _norm_pdf(x) - 0.5).
    This can be verified directly by noting that the cdf of Gamma(1.5) can
    be written as erf(sqrt(x)) - 2*sqrt(x)*exp(-x)/sqrt(Pi).
    We use gammainc instead of the usual definition because it is more precise
    for small chi.
    r¼  rR   r®  )rË  s    r3   Ú
_argus_phir  ›,  s#   € õ Œ;�s˜C ™F 1™HÑ%Ô%¨Ñ)Ð)r5   c                   óF   — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zdd„Z	dd	„Z
d
„ ZdS )Ú	argus_gena  
    Argus distribution

    %(before_notes)s

    Notes
    -----
    The probability density function for `argus` is:

    .. math::

        f(x, \chi) = \frac{\chi^3}{\sqrt{2\pi} \Psi(\chi)} x \sqrt{1-x^2}
                     \exp(-\chi^2 (1 - x^2)/2)

    for :math:`0 < x < 1` and :math:`\chi > 0`, where

    .. math::

        \Psi(\chi) = \Phi(\chi) - \chi \phi(\chi) - 1/2

    with :math:`\Phi` and :math:`\phi` being the CDF and PDF of a standard
    normal distribution, respectively.

    `argus` takes :math:`\chi` as shape a parameter. Details about sampling
    from the ARGUS distribution can be found in [2]_.

    %(after_notes)s

    References
    ----------
    .. [1] "ARGUS distribution",
           https://en.wikipedia.org/wiki/ARGUS_distribution
    .. [2] Christoph Baumgarten "Random variate generation by fast numerical
           inversion in the varying parameter case." Research in Statistics,
           vol. 1, 2023, doi:10.1080/27684520.2023.2279060.

    .. versionadded:: 0.19.0

    %(example)s
    c                 ó@   — t          dddt          j        fd¦  «        gS )NrË  Fr   r  re   rg   s    r3   rh   zargus_gen._shape_infoÒ,  ó   € Ý˜5 %¨!­R¬V¨°nÑEÔEÐFÐFr5   c                 óp  — t          j        d¬¦  «        5  d||z  z
  }dt          j        |¦  «        z  t          z
  t          j        t	          |¦  «        ¦  «        z
  }|t          j        |¦  «        z   dt          j        | |z  ¦  «        z  z   |dz  |z  dz  z
  cd d d ¦  «         S # 1 swxY w Y   d S )Nr5  r6  r†   rƒ  r‘   rR   )rM   r8  rí   r¹   r  r£  )rB   rn   rË  ri  r+  s        r3   rÛ   zargus_gen._logpdfÕ,  sý   € åŒ[ Ð)Ñ)Ô)ð 	Gð 	GØ�a˜‘c‘	ˆAØ•"”&˜‘+”+‘¥Ñ.µ´½
À3¹¼Ñ1HÔ1HÑHˆAØ•r”v˜a‘y”y‘= 3¥r¤x°°°1±¡~¤~Ñ#5Ñ5¸¸Q¹À¹
ÀQ¹ÑFð	Gð 	Gð 	Gð 	Gñ 	Gô 	Gð 	Gð 	Gð 	Gð 	Gð 	Gð 	Gøøøð 	Gð 	Gð 	Gð 	Gð 	Gð 	Gs   –BB+Â+B/Â2B/c                 óR   — t          j        |                      ||¦  «        ¦  «        S rK   rÛ  ©rB   rn   rË  s      r3   ro   zargus_gen._pdfÜ,  s    € ÝŒv�d—l’l 1 cÑ*Ô*Ñ+Ô+Ð+r5   c                 ó4   — d|                       ||¦  «        z
  S r  rä  r!  s      r3   rr   zargus_gen._cdfß,  s   € Ø�T—X’X˜a Ñ%Ô%Ñ%Ð%r5   c                 óv   — t          |t          j        d|dz  z
  ¦  «        z  ¦  «        t          |¦  «        z  S r-  )r  rM   rü   r!  s      r3   rv   zargus_gen._sfâ,  s2   € Ý˜#¥¤¨¨A¨q©D©Ñ 1Ô 1Ñ1Ñ2Ô2µZÀ±_´_ÑDÐDr5   Nc                 ó†  ‡	‡
— t          j        |¦  «        }|j        dk    r|                      |||¬¦  «        }nøt	          |j        |¦  «        \  }Š	t          t          j        |¦  «        ¦  «        }t          j        |¦  «        }t          j	        |gdgdgg¬¦  «        Š
‰
j
        s‰t          ˆ	ˆ
fd„t          t          |¦  «         d¦  «        D ¦   «         ¦  «        }|                      ‰
d         ||¬¦  «        }|                     |¦  «        ||<   ‰
                     ¦   «          ‰
j
        ¯‰|dk    r|d         }|S )	Nr   )rœ  rÕ   rˆ  r‰  rŠ  c              3   ó`   •K  — | ](}‰|         s‰j         |         nt          d ¦  «        V — Œ)d S rK   rŽ  r�  s     €€r3   ru  z!argus_gen._rvs.<locals>.<genexpr>ò,  r“  r5   r   r„   )rM   rø   rÔ   r•  r   rw  rÈ  rý  r–  r—  r˜  r™  rþ  r¡  rN  rš  )rB   rË  rÔ   rÕ   ró  r›  rœ  r�  rò  r‘  r’  s            @@r3   rÖ   zargus_gen._rvså,  sb  øø€ ÝŒj˜‰oŒoˆØŒ8�qŠ=ˆ=Ø×"Ò" 3°4Ø0<ð #ñ >ô >ˆCˆCõ # 3¤9¨dÑ3Ô3‰GˆC�Ý�RœW S™\œ\Ñ*Ô*ˆJÝ”(˜4‘.”.ˆCÝ”˜C˜5Ø"/ Ø&0 \ Nð4ñ 4ô 4ˆBð ”kð Ýð ;ð ;ð ;ð ;ð ;Ý%*­C°©I¬I¨:°qÑ%9Ô%9ð;ñ ;ô ;ñ ;ô ;�à×$Ò$ R¨¤U°zØ2>ð %ñ @ô @�àŸ9š9 S™>œ>��C‘Ø—’‘”�ð ”kð ð �2Š:ˆ:Ø�b”'ˆCØˆ
r5   c                 óä  — t          t          j        |¦  «        ¦  «        }t          t          j        |¦  «        ¦  «        }t          j        |¦  «        }d}||z  }|dk    r«| dz  }	||k     r�||z
  }
|                     |
¬¦  «        }|                     |
¬¦  «        }|dz  }t          j        |¦  «        |	|z  k    }t          j        |¦  «        }|dk    r,t          j	        d||         z
  ¦  «        }|||||z   …<   ||z  }||k     °��nN|dk    rËt          j
        | dz  ¦  «        }||k     r¬||z
  }
|                     |
¬¦  «        }|                     |
¬¦  «        }dt          j        |d|z
  z  |z   ¦  «        z  |z  }|dz  |z   dk    }t          j        |¦  «        }|dk    r,t          j	        d||         z   ¦  «        }|||||z   …<   ||z  }||k     °¬n}||k     rZ||z
  }
|                     d|
¬¦  «        }||dz  k    }t          j        |¦  «        }|dk    r||         ||||z   …<   ||z  }||k     °Zt          j	        dd|z  |z  z
  ¦  «        }t          j        ||¦  «        S )	Nr   r‘   rR   r  rK  r   gÍÌÌÌÌÌü?r¼  )r™  rM   r¦  rÈ  rý  r§  r  rí   r¢  rü   r´   rå  rN  )rB   rË  rœ  rÕ   r­  r®  rn   r¯  r¦  rÌ  r  r  rÉ  r–  r½  r¾  r×  ÚechirÀ  s                      r3   r•  zargus_gen._rvs_scalarý,  s®  € õh •r”} ZÑ0Ô0Ñ1Ô1ˆÝ•”˜‘”Ñ Ô ˆÝŒH�Q‰KŒKˆØˆ	Ø�S‰yˆØ�#Š:ˆ:Ø�˜‘	ˆAØ˜a’-�-Ø˜	‘M�Ø ×(Ò(¨aÐ(Ñ0Ô0�Ø ×(Ò(¨aÐ(Ñ0Ô0�Ø˜‘H�åœ& ™)œ) q¨1¡uÒ,�ÝœV F™^œ^�
Ø ’>�>åœ' ! a¨¤i¡-Ñ0Ô0�CØ<?�A�i ¨ZÑ!7Ð8Ñ9Ø Ñ+�Ið ˜a’-�-ùð �CŠZˆZÝ”6˜4˜% !™)Ñ$Ô$ˆDØ˜a’-�-Ø˜	‘M�Ø ×(Ò(¨aÐ(Ñ0Ô0�Ø ×(Ò(¨aÐ(Ñ0Ô0�Ø�œ˜t q¨1¡u™~°Ñ1Ñ2Ô2Ñ2°TÑ9�ð ˜Q™$ ™( aš-�ÝœV F™^œ^�
Ø ’>�>Ýœ' ! a¨¤i¡-Ñ0Ô0�CØ<?�A�i ¨ZÑ!7Ð8Ñ9Ø Ñ+�Ið ˜a’-�-øð ˜a’-�-Ø˜	‘M�Ø ×/Ò/°¸!Ð/Ñ<Ô<�Ø˜t a™xš-�ÝœV F™^œ^�
Ø ’>�>Ø<=¸f¼I�A�i ¨ZÑ!7Ð8Ñ9Ø Ñ+�Ið ˜a’-�-õ ”˜˜A ™E D™LÑ(Ñ)Ô)ˆAåŒz˜!˜VÑ$Ô$Ð$r5   c                 óØ  — t          j        |t          ¬¦  «        }t          |¦  «        }t          j        t           j        dz  ¦  «        |z  t          j        d|dz  dz  ¦  «        z  |z  }t          j        |¦  «        }|dk    }||         }dd|dz  z  z
  |t          |¦  «        z  ||         z  z   ||<   ||          }g d¢}t          j
        ||¦  «        || <   |||dz  z
  d d fS )	NrË  r*  r   rR   r   gš™™™™™¹?rƒ  )	g„_1gªÛÖ¾r   gWB³éa¿r   g½p|R÷H?r   gE'«å�¡?r   gš™™™™™Ù?)rM   rø   rL  r  rü   rî   rt   rµ  r   r·   rô  )rB   rË  r´  rÊ  rA  rV	  r  Úcoefs           r3   r   zargus_gen._statsb-  sî   € õ Œj˜¥EÐ*Ñ*Ô*ˆÝ˜‰oŒoˆÝŒG•B”E˜!‘GÑÔ˜sÑ"¥R¤V¨A¨s°A©v°a©xÑ%8Ô%8Ñ8¸3Ñ>ˆåŒm˜CÑ Ô ˆØ�SŠyˆØ�ŒIˆØ˜˜A˜q™D™‘L 1¥y°¡|¤|Ñ#3°c¸$´iÑ#?Ñ?ˆˆD‰	Ø��ŒJˆØKÐKÐKˆÝ”Z  aÑ(Ô(ˆˆTˆE‰
Ø�#˜˜1™‘*˜d DÐ(Ð(r5   r   )r€   r�   r‚   rƒ   rh   rÛ   ro   rr   rv   rÖ   r•  r   r„   r5   r3   r  r  ©,  s¯   € € € € € ð'ð 'ðPGð Gð GðGð Gð Gð,ð ,ð ,ð&ð &ð &ðEð Eð Eðð ð ð ð0c%ð c%ð c%ð c%ðJ)ð )ð )ð )ð )r5   r  ÚarguszAn Argus Function)rŠ   r  rˆ   r‰   c                   ó^   ‡ — e Zd ZdZej        Zddœˆ fd„
Zd„ Zd„ Zd„ Z	d„ Z
d	„ Zˆ fd
„Zˆ xZS )Úrv_histograma3  
    Generates a distribution given by a histogram.
    This is useful to generate a template distribution from a binned
    datasample.

