
    \ciI                        d dl Z d dl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ZmZmZmZmZmZmZ g dZ G d d	e          Zd
 Z G d de          Z G d de          Z G d de          Z G d de          Z G d de          Z G d de          Ze j        e         j        Z eD ]Z! ee e!                   e e!         _"        dS )    N)inf)array_api_extra)special)_ufuncs)ContinuousDistributionDiscreteDistribution_RealInterval_IntegerInterval_RealParameter_Parameterization_combine_docs)NormalLogisticUniformBinomialc                       e Zd ZdZ ee ef          Z edef          Z ee ef          Z e	dded          Z
 e	dd	ed
          Z e	ded          Z ee
e          gZeZd ej        dej        z            z  Z ej        dej        z            dz  Zd& fd	Zddd 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  Z#d! Z$d" Z%d# Z&ddge&_'        d$ Z(d% Z) xZ*S )'r   a  Normal distribution with prescribed mean and standard deviation.

    The probability density function of the normal distribution is:

    .. math::

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

    	endpointsr   muz\mu)   symboldomaintypicalsigmaz\sigma)      ?g      ?xr   r   r      Nc                     |(|&t                                          t                    S t                                          |           S N)super__new__StandardNormal)clsr   r   kwargs	__class__s       n/var/www/html/mdtn/previsions/meteo_cartes/venv/lib/python3.11/site-packages/scipy/stats/_new_distributions.pyr$   zNormal.__new__.   s8    :%-77??>222wws###                  ?r   r   c                @     t                      j        d||d| d S )Nr-    r#   __init__)selfr   r   r'   r(   s       r)   r1   zNormal.__init__3   s-    6Be66v66666r*   c                n    t                               | ||z
  |z            t          j        |          z
  S r"   )r%   _logpdf_formulanplogr2   r   r   r   r'   s        r)   r4   zNormal._logpdf_formula6   s-    --dQVUNCCbfUmmSSr*   c                J    t                               | ||z
  |z            |z  S r"   )r%   _pdf_formular7   s        r)   r9   zNormal._pdf_formula9   s%    **4!b&%@@5HHr*   c                D    t                               | ||z
  |z            S r"   )r%   _logcdf_formular7   s        r)   r;   zNormal._logcdf_formula<   s     --dQVUNCCCr*   c                D    t                               | ||z
  |z            S r"   )r%   _cdf_formular7   s        r)   r=   zNormal._cdf_formula?   s     **4!b&%@@@r*   c                D    t                               | ||z
  |z            S r"   )r%   _logccdf_formular7   s        r)   r?   zNormal._logccdf_formulaB   s     ..ta"fe^DDDr*   c                D    t                               | ||z
  |z            S r"   )r%   _ccdf_formular7   s        r)   rA   zNormal._ccdf_formulaE   s     ++D1r65.AAAr*   c                D    t                               | |          |z  |z   S r"   )r%   _icdf_formular7   s        r)   rC   zNormal._icdf_formulaH   s"    ++D!44u<rAAr*   c                D    t                               | |          |z  |z   S r"   )r%   _ilogcdf_formular7   s        r)   rE   zNormal._ilogcdf_formulaK   s"    ..tQ77%?"DDr*   c                D    t                               | |          |z  |z   S r"   )r%   _iccdf_formular7   s        r)   rG   zNormal._iccdf_formulaN   s"    ,,T155=BBr*   c                D    t                               | |          |z  |z   S r"   )r%   _ilogccdf_formular7   s        r)   rI   zNormal._ilogccdf_formulaQ   s"    //a885@2EEr*   c                z    t                               |           t          j        t	          |                    z   S r"   )r%   _entropy_formular5   r6   absr2   r   r   r'   s       r)   rK   zNormal._entropy_formulaT   s+    ..t44rvc%jj7I7IIIr*   c                N   t                               |           }t          j        d          5  t          j        t          j        t          |                    dz             }d d d            n# 1 swxY w Y   t          j        t          j        ||          d          S )Nignoredividey                r   axis)	r%   _logentropy_formular5   errstater6   rL   r   	logsumexpbroadcast_arrays)r2   r   r   r'   lH0llss         r)   rT   zNormal._logentropy_formulaW   s    0066[))) 	0 	0 &E

