+
    0iI                        ^ RI t ^ RIt^ RIHt ^ RIHt ^ RIHt ^ RI	H
t ^ RIHtHtHtHtHtHtHt . ROt ! R R]4      tR t ! R R]4      t ! R R]4      t ! R R]4      t ! R R	]4      t ! R R]4      t ! R R
]4      t] P:                  ],          P>                  t ] F  t!]! ] ]!,          4      ] ]!,          n"        K   	  R# )    N)inf)array_api_extra)special)_ufuncs)ContinuousDistributionDiscreteDistribution_RealInterval_IntegerInterval_RealParameter_Parameterization_combine_docsNormalLogisticUniformBinomialc                     a a ] tR t^t oRt]! ]) ]3R7      t]! ^ ]3R7      t]! ]) ]3R7      t	]
! RR]R R7      t]
! RR]R!R7      t]
! R]	R R	7      t]! ]]4      .t]t^]P$                  ! ^]P&                  ,          4      ,          t]P*                  ! ^]P&                  ,          4      ^,          tR"V 3R
 lltRRRR/V 3R lltR tR tR tR tR tR tR tR t R t!R t"R t#R t$R t%R t&R t'^ ^.]'n(        R t)R t*Rt+Vt,V ;t-# )#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)}

	endpointsmuz\musymboldomaintypicalsigmaz\sigmaxr   r   c                X   < Vf   Vf   \         SV `  \        4      # \         SV `  V 4      # N)super__new__StandardNormal)clsr   r   kwargs	__class__s   &&&,\/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/stats/_new_distributions.pyr    Normal.__new__.   s*    :%-7?>22ws##                  ?c               0   < \         SV `  ! RR VRV/VB  R# )r   r   N r   __init__)selfr   r   r#   r$   s   &$$,r%   r-   Normal.__init__3   s    6B6e6v6r'   c               ~    \         P                  WV,
          V,          4      \        P                  ! V4      ,
          # r   )r!   _logpdf_formulanplogr.   r   r   r   r#   s   &&$$,r%   r1   Normal._logpdf_formula6   s(    --dVUNCbffUmSSr'   c               V    \         P                  WV,
          V,          4      V,          # r   )r!   _pdf_formular4   s   &&$$,r%   r7   Normal._pdf_formula9   s     **4b&%@5HHr'   c               H    \         P                  WV,
          V,          4      # r   )r!   _logcdf_formular4   s   &&$$,r%   r:   Normal._logcdf_formula<   s    --dVUNCCr'   c               H    \         P                  WV,
          V,          4      # r   )r!   _cdf_formular4   s   &&$$,r%   r=   Normal._cdf_formula?   s    **4b&%@@r'   c               H    \         P                  WV,
          V,          4      # r   )r!   _logccdf_formular4   s   &&$$,r%   r@   Normal._logccdf_formulaB   s    ..t"fe^DDr'   c               H    \         P                  WV,
          V,          4      # r   )r!   _ccdf_formular4   s   &&$$,r%   rC   Normal._ccdf_formulaE   s    ++Dr65.AAr'   c               H    \         P                  W4      V,          V,           # r   )r!   _icdf_formular4   s   &&$$,r%   rF   Normal._icdf_formulaH   s    ++D4u<rAAr'   c               H    \         P                  W4      V,          V,           # r   )r!   _ilogcdf_formular4   s   &&$$,r%   rI   Normal._ilogcdf_formulaK   s    ..t7%?"DDr'   c               H    \         P                  W4      V,          V,           # r   )r!   _iccdf_formular4   s   &&$$,r%   rL   Normal._iccdf_formulaN   s    ,,T5=BBr'   c               H    \         P                  W4      V,          V,           # r   )r!   _ilogccdf_formular4   s   &&$$,r%   rO   Normal._ilogccdf_formulaQ   s    //85@2EEr'   c               t    \         P                  V 4      \        P                  ! \	        V4      4      ,           # r   )r!   _entropy_formular2   r3   absr.   r   r   r#   s   &$$,r%   rR   Normal._entropy_formulaT   s%    ..t4rvvc%j7IIIr'   c          	     p   \         P                  V 4      p\        P                  ! R R7      ;_uu_ 4        \        P                  ! \        P                  ! \        V4      4      R,           4      pRRR4       \        P                  ! \        P                  ! VX4      ^ R7      #   + '       g   i     L=; i)ignoredividey                Naxis)	r!   _logentropy_formular2   errstater3   rS   r   	logsumexpbroadcast_arrays)r.   r   r   r#   lH0llss   &$$,  r%   r\   Normal._logentropy_formulaW   ss    006[[)) &&E
+B./C *   !4!4S#!>QGG	 *)s   ;B%%B5	c                   V# r   r+   rT   s   &$$,r%   _median_formulaNormal._median_formula_       	r'   c                   V# r   r+   rT   s   &$$,r%   _mode_formulaNormal._mode_formulab   rf   r'   c               R    V^ 8X  d   \         P                  ! V4      # V^8X  d   V# R# r   N)r2   	ones_liker.   orderr   r   r#   s   &&$$,r%   _moment_raw_formulaNormal._moment_raw_formulae   s'    A:<<##aZIr'   c                   V^ 8X  d   \         P                  ! V4      # V^,          '       d   \         P                  ! V4      # W1,          \        P                  ! \        V4      ^,
          RR7      ,          # )r   T)exact)r2   rl   
zeros_liker   
factorial2intrm   s   &&$$,r%   _moment_central_formulaNormal._moment_central_formulan   sT    A:<<##QYY==$$ <'"4"4SZ!^4"PPPr'   c               6    VP                  W4VR 7      R,          # ))locscalesizer+   normal)r.   