    As a subclass of the `rv_continuous` class, `rv_histogram` inherits from it
    a collection of generic methods (see `rv_continuous` for the full list),
    and implements them based on the properties of the provided binned
    datasample.

    Parameters
    ----------
    histogram : tuple of array_like
        Tuple containing two array_like objects.
        The first containing the content of n bins,
        the second containing the (n+1) bin boundaries.
        In particular, the return value of `numpy.histogram` is accepted.

    density : bool, optional
        If False, assumes the histogram is proportional to counts per bin;
        otherwise, assumes it is proportional to a density.
        For constant bin widths, these are equivalent, but the distinction
        is important when bin widths vary (see Notes).
        If None (default), sets ``density=True`` for backwards compatibility,
        but warns if the bin widths are variable. Set `density` explicitly
        to silence the warning.

        .. versionadded:: 1.10.0

    Notes
    -----
    When a histogram has unequal bin widths, there is a distinction between
    histograms that are proportional to counts per bin and histograms that are
    proportional to probability density over a bin. If `numpy.histogram` is
    called with its default ``density=False``, the resulting histogram is the
    number of counts per bin, so ``density=False`` should be passed to
    `rv_histogram`. If `numpy.histogram` is called with ``density=True``, the
    resulting histogram is in terms of probability density, so ``density=True``
    should be passed to `rv_histogram`. To avoid warnings, always pass
    ``density`` explicitly when the input histogram has unequal bin widths.

    There are no additional shape parameters except for the loc and scale.
    The pdf is defined as a stepwise function from the provided histogram.
    The cdf is a linear interpolation of the pdf.

    .. versionadded:: 0.19.0

    Examples
    --------

    Create a scipy.stats distribution from a numpy histogram

    >>> import scipy.stats
    >>> import numpy as np
    >>> data = scipy.stats.norm.rvs(size=100000, loc=0, scale=1.5,
    ...                             random_state=123)
    >>> hist = np.histogram(data, bins=100)
    >>> hist_dist = scipy.stats.rv_histogram(hist, density=False)

    Behaves like an ordinary scipy rv_continuous distribution

    >>> hist_dist.pdf(1.0)
    0.20538577847618705
    >>> hist_dist.cdf(2.0)
    0.90818568543056499

    PDF is zero above (below) the highest (lowest) bin of the histogram,
    defined by the max (min) of the original dataset

    >>> hist_dist.pdf(np.max(data))
    0.0
    >>> hist_dist.cdf(np.max(data))
    1.0
    >>> hist_dist.pdf(np.min(data))
    7.7591907244498314e-05
    >>> hist_dist.cdf(np.min(data))
    0.0

    PDF and CDF follow the histogram

    >>> import matplotlib.pyplot as plt
    >>> X = np.linspace(-5.0, 5.0, 100)
    >>> fig, ax = plt.subplots()
    >>> ax.set_title("PDF from Template")
    >>> ax.hist(data, density=True, bins=100)
    >>> ax.plot(X, hist_dist.pdf(X), label='PDF')
    >>> ax.plot(X, hist_dist.cdf(X), label='CDF')
    >>> ax.legend()
    >>> fig.show()

    N)Údensityc                ó8  •— || _         || _        t          |¦  «        dk    rt          d¦  «        ‚t	          j        |d         ¦  «        | _        t	          j        |d         ¦  «        | _        t          | j        ¦  «        dz   t          | j        ¦  «        k    rt          d¦  «        ‚| j        dd…         | j        dd…         z
  | _        t	          j	        | j        | j        d         ¦  «         }|€#|r!d}t          j        |t          d¬	¦  «         d
}n|s| j        | j        z  | _        | j        t          t	          j        | j        | j        z  ¦  «        ¦  «        z  | _        t	          j        | j        | j        z  ¦  «        | _        t	          j        d| j        dg¦  «        | _        t	          j        d| j        g¦  «        | _        | j        d         x|d<   | _        | j        d         x|d<   | _         t)          ¦   «         j        |i |¤Ž dS )a5  
        Create a new distribution using the given histogram

