
    (ph3                     .   S SK r S SKrS SKJr  S SKJr  S SKJrJrJ	r	J
r
Jr  SS/r " S S\5      rS r " S	 S
\5      r " S S\5      r " S S\5      r " S S\5      r\ R&                  \   R*                  r\ H  r\" \\   5      \\   l        M     g)    N)inf)special)ContinuousDistribution_RealDomain_RealParameter_Parameterization_combine_docsNormalUniformc                     ^  \ rS rSrSr\" \* \4S9r\" S\4S9r\" \* \4S9r	\
" SS\SS9r\
" S	S
\SS9r\
" S\	SS9r\" \\5      /r\rS\R$                  " S\R&                  -  5      -  r\R*                  " S\R&                  -  5      S-  rS'U 4S jjrSSS.U 4S jjrS rS rS rS rS rS rS rS r S r!S r"S r#S  r$S! r%S" r&S# r'SS/\'l(        S$ r)S% r*S&r+U =r,$ )(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      c                 T   > Uc  Uc  [         TU ]  [        5      $ [         TU ]  U 5      $ N)super__new__StandardNormal)clsr   r   kwargs	__class__s       Q/var/www/html/venv/lib/python3.13/site-packages/scipy/stats/_new_distributions.pyr   Normal.__new__,   s*    :%-7?>22ws##                  ?r   r   c                *   > [         TU ]  " SXS.UD6  g )Nr)    r   __init__)selfr   r   r"   r#   s       r$   r-   Normal.__init__1   s    6B6v6r&   c                f    [         R                  XU-
  U-  5      [        R                  " U5      -
  $ r   )r    _logpdf_formulanplogr.   r   r   r   r"   s        r$   r1   Normal._logpdf_formula4   s(    --dVUNCbffUmSSr&   c                >    [         R                  XU-
  U-  5      U-  $ r   )r    _pdf_formular4   s        r$   r7   Normal._pdf_formula7   s     **4b&%@5HHr&   c                8    [         R                  XU-
  U-  5      $ r   )r    _logcdf_formular4   s        r$   r:   Normal._logcdf_formula:   s    --dVUNCCr&   c                8    [         R                  XU-
  U-  5      $ r   )r    _cdf_formular4   s        r$   r=   Normal._cdf_formula=   s    **4b&%@@r&   c                8    [         R                  XU-
  U-  5      $ r   )r    _logccdf_formular4   s        r$   r@   Normal._logccdf_formula@   s    ..t"fe^DDr&   c                8    [         R                  XU-
  U-  5      $ r   )r    _ccdf_formular4   s        r$   rC   Normal._ccdf_formulaC   s    ++Dr65.AAr&   c                8    [         R                  X5      U-  U-   $ r   )r    _icdf_formular4   s        r$   rF   Normal._icdf_formulaF   s    ++D4u<rAAr&   c                8    [         R                  X5      U-  U-   $ r   )r    _ilogcdf_formular4   s        r$   rI   Normal._ilogcdf_formulaI   s    ..t7%?"DDr&   c                8    [         R                  X5      U-  U-   $ r   )r    _iccdf_formular4   s        r$   rL   Normal._iccdf_formulaL   s    ,,T5=BBr&   c                8    [         R                  X5      U-  U-   $ r   )r    _ilogccdf_formular4   s        r$   rO   Normal._ilogccdf_formulaO   s    //85@2EEr&   c                l    [         R                  U 5      [        R                  " [	        U5      5      -   $ r   )r    _entropy_formular2   r3   absr.   r   r   r"   s       r$   rR   Normal._entropy_formulaR   s%    ..t4rvvc%j7IIIr&   c                H   [         R                  U 5      n[        R                  " SS9   [        R                  " [        R                  " [        U5      5      S-   5      nS S S 5        [        R                  " [        R                  " UW5      SS9$ ! , (       d  f       N8= f)Nignoredividey                r   axis)	r    _logentropy_formular2   errstater3   rS   r   	logsumexpbroadcast_arrays)r.   r   r   r"   lH0llss         r$   r\   Normal._logentropy_formulaU   sp    006[[) &&E
+B./C *   !4!4S#!>QGG	 *)s   7B