++B.//C	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0  !4S#!>!>QGGGGs   7A33A7:A7c                    |S r"   r/   rM   s       r)   _median_formulazNormal._median_formula_       	r*   c                    |S r"   r/   rM   s       r)   _mode_formulazNormal._mode_formulab   r\   r*   c                J    |dk    rt          j        |          S |dk    r|S d S )Nr   r   )r5   	ones_liker2   orderr   r   r'   s        r)   _moment_raw_formulazNormal._moment_raw_formulae   s.    A::<###aZZI4r*   c                    |dk    rt          j        |          S |dz  rt          j        |          S ||z  t          j        t          |          dz
  d          z  S )Nr   r    r   T)exact)r5   r`   
zeros_liker   
factorial2intra   s        r)   _moment_central_formulazNormal._moment_central_formulan   sc    A::<###QY 	Q=$$$ %<'"4SZZ!^4"P"P"PPPr*   c                >    |                     |||          d         S )N)locscalesizer/   normal)r2   
full_shaperngr   r   r'   s         r)   _sample_formulazNormal._sample_formulaw   s    zzbJz??CCr*   )NN)+__name__
__module____qualname____doc__r	   r   
_mu_domain_sigma_domain
_x_supportr   	_mu_param_sigma_param_x_paramr   _parameterizations	_variabler5   sqrtpi_normalizationr6   _log_normalizationr$   r1   r4   r9   r;   r=   r?   rA   rC   rE   rG   rI   rK   rT   r[   r^   rc   ordersri   rr   __classcell__r(   s   @r)   r   r      s       	 	 3$555J!MQH555M3$555JtVJ'.0 0 0I!>')M*46 6 6L~c*gFFFH++I|DDEIwrwqw'''N"%*$ $ $ $ $ $
  r 7 7 7 7 7 7 7T T TI I ID D DA A AE E EB B BB B BE E EC C CF F FJ J JH H H       #$QQ Q QD D D D D D Dr*   r   c                 R    t          j        | |t          j        dz  z   gd          S )Ny              ?r   rR   )r   rV   r5   r   )log_plog_qs     r)   	_log_diffr   {   s'    eU258^41====r*   c                   r   e Zd ZdZ ee ef          Z eded          ZeZ	g Z
d ej        dej        z            z  Z ej        dej        z            dz  Z ej        d          Z ej        d	          Zd
 Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Z d Z!d Z"d Z#d Z$d Z%d Z&dS )r%   zStandard normal distribution.

    The probability density function of the standard normal distribution is:

    .. math::

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

    r   r   )   r   r   r    r+   r,   c                 *    t          j        | fi | d S r"   )r   r1   r2   r'   s     r)   r1   zStandardNormal.__init__   s!    '7777777r*   c                 $    | j         |dz  dz  z    S Nr    )r   r2   r   r'   s      r)   r4   zStandardNormal._logpdf_formula   s    (1a46122r*   c                 H    | j         t          j        |dz   dz            z  S r   )r   r5   expr   s      r)   r9   zStandardNormal._pdf_formula   s"    "RVQTE!G__44r*   c                 *    t          j        |          S r"   r   log_ndtrr   s      r)   r;   zStandardNormal._logcdf_formula   s    """r*   c                 *    t          j        |          S r"   r   ndtrr   s      r)   r=   zStandardNormal._cdf_formula   s    |Ar*   c                 ,    t          j        |           S r"   r   r   s      r)   r?   zStandardNormal._logccdf_formula   s    ###r*   c                 ,    t          j        |           S r"   r   r   s      r)   rA   zStandardNormal._ccdf_formula   s    |QBr*   c                 *    t          j        |          S r"   r   ndtrir   s      r)   rC   zStandardNormal._icdf_formula       }Qr*   c                 *    t          j        |          S r"   r   	ndtri_expr   s      r)   rE   zStandardNormal._ilogcdf_formula        ###r*   c                 ,    t          j        |           S r"   r   r   s      r)   rG   zStandardNormal._iccdf_formula       a    r*   c                 ,    t          j        |           S r"   r   r   s      r)   rI   z StandardNormal._ilogccdf_formula   s    !!$$$$r*   c                 P    dt          j        dt           j        z            z   dz  S Nr   r    )r5   r6   r   r   s     r)   rK   zStandardNormal._entropy_formula   s     BF1RU7OO#Q&&r*   c                     t          j        t          j        dt           j        z                      t          j        d          z
  S r   )r5   log1pr6   r   r   s     r)   rT   z"StandardNormal._logentropy_formula   s-    xqw((26!9944r*   c                     dS Nr   r/   r   s     r)   r[   zStandardNormal._median_formula       qr*   c                     dS r   r/   r   s     r)   r^   zStandardNormal._mode_formula   r   r*   c                 @    ddddddd}|                     |d           S )Nr   r      )r   r   r    r      r   )get)r2   rb   r'   raw_momentss       r)   rc   z"StandardNormal._moment_raw_formula   s+    aA!::ud+++r*   c                      | j         |fi |S r"   rc   r2   rb   r'   s      r)   ri   z&StandardNormal._moment_central_formula       't'88888r*   c                      | j         |fi |S r"   r   r   s      r)   _moment_standardized_formulaz+StandardNormal._moment_standardized_formula   r   r*   c                 :    |                     |          d         S Nrm   r/   rn   r2   rp   rq   r'   s       r)   rr   zStandardNormal._sample_formula   s    zzzz**2..r*   N)'rs   rt   ru   rv   r	   r   ry   r   r|   r~   r}   r5   r   r   r   r6   r   float64r   r   r1   r4   r9   r;   r=   r?   rA   rC   rE   rG   rI   rK   rT   r[   r^   rc   ri   r   rr   r/   r*   r)   r%   r%      s         3$555J~c*gFFFHIwrwqw'''N"%*	BBBJrNNE8 8 83 3 35 5 5# # #  $ $ $          $ $ $! ! !% % %' ' '5 5 5    , , ,9 9 99 9 9/ / / / /r*   r%   c                       e Zd ZdZ ee ef          Z eded          xZZ	dZ
ej         ej        d          z  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dS )r   zStandard logistic distribution.