        Parameters
        ----------
        histogram : tuple of array_like
            Tuple containing two array_like objects.
            The first containing the content of n bins,
            the second containing the (n+1) bin boundaries.
            In particular, the return value of np.histogram is accepted.
        density : bool, optional
            If False, assumes the histogram is proportional to counts per bin;
            otherwise, assumes it is proportional to a density.
            For constant bin widths, these are equivalent.
            If None (default), sets ``density=True`` for backward
            compatibility, but warns if the bin widths are variable. Set
            `density` explicitly to silence the warning.
        rR   z)Expected length 2 for parameter histogramr   r   zbNumber of elements in histogram content and histogram boundaries do not match, expected n and n+1.Nr¼  zjBin widths are not constant. Assuming `density=True`.Specify `density` explicitly to silence this warning.r  Tr…   rˆ   r‰   )Ú
_histogramÚ_densityr¡  r÷   rM   rø   Ú_hpdfÚ_hbinsÚ_hbin_widthsÚallcloser  r  r  rL  r¢  ÚcumsumÚ_hcdfÚhstackrˆ   r‰   r>   rM  )rB   Ú	histogramr-  rD   rÌ
  Ú	bins_varyr
  r“  s          €r3   rM  zrv_histogram.__init__Ô-  sæ  ø€ ð& $ˆŒØˆŒÝˆy‰>Œ>˜QÒÐÝÐHÑIÔIÐIÝ”Z 	¨!¤Ñ-Ô-ˆŒ
Ý”j ¨1¤Ñ.Ô.ˆŒÝˆtŒz‰?Œ?˜QÑ¥# d¤kÑ"2Ô"2Ò2Ð2Ýð 3ñ 4ô 4ð 4ð !œK¨¨¨œO¨d¬k¸#¸2¸#Ô.>Ñ>ˆÔÝœ DÔ$5°tÔ7HÈÔ7KÑLÔLÐLˆ	Øˆ?˜yˆ?ðOˆGåŒM˜'¥>¸aÐ@Ñ@Ô@Ð@ØˆGˆGØð 	8Øœ dÔ&7Ñ7ˆDŒJà”Z¥%­¬¨t¬z¸DÔ<MÑ/MÑ(NÔ(NÑ"OÔ"OÑOˆŒ
Ý”Y˜tœz¨DÔ,=Ñ=Ñ>Ô>ˆŒ
Ý”Y  T¤Z°Ð5Ñ6Ô6ˆŒ
Ý”Y  T¤ZÐ0Ñ1Ô1ˆŒ
à#œ{¨1œ~Ð-ˆˆs‰�d”fØ#œ{¨2œÐ.ˆˆs‰�d”fØ�‰ŒÔ˜$Ð) &Ð)Ð)Ð)Ð)Ð)r5   c                 óP   — | j         t          j        | j        |d¬¦  «                 S )z&
        PDF of the histogram
        rê  )Úside)r1  rM   Úsearchsortedr2  r¦   s     r3   ro   zrv_histogram._pdf.  s$   € ð Œz�"œ/¨$¬+°q¸wÐGÑGÔGÔHÐHr5   c                 óB   — t          j        || j        | j        ¦  «        S )z3
        CDF calculated from the histogram
        )rM   Úinterpr2  r6  r¦   s     r3   rr   zrv_histogram._cdf
.  s   € õ Œy˜˜DœK¨¬Ñ4Ô4Ð4r5   c                 óB   — t          j        || j        | j        ¦  «        S )zC
        Percentile function calculated from the histogram
        )rM   r>  r6  r2  r¦   s     r3   r{   zrv_histogram._ppf.  s   € õ Œy˜˜DœJ¨¬Ñ4Ô4Ð4r5   c                 ó¬   — | j         dd…         |dz   z  | j         dd…         |dz   z  z
  |dz   z  }t          j        | j        dd…         |z  ¦  «        S )z$Compute the n-th non-central moment.r   Nr¼  )r2  rM   r¢  r1  )rB   r_   Ú	integralss      r3   rÿ   zrv_histogram._munp.  s\   € à”[   ”_ q¨¡sÑ+¨d¬k¸#¸2¸#Ô.>ÀÀ1ÁÑ.EÑEÈ!ÈAÉ#ÑNˆ	ÝŒv�d”j  2 Ô&¨Ñ2Ñ3Ô3Ð3r5   c                 óÒ   — t          | j        dd…         dk    | j        dd…         ft          j        d¦  «        }t          j        | j        dd…         |z  | j        z  ¦  «         S )zCompute entropy of distributionr   r¼  r…   )r   r1  rM   rí   r¢  r3  )rB   r¶  s     r3   rï   zrv_histogram._entropy.  si   € å˜œ A b DÔ)¨CÒ/Øœ* Q r TÔ*Ð,ÝœØñô ˆõ ”�t”z ! B $Ô'¨#Ñ-°Ô0AÑAÑBÔBÐBÐBr5   c                 óp   •— t          ¦   «                              ¦   «         }| j        |d<   | j        |d<   |S )zF
        Set the histogram as additional constructor argument
        r8  r-  )r>   Ú_updated_ctor_paramr/  r0  )rB   Údctr“  s     €r3   rD  z rv_histogram._updated_ctor_param#.  s6   ø€ õ ‰gŒg×)Ò)Ñ+Ô+ˆØœ?ˆˆKÑØœˆˆI‰Øˆ
r5   )r€   r�   r‚   rƒ   r   r  rM  ro   rr   r{   rÿ   rï   rD  rÎ  rÏ  s   @r3   r,  r,  v-  sÇ   ø€ € € € € ðZð Zðv "Ô/€Mà15ð .*ð .*ð .*ð .*ð .*ð .*ð .*ð`Ið Ið Ið5ð 5ð 5ð5ð 5ð 5ð4ð 4ð 4ð
Cð Cð Cðð ð ð ð ð ð ð ð r5   r,  c                   ó@   ‡ — e Zd ZdZd„ Zd„ Zˆ fd„Zd„ Zd„ Zd„ Z	ˆ xZ
S )Ústudentized_range_genuO  A studentized range continuous random variable.

    %(before_notes)s

    See Also
    --------
    t: Student's t distribution

    Notes
    -----
    The probability density function for `studentized_range` is:

    .. math::

         f(x; k, \nu) = \frac{k(k-1)\nu^{\nu/2}}{\Gamma(\nu/2)
                        2^{\nu/2-1}} \int_{0}^{\infty} \int_{-\infty}^{\infty}
                        s^{\nu} e^{-\nu s^2/2} \phi(z) \phi(sx + z)
                        [\Phi(sx + z) - \Phi(z)]^{k-2} \,dz \,ds

    for :math:`x â‰¥ 0`, :math:`k > 1`, and :math:`\nu > 0`.

    `studentized_range` takes ``k`` for :math:`k` and ``df`` for :math:`\nu`
    as shape parameters.

    When :math:`\nu` exceeds 100,000, an asymptotic approximation (infinite
    degrees of freedom) is used to compute the cumulative distribution
    function [4]_ and probability distribution function.

    %(after_notes)s

    References
    ----------

    .. [1] "Studentized range distribution",
           https://en.wikipedia.org/wiki/Studentized_range_distribution
    .. [2] Batista, Ben DÃªivide, et al. "Externally Studentized Normal Midrange
           Distribution." CiÃªncia e Agrotecnologia, vol. 41, no. 4, 2017, pp.
           378-389., doi:10.1590/1413-70542017414047716.
    .. [3] Harter, H. Leon. "Tables of Range and Studentized Range." The Annals
           of Mathematical Statistics, vol. 31, no. 4, 1960, pp. 1122-1147.
           JSTOR, www.jstor.org/stable/2237810. Accessed 18 Feb. 2021.
    .. [4] Lund, R. E., and J. R. Lund. "Algorithm AS 190: Probabilities and
           Upper Quantiles for the Studentized Range." Journal of the Royal
           Statistical Society. Series C (Applied Statistics), vol. 32, no. 2,
           1983, pp. 204-210. JSTOR, www.jstor.org/stable/2347300. Accessed 18
           Feb. 2021.

    Examples
    --------
    >>> import numpy as np
    >>> from scipy.stats import studentized_range
    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots(1, 1)

    Display the probability density function (``pdf``):

    >>> k, df = 3, 10
    >>> x = np.linspace(studentized_range.ppf(0.01, k, df),
    ...                 studentized_range.ppf(0.99, k, df), 100)
    >>> ax.plot(x, studentized_range.pdf(x, k, df),
    ...         'r-', lw=5, alpha=0.6, label='studentized_range pdf')

    Alternatively, the distribution object can be called (as a function)
    to fix the shape, location and scale parameters. This returns a "frozen"
    RV object holding the given parameters fixed.