full_shaperngr   r   r#   s   &&&$$,r%   _sample_formulaNormal._sample_formulaw   s    zzbJz?CCr'   r+   )   )      ?g      ?)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   ro   ordersrv   r   __static_attributes____classdictcell____classcell__r$   __classdict__s   @@r%   r   r      sI    	 3$5J!QH5M3$5JtVJ'.0I!')M*46Lc*gFH+I|DEIrwwqw''N"%%*$
7R 7r 7TIDAEBBECFJH #$QQD Dr'   c                 l    \         P                  ! W\        P                  R ,          ,           .^ R7      # )y              ?rZ   )r   r^   r2   r   )log_plog_qs   &&r%   	_log_diffr   {   s$    e2558^41==r'   c                     a  ] tR t^t o Rt]! ]) ]3R7      t]! R]RR7      t	]	t
. t^]P                  ! ^]P                  ,          4      ,          t]P                   ! ^]P                  ,          4      ^,          t]P$                  ! R4      t]P$                  ! R4      tR tR tR	 tR
 tR tR tR tR tR tR tR tR t R t!R t"R t#R t$R t%R t&R t'Rt(V t)R# )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)   c                4    \         P                  ! V 3/ VB  R # r   )r   r-   r.   r#   s   &,r%   r-   StandardNormal.__init__   s    ''77r'   c                F    V P                   V^,          ^,          ,           ) #    )r   r.   r   r#   s   &&,r%   r1   StandardNormal._logpdf_formula   s    ((1a46122r'   c                n    V P                   \        P                  ! V^,          ) ^,          4      ,          # r   )r   r2   expr   s   &&,r%   r7   StandardNormal._pdf_formula   s%    ""RVVQTE!G_44r'   c                .    \         P                  ! V4      # r   r   log_ndtrr   s   &&,r%   r:   StandardNormal._logcdf_formula   s    ""r'   c                .    \         P                  ! V4      # r   r   ndtrr   s   &&,r%   r=   StandardNormal._cdf_formula   s    ||Ar'   c                0    \         P                  ! V) 4      # r   r   r   s   &&,r%   r@   StandardNormal._logccdf_formula   s    ##r'   c                0    \         P                  ! V) 4      # r   r   r   s   &&,r%   rC   StandardNormal._ccdf_formula   s    ||QBr'   c                .    \         P                  ! V4      # r   r   ndtrir   s   &&,r%   rF   StandardNormal._icdf_formula       }}Qr'   c                .    \         P                  ! V4      # r   r   	ndtri_expr   s   &&,r%   rI   StandardNormal._ilogcdf_formula         ##r'   c                0    \         P                  ! V4      ) # r   r   r   s   &&,r%   rL   StandardNormal._iccdf_formula       a   r'   c                0    \         P                  ! V4      ) # r   r   r   s   &&,r%   rO    StandardNormal._ilogccdf_formula   s    !!!$$$r'   c                t    ^\         P                  ! ^\         P                  ,          4      ,           ^,          # r   )r2   r3   r   r   s   &,r%   rR   StandardNormal._entropy_formula   s"    BFF1RUU7O#Q&&r'   c                    \         P                  ! \         P                  ! ^\         P                  ,          4      4      \         P                  ! ^4      ,