    The probability density function of the standard logistic distribution is:

    .. math::

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

    r   r   )i	   r   r/   r   c                     t          j        |           }|dt          j        t          j        |                    z  z
  S r   )r5   rL   r   r   r   )r2   r   r'   ys       r)   r4   zLogistic._logpdf_formula   s3    VAYYJ1w}RVAYY/////r*   c                 <    dt          j        |dz            z  dz  S )Nr   r    )r5   coshr   s      r)   r9   zLogistic._pdf_formula   s    RWQU^^#a''r*   c                 *    t          j        |          S r"   r   	log_expitr   s      r)   r;   zLogistic._logcdf_formula   r   r*   c                 *    t          j        |          S r"   r   expitr   s      r)   r=   zLogistic._cdf_formula   r   r*   c                 ,    t          j        |           S r"   r   r   s      r)   r?   zLogistic._logccdf_formula   s     !$$$r*   c                 ,    t          j        |           S r"   r   r   s      r)   rA   zLogistic._ccdf_formula   s    }aR   r*   c                 *    t          j        |          S r"   r   logitr   s      r)   rC   zLogistic._icdf_formula   r   r*   c                 ,    t          j        |           S r"   r   r   s      r)   rG   zLogistic._iccdf_formula   r   r*   c                     dS )Ng       @r/   r   s     r)   rK   zLogistic._entropy_formula   s    sr*   c                 *    t          j        d          S r   r5   r6   r   s     r)   rT   zLogistic._logentropy_formula   s    vayyr*   c                     dS r   r/   r   s     r)   r[   zLogistic._median_formula   r   r*   c                     dS r   r/   r   s     r)   r^   zLogistic._mode_formula   r   r*   c           	          t          |          }|dz  rdS t          j        |z  t          d|z  dz
  t	          t          j        |          d                   z            z  S )Nr    r+   r   )rh   r5   r   rL   floatr   	bernoulli)r2   rb   r'   ns       r)   rc   zLogistic._moment_raw_formula  s\    JJq5 	3uax#q!tax51B11E1Eb1I+J+JJKKKKr*   c                      | j         |fi |S r"   r   r   s      r)   ri   z Logistic._moment_central_formula	  r   r*   c                 4     | j         |fi || j        |z  z  S r"   )rc   _scaler   s      r)   r   z%Logistic._moment_standardized_formula  s)    't'88884;;MMMr*   c                 :    |                     |          d         S r   )logisticr   s       r)   rr   zLogistic._sample_formula  s    |||,,R00r*   N)rs   rt   ru   rv   r	   r   ry   r   r~   r|   r}   r5   r   r   r   r4   r9   r;   r=   r?   rA   rC   rG   rK   rT   r[   r^   rc   ri   r   rr   r/   r*   r)   r   r      se         3$555J)>#j'RRRRIUWRWQZZF0 0 0( ( ($ $ $     % % %! ! !     ! ! !        L L L9 9 9N N N1 1 1 1 1r*   r   c                       e Zd ZdZ edef          Z edef          Z ee ef          Z edef          Z	 edd          Z
 eded	
          Z eded
          Z edded          Z edde	d          Z ede
d
          Ze                    e           e	                    e           e
                    ee            eee           eee          gZeZddddd fd
ZddZd Zd Z xZS )_LogUniforma  Log-uniform distribution.