    Freeze the distribution and display the frozen ``pdf``:

    >>> rv = studentized_range(k, df)
    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

    Check accuracy of ``cdf`` and ``ppf``:

    >>> vals = studentized_range.ppf([0.001, 0.5, 0.999], k, df)
    >>> np.allclose([0.001, 0.5, 0.999], studentized_range.cdf(vals, k, df))
    True

    Rather than using (``studentized_range.rvs``) to generate random variates,
    which is very slow for this distribution, we can approximate the inverse
    CDF using an interpolator, and then perform inverse transform sampling
    with this approximate inverse CDF.

    This distribution has an infinite but thin right tail, so we focus our
    attention on the leftmost 99.9 percent.

    >>> a, b = studentized_range.ppf([0, .999], k, df)
    >>> a, b
    0, 7.41058083802274

    >>> from scipy.interpolate import interp1d
    >>> rng = np.random.default_rng()
    >>> xs = np.linspace(a, b, 50)
    >>> cdf = studentized_range.cdf(xs, k, df)
    # Create an interpolant of the inverse CDF
    >>> ppf = interp1d(cdf, xs, fill_value='extrapolate')
    # Perform inverse transform sampling using the interpolant
    >>> r = ppf(rng.uniform(size=1000))

    And compare the histogram:

    >>> ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
    >>> ax.legend(loc='best', frameon=False)
    >>> plt.show()

    c                 ó   — |dk    |dk    z  S rK  r„   )rB   r  r£  s      r3   r`   zstudentized_range_gen._argcheck˜.  s   € Ø�A’˜"˜qš&Ñ!Ð!r5   c                 ó‚   — t          dddt          j        fd¦  «        }t          dddt          j        fd¦  «        }||gS )Nr  Fr   r  r£  r   re   )rB   r1  rÀ  s      r3   rh   z!studentized_range_gen._shape_info›.  s>   € Ý˜˜U Q­¬ K°Ñ@Ô@ˆÝ˜˜u q­"¬& k°>ÑBÔBˆØ�CˆyÐr5   c                 óJ   •— t          ¦   «                              |d¬¦  «        S )N)rR   r   rJ  r  r  s     €r3   r’  zstudentized_range_gen._fitstart .  s    ø€ å‰wŒw× Ò  ¨FÐ Ñ3Ô3Ð3r5   c                 óÖ   ‡‡‡— dŠ|                       ¦   «         \  ŠŠˆˆˆfd„}t          j        |dd¦  «        }t          j         ||||¦  «        t          j        ¬¦  «        d         S )NÚ_studentized_range_momentc                 ó˜  •— t          j        ||¦  «        }| |||g}t          j        |t          ¦  «        j                             t
          j        ¦  «        }t          j	        t           ‰|¦  «        }t          j
         t          j
        fdt          j
        f‰	‰
fg}t          dd¬¦  «        }t          j        |||¬¦  «        d         S )Nr   rØ  çê-�™—q=©rZ  rY  ©ÚrangesÚopts)r   Ú_studentized_range_pdf_logconstrM   r[  rL  r\  r]  r^  r   r_  rf   Údictr   Únquad)rQ  r  r£  Ú	log_constÚargÚusr_datarf  rQ  rR  r¤  r£  Úcython_symbols            €€€r3   Ú_single_momentz3studentized_range_gen._munp.<locals>._single_momentª.  sª   ø€ ÝÔ>¸qÀ"ÑEÔEˆIØ�a˜˜YÐ'ˆCÝ”x ¥UÑ+Ô+Ô2×:Ò:½6¼?ÑKÔKˆHå"Ô.­v°}ÀhÑOÔOˆCåœ�w¥¤Ð'¨!­R¬V¨°r¸2°hÐ?ˆFÝ˜u¨UÐ3Ñ3Ô3ˆDå”? 3¨v¸DÐAÑAÔAÀ!ÔDÐDr5   rƒ  r   rË  r„   )r“   rM   Ú
frompyfuncrø   rV  )	rB   rQ  r  r£  rZ  Úufuncr¤  r£  rY  s	         @@@r3   rÿ   zstudentized_range_gen._munp¤.  s†   øøø€ Ø3ˆØ×"Ò"Ñ$Ô$‰ˆˆBð
	Eð 
	Eð 
	Eð 
	Eð 
	Eð 
	Eð 
	Eõ ”˜n¨a°Ñ3Ô3ˆÝŒz˜%˜%  1 b™/œ/µ´Ð<Ñ<Ô<¸RÔ@Ð@r5   c                 ó–   — d„ }t          j        |dd¦  «        }t          j         ||||¦  «        t           j        ¬¦  «        d         S )Nc                 óZ  — |dk     r�d}t          j        ||¦  «        }| |||g}t          j        |t          ¦  «        j                             t
          j        ¦  «        }t          j         t          j        fdt          j        fg}n\d}| |g}t          j        |t          ¦  «        j                             t
          j        ¦  «        }t          j         t          j        fg}t          j
        t           ||¦  «        }t          dd¬¦  «        }	t          j        |||	¬¦  «        d         S )	Né † Ú_studentized_range_pdfr   Ú!_studentized_range_pdf_asymptoticrØ  rN  rO  rP  )r   rS  rM   r[  rL  r\  r]  r^  rf   r   r_  rT  r   rU  ©
rz   r  r£  rY  rV  rW  rX  rQ  rf  rR  s
             r3   Ú_single_pdfz/studentized_range_gen._pdf.<locals>._single_pdf».  sý   € ð �FŠ{ˆ{Ø 8�Ý"ÔBÀ1ÀbÑIÔI�	Ø˜!˜R Ð+�Ýœ8 C­Ñ/Ô/Ô6×>Ò>½v¼ÑOÔO�ÝœF˜7¥B¤FÐ+¨aµ´¨[Ð9��ð !D�Ø˜!�f�Ýœ8 C­Ñ/Ô/Ô6×>Ò>½v¼ÑOÔO�ÝœF˜7¥B¤FÐ+Ð,�å"Ô.­v°}ÀhÑOÔOˆCÝ˜u¨UÐ3Ñ3Ô3ˆDÝ”? 3¨v¸DÐAÑAÔAÀ!ÔDÐDr5   rƒ  r   rË  r„   )rM   r[  rø   rV  )rB   rn   r  r£  rc  r\  s         r3   ro   zstudentized_range_gen._pdf¹.  sQ   € ð	Eð 	Eð 	Eõ( ”˜k¨1¨aÑ0Ô0ˆÝŒz˜%˜%  1 b™/œ/µ´Ð<Ñ<Ô<¸RÔ@Ð@r5   c           	      ó¾   — d„ }t          j        |dd¦  «        }t          j        t          j         ||||¦  «        t           j        ¬¦  «        d         dd¦  «        S )Nc                 óZ  — |dk     r�d}t          j        ||¦  «        }| |||g}t          j        |t          ¦  «        j                             t
          j        ¦  «        }t          j         t          j        fdt          j        fg}n\d}| |g}t          j        |t          ¦  «        j                             t
          j        ¦  «        }t          j         t          j        fg}t          j
        t           ||¦  «        }t          dd¬¦  «        }	t          j        |||	¬¦  «        d         S )	Nr_  Ú_studentized_range_cdfr   Ú!_studentized_range_cdf_asymptoticrØ  rN  rO  rP  )r   Ú_studentized_range_cdf_logconstrM   r[  rL  r\  r]  r^  rf   r   r_  rT  r   rU  rb  s
             r3   Ú_single_cdfz/studentized_range_gen._cdf.<locals>._single_cdfÔ.  sý   € ð
 �FŠ{ˆ{Ø 8�Ý"ÔBÀ1ÀbÑIÔI�	Ø˜!˜R Ð+�Ýœ8 C­Ñ/Ô/Ô6×>Ò>½v¼ÑOÔO�ÝœF˜7¥B¤FÐ+¨aµ´¨[Ð9��ð !D�Ø˜!�f�Ýœ8 C­Ñ/Ô/Ô6×>Ò>½v¼ÑOÔO�ÝœF˜7¥B¤FÐ+Ð,�å"Ô.­v°}ÀhÑOÔOˆCÝ˜u¨UÐ3Ñ3Ô3ˆDÝ”? 3¨v¸DÐAÑAÔAÀ!ÔDÐDr5   rƒ  r   rË  r„   r   )rM   r[  r6	  rø   rV  )rB   rn   r  r£  ri  r\  s         r3   rr   zstudentized_range_gen._cdfÒ.  sa   € ð	Eð 	Eð 	Eõ, ”˜k¨1¨aÑ0Ô0ˆõ Œw•r”z % %¨¨1¨b¡/¤/½¼ÐDÑDÔDÀRÔHÈ!ÈQÑOÔOÐOr5   )r€   r�   r‚   rƒ   r`   rh   r’  rÿ   ro   rr   rÎ  rÏ  s   @r3   rG  rG  -.  s�   ø€ € € € € ðhð hðT"ð "ð "ðð ð ð
4ð 4ð 4ð 4ð 4ðAð Að Að*Að Að Að2Pð Pð Pð Pð Pð Pð Pr5   rG  Ústudentized_range)rŠ   rˆ   r‰   c                   óh   ‡ — e Zd ZdZd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z	 e
e¦  «        ˆ fd„¦   «         Zˆ xZS )	Úrel_breitwigner_genaÿ  A relativistic Breit-Wigner random variable.