          # r   )r2   log1pr3   r   r   s   &,r%   r\   "StandardNormal._logentropy_formula   s.    xxqw(266!944r'   c                    ^ # r   r+   r   s   &,r%   rd   StandardNormal._median_formula       r'   c                    ^ # r   r+   r   s   &,r%   rh   StandardNormal._mode_formula   r   r'   c                B    ^ ^^^ ^^^^ ^^^^ /pVP                  VR4      # rk   )get)r.   rn   r#   raw_momentss   &&, r%   ro   "StandardNormal._moment_raw_formula   s1    !Q1aAq!Q:ud++r'   c                (    V P                   ! V3/ VB # r   ro   r.   rn   r#   s   &&,r%   rv   &StandardNormal._moment_central_formula       ''888r'   c                (    V P                   ! V3/ VB # r   r   r   s   &&,r%   _moment_standardized_formula+StandardNormal._moment_standardized_formula   r   r'   c                4    VP                  VR 7      R,          # )r{   r+   r|   r.   r~   r   r#   s   &&&,r%   r   StandardNormal._sample_formula   s    zzzz*2..r'   r+   N)   )*r   r   r   r   r   r	   r   r   r   r   r   r   r2   r   r   r   r3   r   float64r   r   r-   r1   r7   r:   r=   r@   rC   rF   rI   rL   rO   rR   r\   rd   rh   ro   rv   r   r   r   r   r   s   @r%   r!   r!      s      3$5Jc*gFHIrwwqw''N"%%*	BBJJrNE835#$  $!%'5,99/ /r'   r!   c                      a  ] tR t^t o Rt]! ]) ]3R7      t]! R]RR7      ;t	t
Rt]P                  ]P                  ! ^4      ,          tR tR tR tR tR	 tR
 tR tR tR tR tR tR tR tR tR tR tRt V t!R# )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   r   c                    \         P                  ! V4      ) pV^\        P                  ! \         P                  ! V4      4      ,          ,
          # r   )r2   rS   r   r   r   )r.   r   r#   ys   &&, r%   r1   Logistic._logpdf_formula   s2    VVAYJ1w}}RVVAY////r'   c                X    R \         P                  ! V^,          4      ,          ^,          # r   )r2   coshr   s   &&,r%   r7   Logistic._pdf_formula   s    RWWQU^#a''r'   c                .    \         P                  ! V4      # r   r   	log_expitr   s   &&,r%   r:   Logistic._logcdf_formula   r   r'   c                .    \         P                  ! V4      # r   r   expitr   s   &&,r%   r=   Logistic._cdf_formula   r   r'   c                0    \         P                  ! V) 4      # r   r   r   s   &&,r%   r@   Logistic._logccdf_formula   s      !$$r'   c                0    \         P                  ! V) 4      # r   r   r   s   &&,r%   rC   Logistic._ccdf_formula   s    }}aR  r'   c                .    \         P                  ! V4      # r   r   logitr   s   &&,r%   rF   Logistic._icdf_formula   r   r'   c                0    \         P                  ! V4      ) # r   r   r   s   &&,r%   rL   Logistic._iccdf_formula   r   r'   c                    R # )g       @r+   r   s   &,r%   rR   Logistic._entropy_formula   s    r'   c                .    \         P                  ! ^4      # r   r2   r3   r   s   &,r%   r\   Logistic._logentropy_formula   s    vvayr'   c                    ^ # r   r+   r   s   &,r%   rd   Logistic._median_formula   r   r'   c                    ^ # r   r+   r   s   &,r%   rh   Logistic._mode_formula   r   r'   c           	         \        V4      pV^,          '       d   R# \        P                  V,          \        ^V,          ^,
          \	        \
        P                  ! V4      R,          4      ,          4      ,          # )r   r(   r   )ru   r2   r   rS   floatr   	bernoulli)r.   rn   r#   ns   &&, r%   ro   Logistic._moment_raw_formula  sQ    Jq55uuax#q!tax51B1B11Eb1I+JJKKKr'   c                (    V P                   ! V3/ VB # r   r   r   s   &&,r%   rv    Logistic._moment_central_formula	  r   r'   c                X    V P                   ! V3/ VB V P                  V,          ,          # r   )ro   _scaler   s   &&,r%   r   %Logistic._moment_standardized_formula  s&    ''884;;;MMMr'   c                4    VP                  VR 7      R,          # r   )logisticr   s   &&&,r%   r   Logistic._sample_formula  s    |||,R00r'   r+   N)i	   )"r   r   r   r   r   r	   r   r   r   r   r   r   r2   r   r   r  r1   r7   r:   r=   r@   rC   rF   rL   rR   r\   rd   rh   ro   rv   r   r   r   r   r   s   @r%   r   r      s      3$5J)#j'RRIUURWWQZF0($ %! !L9N1 1r'   c                     a a ] tR tRt oRt]! ^ ]3R7      t]! R]3R7      t]! ]) ]3R7      t	]! R]3R7      t