B!c                    U$ r   r+   rT   s       r$   _median_formulaNormal._median_formula]       	r&   c                    U$ r   r+   rT   s       r$   _mode_formulaNormal._mode_formula`   rf   r&   c                L    US:X  a  [         R                  " U5      $ US:X  a  U$ g )Nr   r   )r2   	ones_liker.   orderr   r   r"   s        r$   _moment_raw_formulaNormal._moment_raw_formulac   s'    A:<<##aZIr&   c                    US:X  a  [         R                  " U5      $ US-  (       a  [         R                  " U5      $ X1-  [        R                  " [        U5      S-
  SS9-  $ )Nr   r   r   T)exact)r2   rk   
zeros_liker   
factorial2intrl   s        r$   _moment_central_formulaNormal._moment_central_formulal   sR    A:<<##QY==$$ <'"4"4SZ!^4"PPPr&   c                (    UR                  XEUS9S   $ )N)locscalesizer+   normal)r.   sample_shape
full_shaperngr   r   r"   s          r$   _sample_formulaNormal._sample_formulau   s    zzbJz?CCr&   r+   )NN)-__name__
__module____qualname____firstlineno____doc__r   r   
_mu_domain_sigma_domain
_x_supportr   	_mu_param_sigma_param_x_paramr   _parameterizations	_variabler2   sqrtpi_normalizationr3   _log_normalizationr   r-   r1   r7   r:   r=   r@   rC   rF   rI   rL   rO   rR   r\   rd   rh   rn   ordersru   r   __static_attributes____classcell__r#   s   @r$   r
   r
      sE   	 c{3J1c(3Mc{3JtVJ'.0I!')M*46Lc*gFH+I|DEIrwwqw''N"%%*$
  r 7 7TIDAEBBECFJH #$QQD Dr&   c                 V    [         R                  " X[        R                  S-  -   /SS9$ )Ny              ?r   rZ   )r   r^   r2   r   )log_plog_qs     r$   	_log_diffr   y   s$    e2558^41==r&   c                      \ rS rSrSr\" \* \4S9r\" S\SS9r	\	r
/ rS\R                  " S\R                  -  5      -  r\R                   " S\R                  -  5      S-  r\R$                  " S	5      r\R$                  " S
5      rS rS rS rS rS rS rS rS rS rS rS rS r S r!S r"S r#S r$S r%S r&S r'Sr(g) 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                 2    [         R                  " U 40 UD6  g r   )r   r-   r.   r"   s     r$   r-   StandardNormal.__init__   s    ''77r&   c                 .    U R                   US-  S-  -   * $ Nr   )r   r.   r   r"   s      r$   r1   StandardNormal._logpdf_formula   s    ((1a46122r&   c                 V    U R                   [        R                  " US-  * S-  5      -  $ r   )r   r2   expr   s      r$   r7   StandardNormal._pdf_formula   s%    ""RVVQTE!G_44r&   c                 .    [         R                  " U5      $ r   r   log_ndtrr   s      r$   r:   StandardNormal._logcdf_formula   s    ""r&   c                 .    [         R                  " U5      $ r   r   ndtrr   s      r$   r=   StandardNormal._cdf_formula   s    ||Ar&   c                 0    [         R                  " U* 5      $ r   r   r   s      r$   r@   StandardNormal._logccdf_formula   s    ##r&   c                 0    [         R                  " U* 5      $ r   r   r   s      r$   rC   StandardNormal._ccdf_formula   s    ||QBr&   c                 .    [         R                  " U5      $ r   r   ndtrir   s      r$   rF   StandardNormal._icdf_formula   s    }}Qr&   c                 .    [         R                  " U5      $ r   r   	ndtri_expr   s      r$   rI   StandardNormal._ilogcdf_formula   s      ##r&   c                 0    [         R                  " U5      * $ r   r   r   s      r$   rL   StandardNormal._iccdf_formula   s    a   r&   c                 0    [         R                  " U5      * $ r   r   r   s      r$   rO    StandardNormal._ilogccdf_formula   s    !!!$$$r&   c                 \    S[         R                  " S[         R                  -  5      -   S-  $ )Nr   r   )r2   r3   r   r   s     r$   rR   StandardNormal._entropy_formula   s"    BFF1RUU7O#Q&&r&   c                     [         R                  " [         R                  " S[         R                  -  5      5      [         R                  " S5      -