    %(before_notes)s

    See Also
    --------
    cauchy: Cauchy distribution, also known as the Breit-Wigner distribution.

    Notes
    -----

    The probability density function for `rel_breitwigner` is

    .. math::

        f(x, \rho) = \frac{k}{(x^2 - \rho^2)^2 + \rho^2}

    where

    .. math::
        k = \frac{2\sqrt{2}\rho^2\sqrt{\rho^2 + 1}}
            {\pi\sqrt{\rho^2 + \rho\sqrt{\rho^2 + 1}}}

    The relativistic Breit-Wigner distribution is used in high energy physics
    to model resonances [1]_. It gives the uncertainty in the invariant mass,
    :math:`M` [2]_, of a resonance with characteristic mass :math:`M_0` and
    decay-width :math:`\Gamma`, where :math:`M`, :math:`M_0` and :math:`\Gamma`
    are expressed in natural units. In SciPy's parametrization, the shape
    parameter :math:`\rho` is equal to :math:`M_0/\Gamma` and takes values in
    :math:`(0, \infty)`.

    Equivalently, the relativistic Breit-Wigner distribution is said to give
    the uncertainty in the center-of-mass energy :math:`E_{\text{cm}}`. In
    natural units, the speed of light :math:`c` is equal to 1 and the invariant
    mass :math:`M` is equal to the rest energy :math:`Mc^2`. In the
    center-of-mass frame, the rest energy is equal to the total energy [3]_.

    %(after_notes)s

    :math:`\rho = M/\Gamma` and :math:`\Gamma` is the scale parameter. For
    example, if one seeks to model the :math:`Z^0` boson with :math:`M_0
    \approx 91.1876 \text{ GeV}` and :math:`\Gamma \approx 2.4952\text{ GeV}`
    [4]_ one can set ``rho=91.1876/2.4952`` and ``scale=2.4952``.

    To ensure a physically meaningful result when using the `fit` method, one
    should set ``floc=0`` to fix the location parameter to 0.

    References
    ----------
    .. [1] Relativistic Breit-Wigner distribution, Wikipedia,
           https://en.wikipedia.org/wiki/Relativistic_Breit-Wigner_distribution
    .. [2] Invariant mass, Wikipedia,
           https://en.wikipedia.org/wiki/Invariant_mass
    .. [3] Center-of-momentum frame, Wikipedia,
           https://en.wikipedia.org/wiki/Center-of-momentum_frame
    .. [4] M. Tanabashi et al. (Particle Data Group) Phys. Rev. D 98, 030001 -
           Published 17 August 2018