]! RRR7      t]! R]RR7      t]! R]RR7      t]! RR	]	RR
7      t]! RR]
RR
7      t]! R]RR7      t]P%                  ]4       ]
P%                  ]4       ]P%                  ]]4       ]! ]]4      ]! ]]4      .t]tRRRRRRRR/V 3R lltRR ltR tR tRtVtV ;t# )_LogUniformi  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   alog_abr   	inclusiver   z\log(a)r   log_bz\log(b)r   Nc               8   < \         SV `  ! RR VRVRVRV/VB  R# )r  r  r  r  Nr+   r,   )r.   r  r  r  r  r#   r$   s   &$$$$,r%   r-   _LogUniform.__init__:  s'    F1FFFeFvFr'   c           	        Vf   \         P                  ! V4      MTpVf   \         P                  ! V4      MTpVf   \         P                  ! V4      MTpVf   \         P                  ! V4      MTpVP                  \	        WW4R7      4       V# )N)r  r  r  r  )r2   r   r3   updatedict)r.   r  r  r  r  r#   s   &&&&&,r%   _process_parameters_LogUniform._process_parameters=  sf    YBFF5MAYBFF5MA"]q	"]q	dQ5>?r'   c               .    W2,
          V,          R,          # )r   r   r+   )r.   r   r  r  r#   s   &&$$,r%   r7   _LogUniform._pdf_formulaH  s    !B&&r'   c           	         V^ 8X  d   V P                   # V P                   W2,
          ,          V,          p\        P                  ! \        P                  ! \	        W,          W,          4      4      4      pWV,          # r   )_oner2   realr   r   )r.   rn   r  r  r#   t1t2s   &&&&,  r%   ro   _LogUniform._moment_raw_formulaN  sQ    A:99YY%-(50WWRVVIemU]CDEwr'   r+   r  r  TTgMbP?g?g?g     @@)g)皙?   )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   ro   r   r   r   r   s   @@r%   r  r    s,     C1Ic
3I!cT3K8M!WcN;M|LJc)[IHc)ZHH!'*)6
LL!'*)6JLc*jIH)##L1  84+L,G+Hh?AIGD GD G GD G' r'   r  c                     a a ] tR tRt oRt]! ]) ]3R7      t]! R]3R7      t]! RRR7      t	]
! R]RR7      t]
! R]RR7      t]
! R]	RR7      t]P                  ]4       ]	P                  ]]4       ]! ]]4      .t]tRR	RR	/V 3R
 lltRR ltR tR tR tR tR tR tR tR tR tR tR tR tR t ^.] n!        R t"Rt#Vt$V ;t%# ) r   iV  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   Nc               0   < \         SV `  ! RR VRV/VB  R# )r  r  Nr+   r,   )r.   r  r  r#   r$   s   &$$,r%   r-   Uniform.__init__p      ,1,,V,r'   c                N    W!,
          pVP                  \        WVR 7      4       V# ))r  r  ab)r#  r$  r.   r  r  rD  r#   s   &&&&,r%   r%  Uniform._process_parameterss  s!    UdQ+,r'   c                   \         P                  ! \         P                  ! V4      \         P                  \         P                  ! V4      ) 4      # r   )r2   whereisnannanr3   r.   r   rD  r#   s   &&$,r%   r1   Uniform._logpdf_formulax  s+    xxRVVbffRj[99r'   c                   \         P                  ! \         P                  ! V4      \         P                  ^V,          4      # r   )r2   rH  rI  rJ  rK  s   &&$,r%   r7   Uniform._pdf_formula{  s%    xxRVVQrT22r'   c                   \         P                  ! R R7      ;_uu_ 4        \         P                  ! W,
          4      \         P                  ! V4      ,
          uuRRR4       #   + '       g   i     R# ; irW   rX   Nr2   r]   r3   r.   r   r  rD  r#   s   &&$$,r%   r:   Uniform._logcdf_formula~  :    [[))66!%=266":- *)))   7A""A3	c                    W,