    The probability density function of the log-uniform distribution is:

    .. math::

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

    If :math:`\log(X)` is a random variable that follows a uniform distribution
    between :math:`\log(a)` and :math:`\log(b)`, then :math:`X` is log-uniformly
    distributed with shape parameters :math:`a` and :math:`b`.

    r   r   alog_ar   bTTr   	inclusivegMbP?g?r   r   g?g     @@z\log(a))gr   log_bz\log(b))皙?r   r   Nr   r   r   r   c                D     t                      j        d||||d| d S )Nr   r/   r0   )r2   r   r   r   r   r'   r(   s         r)   r1   z_LogUniform.__init__:  s1    F1eFFvFFFFFr*   c                    |t          j        |          n|}|t          j        |          n|}|t          j        |          n|}|t          j        |          n|}|                    t	          ||||                     |S )Nr   )r5   r   r6   updatedict)r2   r   r   r   r   r'   s         r)   _process_parametersz_LogUniform._process_parameters=  s~    YBF5MMMAYBF5MMMA"]q			"]q			dQ!5>>>???r*   c                    ||z
  |z  dz  S )Nr   r/   )r2   r   r   r   r'   s        r)   r9   z_LogUniform._pdf_formulaH  s    !B&&r*   c           	          |dk    r| j         S | j         ||z
  z  |z  }t          j        t          j        t	          ||z  ||z                                }||z  S r   )_oner5   realr   r   )r2   rb   r   r   r'   t1t2s          r)   rc   z_LogUniform._moment_raw_formulaN  s\    A::9Y%%-(50WRVIeemUU]CCDDEEBwr*   )NNNN)rs   rt   ru   rv   r	   r   	_a_domain	_b_domain_log_a_domain_log_b_domainry   r   _a_param_b_param_log_a_param_log_b_paramr|   define_parametersr   r}   r~   r1   r   r9   rc   r   r   s   @r)   r   r     s         C111Ic
333I!McT3K888M!MWcN;;;M|LLLJ~c)[IIIH~c)ZHHHH!>'*)6
L L LL!>'*)6J J JL~c*jIIIH)))##L111  8444++L,GG++Hh??AI DD G G G G G G G   ' ' '      r*   r   c                       e Zd ZdZ ee ef          Z edef          Z edd          Z e	ded          Z
 e	d	ed
          Z e	ded          Ze                    e
           e                    e
e            ee
e          gZeZddd f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 Zd Zd Zdge_         d Z! xZ"S )r   zUniform distribution.

    The probability density function of the uniform distribution is:

    .. math::