    %(example)s

    c                 ó   — |dk    S r®  r„   ©rB   Úrhos     r3   r`   zrel_breitwigner_gen._argcheck2/  s   € Ø�QŠwˆr5   c                 ó@   — t          dddt          j        fd¦  «        gS )Nro  Fr   r  re   rg   s    r3   rh   zrel_breitwigner_gen._shape_info5/  r  r5   c           
      ó0  — t          j        ddd|dz  z  z   z  dt          j        dd|dz  z  z   ¦  «        z   z  ¦  «        dz  t           j        z  }t          j        d¬¦  «        5  |||z
  ||z   z  |z  dz  dz   z  cd d d ¦  «         S # 1 swxY w Y   d S )NrR   r   r5  rn  )rM   rü   rî   r8  )rB   rn   ro  r  s       r3   ro   zrel_breitwigner_gen._pdf8/  sö   € åŒGØ��Q�s˜A‘v‘X‘Ñ !¥b¤g¨a°!°C¸±F±(©lÑ&;Ô&;Ñ";Ñ<ñ
ô 
àñå”ñˆõ Œ[˜hÐ'Ñ'Ô'ð 	:ð 	:Ø˜!˜c™' A¨¡GÑ,¨SÑ0°1Ñ4°qÑ8Ñ9ð	:ð 	:ð 	:ð 	:ñ 	:ô 	:ð 	:ð 	:ð 	:ð 	:ð 	:ð 	:øøøð 	:ð 	:ð 	:ð 	:ð 	:ð 	:s   Á'BÂBÂBc           
      ó|  — t          j        ddt          j        dd|dz  z  z   ¦  «        z   z  ¦  «        t           j        z  }t          j        dd|z  z   ¦  «        t          j        |t          j        | |dz   z  ¦  «        z  ¦  «        z  }|dz  t          j        |¦  «        z  }t          j        |d d¦  «        S )NrR   r   r¼  rú
  )rM   rü   rî   rˆ  Úimagr6	  )rB   rn   ro  r  rß  s        r3   rr   zrel_breitwigner_gen._cdf@/  s©   € åŒG�A�q�2œ7 1 q¨¨a©¡x¡<Ñ0Ô0Ñ0Ñ1Ñ2Ô2µ2´5Ñ8ˆåŒG�B˜˜C™‘KÑ Ô ÝŒi˜�"œ' 3 $¨¨b©¡/Ñ2Ô2Ñ2Ñ3Ô3ñ4ð 	ð �Q‘�œ ™œÑ(ˆåŒw�v˜t QÑ'Ô'Ð'r5   c                 ó$  — |dk    rxt          j        ddd|dz  z  z   z  dt          j        dd|dz  z  z   ¦  «        z   z  ¦  «        t           j        z  |z  }|t           j        dz  t          j        |¦  «        z   z  S |dk    r�t          j        dd|dz  z  z   ddt          j        dd|dz  z  z   ¦  «        z   z  z  ¦  «        |z  }d|dz  z
  t          j        dd|z  z
  ¦  «        z  }d|z  t          j        |¦  «        z  S t           j        S )Nr   rR   rú
  r¼  )rM   rü   rî   rˆ  r–  rf   )rB   r_   ro  r  rß  s        r3   rÿ   zrel_breitwigner_gen._munpK/  s  € Ø�Š6ˆ6å”Ø�Q˜˜3 ™6™‘\Ñ" a­"¬'°!°a¸¸Q¹±h±,Ñ*?Ô*?Ñ&?Ñ@ñô å”ñàñˆAð �œ˜a™¥"¤)¨C¡.¤.Ñ0Ñ1Ð1Ø�Š6ˆ6å”Ø�Q�s˜A‘v‘X‘ ! q­2¬7°1°q¸¸a¹±x±<Ñ+@Ô+@Ñ'@Ñ"AÑBñô àñˆAð ˜# ™(‘l¥b¤g¨b°2°c±6©kÑ&:Ô&:Ñ:ˆFØ�q‘5�2œ7 6™?œ?Ñ*Ð*å”6ˆMr5   c                 ó6   — d d t           j        t           j        fS rK   r�  rn  s     r3   r   zrel_breitwigner_gen._stats\/  s   € ð �T�2œ6¥2¤6Ð)Ð)r5   c                 óÒ  •— t          | |||¦  «        \  }}}}t          |t          ¦  «        }|r!|                     ¦   «         dk    r	|j        }d}|�|r t          ¦   «         j        |g|¢R i |¤ŽS |€7t          j        ||z
  g d¢¦  «        \  }}	}
|
|z
  }|	|z  }|s|g}d|vr||d<   n!t          j	        ||z
  ¦  «        }||z  }|s|g} t          ¦   «         j        |g|¢R i |¤ŽS )Nr   F)rž  r‘   g      è?r-   )
r  r<   r(   r=   rA   r>   r@   rM   ÚquantilerH  )rB   rC   rD   r2   rÇ  ró   rô   rE   r›  rœ  r�  Úscale_0Úrho_0ÚM_0r“  s                 €r3   r@   zrel_breitwigner_gen.fitb/  sD  ø€ õ !<Ø�$˜˜dñ!
ô !
Ñˆˆa��võ ˜d¥LÑ1Ô1ˆØð 	!Ø× Ò Ñ"Ô" aÒ'Ð'ð Ô'�Ø �àˆ<˜8ˆ<Ø•5‘7”7”;˜tÐ3 dÐ3Ð3Ð3¨dÐ3Ð3Ð3àˆ>õ œK¨¨t©Ð5FÐ5FÐ5FÑGÔG‰MˆC��cØ˜C‘iˆGØ˜'‘MˆEØð Ø�w�Ø˜dÐ"Ð"Ø '��W‘øå”)˜D 4™KÑ(Ô(ˆCØ˜&‘LˆEØð Ø�w�Ø�u‰wŒwŒ{˜4Ð/ $Ð/Ð/Ð/¨$Ð/Ð/Ð/r5   )r€   r�   r‚   rƒ   r`   rh   ro   rr   rÿ   r   r   r   r@   rÎ  rÏ  s   @r3   rl  rl  ô.  s¸   ø€ € € € € ð<ð <ðzð ð ðGð Gð Gð:ð :ð :ð	(ð 	(ð 	(ðð ð ð"*ð *ð *ð Ð˜MÑ*Ô*ð 0ð  0ð  0ð  0ñ +Ô*ð 0ð  0ð  0ð  0ð  0r5   rl  Úrel_breitwignerrK   (I  r  Úcollections.abcr   Ú	functoolsr   r   r\  ÚnumpyrM   Únumpy.polynomialr   Úscipy.interpolater   Úscipy._lib.doccerr	   r
   r   Úscipy._lib._ccallbackr   Úscipyr   r   Úscipy.specialÚspecialrt   Úscipy.special._ufuncsr�  rk   Úscipy._lib._utilr   r   rR  r   Ú_tukeylambda_statsr   r  r   r€  Ú_distn_infrastructurer   r   r   r   r   r   r   r   r   Ú_ksstatsr   r   r    Ú
_constantsr!   r"   r#   r$   r%   r&   r'   Ú_censored_datar(   Úscipy.optimizer)   Úscipy.stats._warnings_errorsr*   Úscipy.statsrð  r4   rH   rW   rY   r‡   rŒ   rž   r¡   r°   rü   rî   rµ   rí   r¹   r·   rº   r½   rÀ   rÄ   rÇ   rÊ   rÍ   rÏ   r  r  r  r  r0  r2  rF  r÷   rH  rT   r\  r`  rb  rk  rÑ  r  r  r  r  rZ  r\  rm  ro  r€  r‚  rž  r   rË  rÍ  r¦  ré  rÿ  r  r  r  r2  r4  rJ  rO  rf  rj  rl  r|  r~  r‘  r“  rª  r¬  r½  r¿  r‡  rã  rð  rò  r  r  r7  r9  rE  rG  r`  rb  rŠ  rŒ  rš  rœ  rÓ  rß  rá  rÖ  r   r  r  r1  r3  r>  r@  r„  r†  r“  r™  r›  r·  r¹  rÊ  rÌ  rÙ  ré  r  r	  r  r  r+  r-  r6  r8  rM  rO  rn  rt  ro  rÒ  ró  rõ  r  r  r  r  r%  r'  r8  r:  r=  rJ  r]  r  rr  r€  r‚  r‹  r�  r�  r§  rÇ  rÉ  rØ  rÜ  rÞ  r  r  r  r  r-  r/  r<  r>  rz  r|  r‹  r�  rž  r   r²  r¹  r»  rå  rç  r	  r	  r˜  r1	  rJ	  rL	  r[	  rh	  rs	  ru	  r�	  r’	  r 	  r½	  rÉ	  rË	  rÕ	  r×	  rá	  rã	  rù	  rý	  r
  r
  r
  r 
  r"
  rC
  rE
  rQ
  rS
  r]
  r_
  ri
  rk
  r—
  r™
  rº
  r·
  r¾
  r¿
  Ú_method_namesrÈ
  rÊ  ÚsetattrrÎ
  rä
  ræ
  ró
  rø
  r
  r  r  r=  r?  rk  rt  r„  r†  r‰  r  r”  r˜  r³  ro  rU  rÄ  rÓ  rÕ  ré  rë  rô  rö  r  r  r  r*  r,  rG  rf   rj  rl  r{  ÚlistÚglobalsrw	  ÚitemsÚpairsÚ_distn_namesÚ_distn_gen_namesÚ__all__r„   r5   r3   ú<module>r™     sz#  ðð
 €€€Ø $Ð $Ð $Ð $Ð $Ð $Ø ,Ð ,Ð ,Ð ,Ð ,Ð ,Ð ,Ð ,Ø €€€à Ð Ð Ð Ø 'Ð 'Ð 'Ð 'Ð 'Ð 'Ø %Ð %Ð %Ð %Ð %Ð %ð7ð 7ð 7ð 7ð 7ð 7ð 7ð 7ð 7ð 7ð 3Ð 2Ð 2Ð 2Ð 2Ð 2Ø Ð Ð Ð Ð Ð Ø Ð Ð Ð Ð Ð Ø Ð Ð Ð Ð Ð à #Ð #Ð #Ð #Ð #Ð #Ð #Ð #Ð #Ø 4Ð 4Ð 4Ð 4Ð 4Ð 4Ð 4Ð 4à Ð Ð Ð Ð Ð ðBð Bð Bð Bð Bð Bð Bð BðJð Jð Jð Jð Jð Jð Jð Jð Jð Jð Jð Jð Jð Jð Jð Jð Jð Jð Jð Jð Jð Jð 2Ð 1Ð 1Ð 1Ð 1Ð 1Ð 1Ð 1Ð 1Ð 1ð?ð ?ð ?ð ?ð ?ð ?ð ?ð ?ð ?ð ?ð ?ð ?ð ?ð ?ð ?ð ?ð ?ð ?à (Ð (Ð (Ð (Ð (Ð (Ø &Ð &Ð &Ð &Ð &Ð &Ø 1Ð 1Ð 1Ð 1Ð 1Ð 1Ø Ð Ð Ð Ð Ð ð9ð 9ð 9ð&ð ð ñ*ð ð ð ð.W!ð W!ð W!ð W!ð W!�ñ W!ô W!ð W!ðt 	ˆ	�C˜3 WÐ-Ñ-Ô-€ðZ)ð Z)ð Z)ð Z)ð Z)�ñ Z)ô Z)ð Z)ð| 	ˆ	˜!˜s c°Ð8Ñ8Ô8€ð5ð 5ð 5ð 5ð 5�Mñ 5ô 5ð 5ðp ˆM˜C kÐ2Ñ2Ô2€	ð ˆbŒg�a˜œ‘gÑÔ€Ø�”˜Ñ$Ô$€ð+ð +ð +ð(ð (ð (ðð ð ðð ð ðð ð ðð ð ðð ð ðð ð ðkð kð kð kð kˆ}ñ kô kð kð\ €x�VÐÑÔ€ð3'ð 3'ð 3'ð 3'ð 3'�ñ 3'ô 3'ð 3'ðl 	ˆ	�C˜gÐ&Ñ&Ô&€ð(ð (ð (ð (ð (�ñ (ô (ð (ðV 
ˆ�r”u�f˜Q‘h "¤%¨¡'°Ð	9Ñ	9Ô	9€ð*'ð *'ð *'ð *'ð *'�-ñ *'ô *'ð *'ðZ ˆ+˜˜s¨Ð
3Ñ
3Ô
3€ð