  $ r   )r2   log1pr3   r   r   s     r$   r\   "StandardNormal._logentropy_formula   s.    xxqw(266!944r&   c                     gNr   r+   r   s     r$   rd   StandardNormal._median_formula       r&   c                     gr   r+   r   s     r$   rh   StandardNormal._mode_formula   r   r&   c                 8    SSSSSSS.nUR                  US 5      $ )Nr   r      )r   r   r   r      r   )get)r.   rm   r"   raw_momentss       r$   rn   "StandardNormal._moment_raw_formula   s%    aA!:ud++r&   c                 (    U R                   " U40 UD6$ r   rn   r.   rm   r"   s      r$   ru   &StandardNormal._moment_central_formula       ''888r&   c                 (    U R                   " U40 UD6$ r   r   r   s      r$   _moment_standardized_formula+StandardNormal._moment_standardized_formula   r   r&   c                 &    UR                  US9S   $ )Nrz   r+   r{   )r.   r}   r~   r   r"   s        r$   r   StandardNormal._sample_formula   s    zzzz*2..r&   r+   N))r   r   r   r   r   r   r   r   r   r   r   r   r2   r   r   r   r3   r   float64r   r   r-   r1   r7   r:   r=   r@   rC   rF   rI   rL   rO   rR   r\   rd   rh   rn   ru   r   r   r   r+   r&   r$   r    r    }   s     c{3Jc*gFHIrwwqw''N"%%*	BBJJrNE835#$  $!%'5,99/r&   r    c                     ^  \ rS rSrSr\" S\4S9r\" S\4S9r\" \* \4S9r	\" S\4S9r
\" SSS	9r\" S\S
S9r\" S\SS9r\" SS\	SS9r\" SS\
SS9r\" S\SS9r\R%                  \5        \
R%                  \5        \R%                  \\5        \" \\5      \" \\5      /r\rSSSSS.U 4S jjrSS jrS rS rSrU =r$ )_LogUniform   a  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                ,   > [         TU ]  " SXX4S.UD6  g )Nr   r+   r,   )r.   r   r   r   r   r"   r#   s         r$   r-   _LogUniform.__init__   s    F1FvFr&   c           	         Uc  [         R                  " U5      OUnUc  [         R                  " U5      OUnUc  [         R                  " U5      OUnUc  [         R                  " U5      OUnUR                  [	        XX4S95        U$ )Nr   )r2   r   r3   updatedict)r.   r   r   r   r   r"   s         r$   _process_parameters_LogUniform._process_parameters   sf    YBFF5MAYBFF5MA"]q	"]q	dQ5>?r&   c                    X2-
  U-  S-  $ )Nr   r+   )r.   r   r   r   r"   s        r$   r7   _LogUniform._pdf_formula   s    !B&&r&   c           	          US:X  a  U R                   $ U R                   X2-
  -  U-  n[        R                  " [        R                  " [	        X-  X-  5      5      5      nXV-  $ r   )_oner2   realr   r   )r.   rm   r   r   r"   t1t2s          r$   rn   _LogUniform._moment_raw_formula  sQ    A:99YY%-(50WWRVVIemU]CDEwr&   r+   )NNNN)r   r   r   r   r   r   r   	_a_domain	_b_domain_log_a_domain_log_b_domainr   r   _a_param_b_param_log_a_param_log_b_paramr   define_parametersr   r   r   r-   r   r7   rn   r   r   r   s   @r$   r   r      s    q#h/IsCj1IC4+6M7C.9Mz\JJc)[IHc)ZHH!'*)6
LL!'*)6JLc*jIH)##L1  84+L,G+Hh?AI DD G G' r&   r   c                   b  ^  \ rS rSrSr\" \* \4S9r\" S\4S9r\" SSS9r	\
" S\SS	9r\
" S
\SS	9r\
" S\	SS	9r\R                  \5        \	R                  \\5        \" \\5      /r\rSSS.U 4S jjrS S jrS rS rS rS rS rS rS rS rS rS rS rS rS r S/\ l!        S r"Sr#U =r$$ )!r   i  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U ]  " SXS.UD6  g )Nr   r+   r,   )r.   r   r   r"   r#   s       r$   r-   Uniform.__init__(  s    ,1,V,r&   c                 @    X!-