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

    r   r   r   r   r   r   r   r   r   r   Nc                @     t                      j        d||d| d S )Nr   r/   r0   )r2   r   r   r'   r(   s       r)   r1   zUniform.__init__p  -    ,1,,V,,,,,r*   c                 Z    ||z
  }|                     t          |||                     |S )N)r   r   ab)r   r   r2   r   r   r  r'   s        r)   r   zUniform._process_parameterss  s1    UdQ!+++,,,r*   c                    t          j        t          j        |          t           j        t          j        |                     S r"   )r5   whereisnannanr6   r2   r   r  r'   s       r)   r4   zUniform._logpdf_formulax  s*    xRVbfRjj[999r*   c                l    t          j        t          j        |          t           j        d|z            S Nr   )r5   r	  r
  r  r  s       r)   r9   zUniform._pdf_formula{  s$    xRVQrT222r*   c                    t          j        d          5  t          j        ||z
            t          j        |          z
  cd d d            S # 1 swxY w Y   d S NrO   rP   r5   rU   r6   r2   r   r   r  r'   s        r)   r;   zUniform._logcdf_formula~      [))) 	. 	.6!a%==26"::-	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	. 	.   ,AAAc                    ||z
  |z  S r"   r/   r  s        r)   r=   zUniform._cdf_formula      A|r*   c                    t          j        d          5  t          j        ||z
            t          j        |          z
  cd d d            S # 1 swxY w Y   d S r  r  r2   r   r   r  r'   s        r)   r?   zUniform._logccdf_formula  r  r  c                    ||z
  |z  S r"   r/   r  s        r)   rA   zUniform._ccdf_formula  r  r*   c                    |||z  z   S r"   r/   )r2   pr   r  r'   s        r)   rC   zUniform._icdf_formula      2a4xr*   c                    |||z  z
  S r"   r/   )r2   r  r   r  r'   s        r)   rG   zUniform._iccdf_formula  r  r*   c                *    t          j        |          S r"   r   )r2   r  r'   s      r)   rK   zUniform._entropy_formula  s    vbzzr*   c                    |d|z  z   S Nr   r/   r  s        r)   r^   zUniform._mode_formula      3r6zr*   c                    |d|z  z   S r   r/   r  s        r)   r[   zUniform._median_formula  r!  r*   c                 .    |dz   }||z  ||z  z
  ||z  z  S r  r/   )r2   rb   r   r   r  r'   np1s          r)   rc   zUniform._moment_raw_formula  s&    ai3CC"H--r*   c                 "    |dk    r|dz  dz  nd S )Nr       r/   )r2   rb   r  r'   s       r)   ri   zUniform._moment_central_formula  s     A::r1uRxx4/r*   r    c                     	 |                     |||          d         S # t          $ r! |                     dd|          |z  |z   cY S w xY w)Nr   r/   r   r   )uniformOverflowError)r2   rp   rq   r   r   r  r'   s          r)   rr   zUniform._sample_formula  sg    	=;;q!*;55b99 	= 	= 	=;;q!*;55b81<<<<	=s     (A
A)NNN)#rs   rt   ru   rv   r	   r   r   r   ry   r   r   r   r|   r  r   r}   r~   r1   r   r4   r9   r;   r=   r?   rA   rC   rG   rK   r^   r[   rc   ri   r   rr   r   r   s   @r)   r   r   V  s       	 	 #s444Ic
333I|LLLJ~c)[IIIH~c)ZHHHH~c*jIIIH)))  8444++Hh??@I D - - - - - - -   
: : :3 3 3. . .  . . .            . . .0 0 0 '(S"= = = = = = =r*   r   c                       e Zd Z edef          Z edefd          Z eded          Z eded          Z	 e
e          gZe	Zd	 Zd
S )_Gammar   r   FFr   r   )r   
   r   r   c                h    ||dz
  z  t          j        |           z  t          j        |          z  S r  )r5   r   r   gamma)r2   r   r   r'   s       r)   r9   z_Gamma._pdf_formula  s.    QU|bfaRjj(7=+;+;;;r*   N)rs   rt   ru   r	   r   r   ry   r   r   r|   r   r}   r~   r9   r/   r*   r)   r+  r+    s        C111I!S^LLLJ~c)YGGGH~c*iHHHH++H556I< < < < <r*   r+  c                   L    e Zd ZdZ edefd          Z edd          Z edd          Z	 e
ded	
          Z e
ded
          Z e
de	d
          Z eee          gZeZ fdZd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zddge_        d Zg de_         xZS )r   zBinomial distribution with prescribed success probability and number of trials

    The probability density function of the binomial distribution is:

    .. math::