ð 

ð 

ð 

ð 

�:ñ 

ô 

ð 

ð	ð 	ð 	ð 	ð 	�Xñ 	ô 	ð 	ðð ð ðð ð ðo!ð o!ð o!ð o!ð o!ˆ}ñ o!ô o!ð o!ðd €x�#˜ 6Ð*Ñ*Ô*€ðið ið ið ið i�Mñ iô ið iðX ˆM˜C kÐ2Ñ2Ô2€	ð4#ð 4#ð 4#ð 4#ð 4#�=ñ 4#ô 4#ð 4#ðn ˆ<˜# ¨:Ð6Ñ6Ô6€ð~"ð ~"ð ~"ð ~"ð ~"ˆ}ñ ~"ô ~"ð ~"ðB €x�#˜FÐ#Ñ#Ô#€ðT,ð T,ð T,ð T,ð T,�ñ T,ô T,ð T,ðn 
ˆ�c Ð	)Ñ	)Ô	)€ðOð Oð Oð Oð Oˆxñ Oô Oð Oðd €x�#˜FÐ#Ñ#Ô#€ð2"ð 2"ð 2"ð 2"ð 2"�ñ 2"ô 2"ð 2"ðj 
ˆ˜Ð	"Ñ	"Ô	"€ðO1ð O1ð O1ð O1ð O1ˆmñ O1ô O1ð O1ðd €g�˜%Ð Ñ Ô €ðV1ð V1ð V1ð V1ð V1ˆ}ñ V1ô V1ð V1ðr €x�#˜FÐ#Ñ#Ô#€ð4#ð 4#ð 4#ð 4#ð 4#�ñ 4#ô 4#ð 4#ðn 
ˆ�r”u�f ¤¨HÐ	5Ñ	5Ô	5€ðJ6ð J6ð J6ð J6ð J6�ñ J6ô J6ð J6ðZ 
ˆ˜Ð	"Ñ	"Ô	"€ðEð Eð Eð Eð E�=ñ Eô Eð EðP ˆ<˜ZÐ(Ñ(Ô(€ðj(ð j(ð j(ð j(ð j(�ñ j(ô j(ð j(ðZ 	ˆ	�C˜gÐ&Ñ&Ô&€ðK!ð K!ð K!ð K!ð K!�Mñ K!ô K!ð K!ð\ ˆM˜{Ð+Ñ+Ô+€	ð&ð &ð &ð&E4ð E4ð E4ð E4ð E4�Mñ E4ô E4ð E4ðP ˆM˜C kÐ2Ñ2Ô2€	ð23ð 23ð 23ð 23ð 23�=ñ 23ô 23ð 23ðj ˆ<˜# JÐ/Ñ/Ô/€ðJð Jð Jð Jð J�mñ Jô Jð JðZ ˆo ¨-Ð8Ñ8Ô8€ð-.ð -.ð -.ð -.ð -.�]ñ -.ô -.ð -.ð` ˆ^˜c¨Ð5Ñ5Ô5€
ðk@ð k@ð k@ð k@ð k@ˆMñ k@ô k@ð k@ð\ 
€EˆC�cÐÑÔ€ð;ð ;ð ;ð ;ð ;�=ñ ;ô ;ð ;ð| ˆ<˜# JÐ/Ñ/Ô/€ð^Fð ^Fð ^Fð ^Fð ^F�mñ ^Fô ^Fð ^FðB ˆo ¨-Ð8Ñ8Ô8€ðh!ð h!ð h!ð h!ð h!˜=ñ h!ô h!ð h!ðV (Ð'Ð-?Ð@Ñ@Ô@Ð ðD4ð D4ð D4ð D4ð D4�mñ D4ô D4ð D4ðN ˆo ¨-Ð8Ñ8Ô8€ðQ?ð Q?ð Q?ð Q?ð Q?�mñ Q?ô Q?ð Q?ðh ˆo =Ð1Ñ1Ô1€ðuð uð uð uð u�Mñ uô uð uðp ˆM˜C kÐ2Ñ2Ô2€	ð=;ð =;ð =;ð =;ð =;�=ñ =;ô =;ð =;ð@ ˆ<˜# JÐ/Ñ/Ô/€ðR"ð R"ð R"ð R"ð R"�]ñ R"ô R"ð R"ðj ˆ^ Ð.Ñ.Ô.€
ð)ð )ð )ðdMð Mð Mð Mð M�ñ Mô Mð Mð` 	ˆ	�C˜gÐ&Ñ&Ô&€ð40ð 40ð 40ð 40ð 40�ñ 40ô 40ð 40ðn 
ˆ�c Ð	)Ñ	)Ô	)€ð^ð ^ð ^ð ^ð ^�=ñ ^ô ^ð ^ðB ˆ<˜# JÐ/Ñ/Ô/€ð/%ð /%ð /%ð /%ð /%˜-ñ /%ô /%ð /%ðd &Ð%¨Ð2CÐDÑDÔD€ðeð eð eð eð e˜ñ eô eð eðP "Ð! Ð7Ñ7Ô7€ð->ð ->ð ->ð ->ð ->�=ñ ->ô ->ð ->ð` ˆ<˜# JÐ/Ñ/Ô/€ð*ð *ð *ð|ð |ð |ð |ð |�=ñ |ô |ð |ð~ ˆ<˜ZÐ(Ñ(Ô(€ðIð Ið Ið Ið I�=ñ Iô Ið IðX ˆ<˜ZÐ(Ñ(Ô(€ðWð Wð Wð Wð W�]ñ Wô Wð Wðt ˆ^˜c¨Ð5Ñ5Ô5€
ðyð yð yð yð y�}ñ yô yð yðx  Ð #¨NÐ;Ñ;Ô;€ðPð Pð Pð Pð P�=ñ Pô Pð Pðf ˆ<˜# JÐ/Ñ/Ô/€ð+ð +ð +ð +ð +�Mñ +ô +ð +ð\ ˆM˜{Ð+Ñ+Ô+€	ð5ð 5ð 5ð 5ð 5�]ñ 5ô 5ð 5ðp ˆ^˜c S¨|Ð<Ñ<Ô<€
ðSð Sð Sð Sð S�=ñ Sô Sð Sðl ˆ<˜# JÐ/Ñ/Ô/€ðM!ð M!ð M!ð M!ð M!�=ñ M!ô M!ð M!ð` ˆ<˜# JÐ/Ñ/Ô/€ðzð zð zð zð z�mñ zô zð zðz	 ˆo ¨-Ð8Ñ8Ô8€ðP2ð P2ð P2ð P2ð P2�}ñ P2ô P2ð P2ðf  Ð ^Ð4Ñ4Ô4€ð@2ð @2ð @2ð @2ð @2�]ñ @2ô @2ð @2ðF ˆ^˜a lÐ3Ñ3Ô3€
ð]
ð ]
ð ]
ð ]
ð ]
�Mñ ]
ô ]
ð ]
ð@ ˆM˜{Ð+Ñ+Ô+€	ð56ð 56ð 56ð 56ð 56�Mñ 56ô 56ð 56ðp ˆM˜C 3¨[Ð9Ñ9Ô9€	ðZð Zð Zð Zð Z�Mñ Zô Zð Zðz ˆM˜{Ð+Ñ+Ô+€	ðEð Eð Eð Eð E�-ñ Eô Eð EðP ˆ+˜9Ð
%Ñ
%Ô
%€ð])ð ])ð ])ð ])ð ])˜]ñ ])ô ])ð ])ð@ ,Ð+Ð1EÐFÑFÔFÐ ð.*ð .*ð .*ðbb.ð b.ð b.ð b.ð b.ˆ}ñ b.ô b.ð b.ðJ €x�#˜FÐ#Ñ#Ô#€ðb.ð b.ð b.ð b.ð b.�ñ b.ô b.ð b.ðJ 