  nUR                  [        XUS95        U$ )N)r   r   ab)r   r   r.   r   r   r
  r"   s        r$   r   Uniform._process_parameters+  s!    UdQ+,r&   c                    [         R                  " [         R                  " U5      [         R                  [         R                  " U5      * 5      $ r   )r2   whereisnannanr3   r.   r   r
  r"   s       r$   r1   Uniform._logpdf_formula0  s+    xxRVVbffRj[99r&   c                |    [         R                  " [         R                  " U5      [         R                  SU-  5      $ Nr   )r2   r  r  r  r  s       r$   r7   Uniform._pdf_formula3  s%    xxRVVQrT22r&   c                    [         R                  " SS9   [         R                  " X-
  5      [         R                  " U5      -
  sS S S 5        $ ! , (       d  f       g = fNrW   rX   r2   r]   r3   r.   r   r   r
  r"   s        r$   r:   Uniform._logcdf_formula6  4    [[)66!%=266":- *))   /A
Ac                    X-
  U-  $ r   r+   r  s        r$   r=   Uniform._cdf_formula:      |r&   c                    [         R                  " SS9   [         R                  " X!-
  5      [         R                  " U5      -
  sS S S 5        $ ! , (       d  f       g = fr  r  r.   r   r   r
  r"   s        r$   r@   Uniform._logccdf_formula=  r  r  c                    X!-
  U-  $ r   r+   r!  s        r$   rC   Uniform._ccdf_formulaA  r  r&   c                    X#U-  -   $ r   r+   )r.   pr   r
  r"   s        r$   rF   Uniform._icdf_formulaD      a4xr&   c                    X#U-  -
  $ r   r+   )r.   r&  r   r
  r"   s        r$   rL   Uniform._iccdf_formulaG  r(  r&   c                .    [         R                  " U5      $ r   )r2   r3   )r.   r
  r"   s      r$   rR   Uniform._entropy_formulaJ  s    vvbzr&   c                    USU-  -   $ Nr   r+   r  s        r$   rh   Uniform._mode_formulaM      3r6zr&   c                    USU-  -   $ r.  r+   r  s        r$   rd   Uniform._median_formulaP  r0  r&   c                 (    US-   nX6-  X&-  -
  Xd-  -  $ r  r+   )r.   rm   r   r   r
  r"   np1s          r$   rn   Uniform._moment_raw_formulaS  s     aiCH--r&   c                 "    US:X  a  US-  S-  $ S $ )Nr      r+   )r.   rm   r
  r"   s       r$   ru   Uniform._moment_central_formulaW  s     A:r1uRx/4/r&   r   c                 x     UR                  XEUS9S   $ ! [         a    UR                  SSUS9U-  U-   s $ f = f)Nr   r+   r   r   )uniformOverflowError)r.   r}   r~   r   r   r   r
  r"   s           r$   r   Uniform._sample_formula\  sM    	=;;q*;5b99 	=;;q!*;5b81<<	=s    !99r+   )NNN)%r   r   r   r   r   r   r   r   r   r   r   r  r  r   r  r   r   r   r-   r   r1   r7   r:   r=   r@   rC   rF   rL   rR   rh   rd   rn   ru   r   r   r   r   r   s   @r$   r   r     s    	 tSk2IsCj1Iz\JJc)[IHc)ZHHc*jIH)  84+Hh?@I D - -
:3...0 '(S"= =r&   c                   r    \ rS rSr\" S\4S9r\" S\4SS9r\" S\SS9r	\" S	\SS9r
\" \	5      /r\
rS
 rSrg)_Gammaic  r   r   )FFr   r   )r   
   r   r   c                n    XS-
  -  [         R                  " U* 5      -  [        R                  " U5      -  $ r  )r2   r   r   gamma)r.   r   r   r"   s       r$   r7   _Gamma._pdf_formulan  s+    U|bffaRj(7==+;;;r&   r+   N)r   r   r   r   r   r   r   r   r   r  r   r   r   r   r7   r   r+   r&   r$   r>  r>  c  sT    q#h/I3x>JJc)YGHc*iHH+H56I<r&   r>  )sysnumpyr2   r   scipyr   (scipy.stats._distribution_infrastructurer   r   r   r   r	   __all__r
   r   r    r   r   r>  modulesr   __dict___module	dist_namer   r+   r&   r$   <module>rL     s    
     Y
hD# hDV>K/V K/^?( ?DR=$ R=j<# <$ ++h

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(I!.wy/A!BGI r&   