        f(x) = {n \choose x} p^x (1 - p)^{n-x}

    r   r,  r   )r   r   )r   r   r   r   )r-     r   r  )g      ?g      ?r   )r   r-  c                @     t                      j        d||d| d S )Nr   r  r/   r0   )r2   r   r  r'   r(   s       r)   r1   zBinomial.__init__  r  r*   c                .    t          j        |||          S r"   )scu
_binom_pmfr2   r   r   r  r'   s        r)   _pmf_formulazBinomial._pmf_formula      ~aA&&&r*   c                    t          j        |dz             t          j        |dz             t          j        ||z
  dz             z   z
  }|t          j        ||          z   t          j        ||z
  |           z   S r  )r   gammalnxlogyxlog1py)r2   r   r   r  r'   combilns         r)   _logpmf_formulazBinomial._logpmf_formula  st    
 OAaC  GOAaC$8$87?1Q3q5;Q;Q$QR 	 q!,,,wqsQB/G/GGGr*   c                .    t          j        |||          S r"   )r5  
_binom_cdfr7  s        r)   r=   zBinomial._cdf_formula  r9  r*   c                r    |                      d||          }t          j        ||k     |||fd d           S )Nr   r3  c                  B    t          j        t          j        |            S r"   )r5   r6   r5  rA  argss    r)   <lambda>z*Binomial._logcdf_formula.<locals>.<lambda>  s    "&!677 r*   c                  D    t          j        t          j        |             S r"   )r5   r   r5  	_binom_sfrD  s    r)   rF  z*Binomial._logcdf_formula.<locals>.<lambda>  s    "(CM4$8#899 r*   rC   xpxapply_wherer2   r   r   r  r'   medians         r)   r;   zBinomial._logcdf_formula  sL     ##C1#22q6zAq!97799
 
 	
r*   c                .    t          j        |||          S r"   )r5  rH  r7  s        r)   rA   zBinomial._ccdf_formula  s    }Q1%%%r*   c                r    |                      d||          }t          j        ||k     |||fd d           S )Nr   r3  c                  D    t          j        t          j        |             S r"   )r5   r   r5  rA  rD  s    r)   rF  z+Binomial._logccdf_formula.<locals>.<lambda>  s    "(CND$9#9:: r*   c                  B    t          j        t          j        |            S r"   )r5   r6   r5  rH  rD  s    r)   rF  z+Binomial._logccdf_formula.<locals>.<lambda>  s    "&!566 r*   rI  rL  s         r)   r?   zBinomial._logccdf_formula  sJ    ##C1#22q6zAq!9::66
 
 	
r*   c                .    t          j        |||          S r"   )r5  
_binom_ppfr7  s        r)   rC   zBinomial._icdf_formula  r9  r*   c                .    t          j        |||          S r"   )r5  
_binom_isfr7  s        r)   rG   zBinomial._iccdf_formula  r9  r*   c                    t          j        |dz   |z            }t          j        |dk    |dz
  |          }|d         S )Nr   r/   )r5   floorr	  )r2   r   r  r'   modes        r)   r^   zBinomial._mode_formula  s=    x1a  xQq$//Bxr*   c                J    |dk    r||z  S |dk    r||z  d|z
  ||z  z   z  S d S r   r/   r2   rb   r   r  r'   s        r)   rc   zBinomial._moment_raw_formula   s=    A::Q3JA::Q3A!$$tr*   r   r    c                    |dk    rt          j        |          S |dk    r||z  d|z
  z  S |dk    r||z  d|z
  z  dd|z  z
  z  S |dk    r ||z  d|z
  z  dd|z  dz
  |z  d|z
  z  z   z  S d S )Nr   r    r   r      )r5   rf   rZ  s        r)   ri   z Binomial._moment_central_formula	  s    A::=###A::Q3A;A::Q3A;AaC((A::Q3A;QqS1WaKQ$7 788tr*   )r   r    r   r   )rs   rt   ru   rv   r
   r   	_n_domainr	   	_p_domainry   r   _n_param_p_paramr|   r   r}   r~   r1   r8  r?  r=   r;   rA   r?   rC   rG   r^   rc   r   ri   r   r   s   @r)   r   r     s         ! As8~NNNI.IIII!!HMMMJ~c)XFFFH~c)\JJJH~c*gFFFH++Hh??@I- - - - -' ' 'H H H' ' '
 
 
& & &
 
 
' ' '' ' '     #$Q
 
 
 &2\\"""""r*   r   )#sysnumpyr5   r   
scipy._libr   rJ  scipyr   scipy.specialr   r5  (scipy.stats._distribution_infrastructurer   r   r	   r
   r   r   r   __all__r   r   r%   r   r   r   r+  r   modulesrs   __dict___module	dist_namerv   r/   r*   r)   <module>rl     s   



           - - - - - -       ( ( ( ( ( (6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 8
7
7hD hD hD hD hD# hD hD hDV> > >K/ K/ K/ K/ K/V K/ K/ K/\C1 C1 C1 C1 C1% C1 C1 C1N? ? ? ? ?( ? ? ?DR= R= R= R= R=$ R= R= R=j< < < < <# < < <Z2 Z2 Z2 Z2 Z2# Z2 Z2 Z2@ +h

( C CI!.wy/A!B!BGIC Cr*   