ˆ�c Ð	)Ñ	)Ô	)€ðq7ð q7ð q7ð q7ð q7�=ñ q7ô q7ð q7ðh ˆ<˜ZÐ(Ñ(Ô(€ðoð oð oð oð o�=ñ oô oð oðd ˆ<˜ZÐ(Ñ(Ô(€ð^ð ^ð ^ð ^ð ^�]ñ ^ô ^ð ^ð@ ˆ^˜c¨Ð5Ñ5Ô5€
ðð ð ðC!ð C!ð C!ð C!ð C!�-ñ C!ô C!ð C!ðL ˆ+˜ )Ð
,Ñ
,Ô
,€ð8-ð 8-ð 8-ð 8-ð 8-�ñ 8-ô 8-ð 8-ðv 
ˆ�c Ð	)Ñ	)Ô	)€ð>0ð >0ð >0ð >0ð >0�-ñ >0ô >0ð >0ðB ˆ+˜ )Ð
,Ñ
,Ô
,€ð;@ð ;@ð ;@ð ;@ð ;@�ñ ;@ô ;@ð ;@ð| 
ˆ�c Ð	)Ñ	)Ô	)€ðLIð LIð LIð LIð LI�ñ LIô LIð LIð^ 
ˆ˜Ð	"Ñ	"Ô	"€ðJIð JIð JIð JIð JI�ñ JIô JIð JIðZ 
ˆ�c Ð	)Ñ	)Ô	)€ðY$ð Y$ð Y$ð Y$ñ Y$�ñ Y$ô Y$ð Y$ðx 	ˆ	‘wÐÑÔ€ða#ð a#ñ a#ð a#ñ a#�=ñ a#ô a#ð a#ðH ˆ<˜#¡JÐ/Ñ/Ô/€ñð ð ð X
ð X
ñ X
ð X
ñ X
ˆ}ñ X
ô X
ð X
ðv €x�#™FÐ#Ñ#Ô#€ðYð Yñ Yð Yñ Yˆmñ Yô Yð Yðx €g�™%Ð Ñ Ô €ðsð sñ sð sñ sˆMñ sô sð sðl 
€E‰s€O�O„O€ðNð Nñ Nð Nñ Nˆmñ Nô Nð Nðb €g‘5ÐÑÔ€ð[!ð [!ñ [!ð [!ñ [!�ñ [!ô [!ð [!ð| 
ˆ�c¡Ð	)Ñ	)Ô	)€ð6!ð 6!ñ 6!ð 6!ñ 6!�ñ 6!ô 6!ð 6!ðr 	ˆ	�C™gÐ&Ñ&Ô&€ðADð ADñ ADð ADñ AD�=ñ ADô ADð ADðH ˆ<™ZÐ(Ñ(Ô(€ðW4ð W4ñ W4ð W4ñ W4�=ñ W4ô W4ð W4ðt ˆ<˜# ©:Ð6Ñ6Ô6€ð40ð 40ñ 40ð 40ñ 40�}ñ 40ô 40ð 40ðn  Ð #©NÐ;Ñ;Ô;€ð31ð 31ñ 31ð 31ñ 31�Mñ 31ô 31ð 31ðl ˆM™{Ð+Ñ+Ô+€	ð:3ð :3ñ :3ð :3ñ :3�ñ :3ô :3ð :3ðz 	ˆ	‘D˜C¡gÐ.Ñ.Ô.�ðvð vñ vð vñ v�=ñ vô vñ vðr ‰<˜#¡JÐ/Ñ/Ô/�ða?ð a?ñ a?ð a?ñ a?�]ñ a?ô a?ñ a?ðP ‰^¡Ð.Ñ.Ô.�
Ø‰^¡Ð.Ñ.Ô.�
ð<&ð <&ñ <&ð <&ñ <&ˆ}ñ <&ô <&ñ <&ð~ �x�#™FÐ#Ñ#Ô#�ð|&ð |&ñ |&ð |&ñ |&�Mñ |&ô |&ñ |&ð| ‰M™{Ð+Ñ+Ô+�	ð29ð 29ñ 29ð 29ñ 29˜ñ 29ô 29ñ 29ðj "Ñ! C©oÐ>Ñ>Ô>�ð9&ð 9&ñ 9&ð 9&ñ 9&�}ñ 9&ô 9&ñ 9&ðx  Ñ¡$¨#±NÐCÑCÔC�ð@'ð @'ñ @'ð @'ñ @'�]ñ @'ô @'ñ @'ðF ‰^¡Ð.Ñ.Ô.�
ðYFð YFñ YFð YFñ YF�=ñ YFô YFñ YFðx ‰<™ZÐ(Ñ(Ô(�ðgEð gEñ gEð gEñ gE�Mñ gEô gEñ gEñV2�ð*ð *ñ *ð *ñ *‘ñ *ô *ñ *ð ‰M˜C 3©[Ð9Ñ9Ô9�	Ø‰	�C˜3¡WÐ-Ñ-Ô-�ðñ ð �ð	,ð 	,ñ 	,ð 	,ñ 	,ñ 	,ô 	,ñ 	,ñ 
ð .ð .�AØ�G‰E‘1Ð)Ñ)©!Ñ,Ô,Ñ-Ô-Ð-Ð-ðFð Fñ Fð Fñ F�ñ Fô Fñ FðR 
‰�c˜S¡xÐ	0Ñ	0Ô	0�ð<4ð <4ñ <4ð <4ñ <4�]ñ <4ô <4ñ <4ð~ ‰^˜c©Ð5Ñ5Ô5�
ñ0ð 0ñ 0ñ
9ð 9ñ 9ñ%ð %ñ %ðPg7ð g7ñ g7ð g7ñ g7�Mñ g7ô g7ñ g7ðT ‰M™{°AÑ6Ñ6Ô6�	ðzð zñ zð zñ z�mñ zô zñ zðz	 ‰o ©-Ð8Ñ8Ô8�ð/.ð /.ñ /.ð /.ñ /.�mñ /.ô /.ñ /.ðd ‰o¡=Ð1Ñ1Ô1�ð
ð 
ñ 
ð 
ñ 
 Lñ 
ô 
ñ 
ðt(ð t(ñ t(ð t(ñ t(�-ñ t(ô t(ñ t(ðn ‰+˜˜s©Ð
3Ñ
3Ô
3�ðoð oñ oð oñ o�=ñ oô oñ oðd ‰<™ZÐ(Ñ(Ô(�Ø‘ ¤˜v¨¬±_ÐEÑEÔE�ð:&ð :&ñ :&ð :&ñ :&ˆ|ñ :&ô :&ñ :&ðz �x�#™FÐ#Ñ#Ô#�ð<9ð <9ñ <9ð <9ñ <9�]ñ <9ô <9ñ <9ð~ ‰^˜c Q r¤u¡W±<Ð@Ñ@Ô@�
ðTð Tñ Tð Tñ T�-ñ Tô Tñ Tðn ‰+™9Ð
%Ñ
%Ô
%�ð=>ð =>ñ =>ð =>ñ =>�mñ =>ô =>ñ =>ð@ ‰o ©Ð6Ñ6Ô6�ðU&ð U&ñ U&ð U&ñ U&�mñ U&ô U&ñ U&ðp ‰o¡=Ñ;SÑTÑTÔT�ñ*ð *ñ *ðG)ð G)ñ G)ð G)ñ G)�ñ G)ô G)ñ G)ðT 	‰	‘wÑ)<ÀÀsÑKÑKÔK�ðtð tñ tð tñ t�=ñ tô tñ tðn@Pð @Pñ @Pð @Pñ @P˜Mñ @Pô @Pñ @PðF *Ñ)Ñ/BÀaØ,.­Fñ4ñ 4ô 4Ñ ðO0ð O0ñ O0ð O0ñ O0˜-ñ O0ô O0ñ O0ðd &Ñ%¨Ñ2CÐDÑDÔD�ð 	‰ˆW‰W‰YŒY�^‹^ÑÔ×#Ó#Ñ%Ô%Ñ&Ô&�Ø!7Ð!7¹¸}Ñ!MÔ!MÑ �Ñá
Ñ)Ñ
)©^Ð,<Ñ
<�€€r5   