          V,          # r   r+   rR  s   &&$$,r%   r=   Uniform._cdf_formula      |r'   c                   \         P                  ! R R7      ;_uu_ 4        \         P                  ! W!,
          4      \         P                  ! V4      ,
          uuRRR4       #   + '       g   i     R# ; irP  rQ  r.   r   r  rD  r#   s   &&$$,r%   r@   Uniform._logccdf_formula  rT  rU  c                    W!,
          V,          # r   r+   rZ  s   &&$$,r%   rC   Uniform._ccdf_formula  rX  r'   c                    W#V,          ,           # r   r+   )r.   pr  rD  r#   s   &&$$,r%   rF   Uniform._icdf_formula      a4xr'   c                    W#V,          ,
          # r   r+   )r.   r_  r  rD  r#   s   &&$$,r%   rL   Uniform._iccdf_formula  ra  r'   c               .    \         P                  ! V4      # r   r  )r.   rD  r#   s   &$,r%   rR   Uniform._entropy_formula  s    vvbzr'   c               "    VR V,          ,           # r   r+   rE  s   &$$$,r%   rh   Uniform._mode_formula      3r6zr'   c               "    VR V,          ,           # r   r+   rE  s   &$$$,r%   rd   Uniform._median_formula  rh  r'   c                X    V^,           pW6,          W&,          ,
          Wd,          ,          # r   r+   )r.   rn   r  r  rD  r#   np1s   &&&&&, r%   ro   Uniform._moment_raw_formula  s     aiCH--r'   c                4    V^8X  d   V^,          ^,          # R# )r   Nr+   )r.   rn   rD  r#   s   &&&,r%   rv   Uniform._moment_central_formula  s     A:r1uRx/4/r'   c                     VP                  W4VR 7      R,          #   \         d&    TP                  ^ ^TR 7      T,          T,           u # i ; ir   )uniformOverflowError)r.   r~   r   r  r  rD  r#   s   &&&&&&,r%   r   Uniform._sample_formula  sM    	=;;q*;5b99 	=;;q!*;5b81<<	=s    -AAr+   r/  r0  r1  r2  )NNN)&r   r   r   r   r   r	   r   r6  r7  r   r   r:  r;  r   r>  r   r   r   r-   r%  r1   r7   r:   r=   r@   rC   rF   rL   rR   rh   rd   ro   rv   r   r   r   r   r   r   s   @@r%   r   r   V  s    	 #s4Ic
3I|LJc)[IHc)ZHHc*jIH)  84+Hh?@I-D -D -
:3...0 '(S"= =r'   c                      a  ] tR tRt o ]! ^ ]3R7      t]! ^ ]3R
R7      t]! R]RR7      t	]! R]RR7      t
]! ]	4      .t]
tR tRtV tR	# )_Gammai  r   r  r  r   r   c                   W^,
          ,          \         P                  ! V) 4      ,          \        P                  ! V4      ,          # r   )r2   r   r   gamma)r.   r   r  r#   s   &&$,r%   r7   _Gamma._pdf_formula  s+    U|bffaRj(7==+;;;r'   r+   NFF)r4  
   )r   r   r   r   r	   r   r6  r   r   r:  r   r   r   r   r7   r   r   r   s   @r%   ru  ru    s\     C1I!S^LJc)YGHc*iHH+H56I< <r'   ru  c                   6  a a ] tR tRt oRt]! ^ ]3RR7      t]! RRR7      t	]! RRR7      t
]! R]RR7      t]! R]	RR7      t]! R]
RR7      t]! ]]4      .t]tV 3R ltR	 tR
 tR tR tR tR tR tR tR tR t^^.]n        R t. RO]n        RtVt V ;t!# )r   i  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   c               0   < \         SV `  ! RR VRV/VB  R# )r  r_  Nr+   r,   )r.   r  r_  r#   r$   s   &$$,r%   r-   Binomial.__init__  rB  r'   c               0    \         P                  ! WV4      # r   )scu
_binom_pmfr.   r   r  r_  r#   s   &&$$,r%   _pmf_formulaBinomial._pmf_formula      ~~aA&&r'   c               P   \         P                  ! V^,           4      \         P                  ! V^,           4      \         P                  ! W!,
          ^,           4      ,           ,
          pV\         P                  ! W4      ,           \         P                  ! W!,
          V) 4      ,           # r   )r   gammalnxlogyxlog1py)r.   r   r  r_  r#   combilns   &&$$, r%   _logpmf_formulaBinomial._logpmf_formula  si    
 OOAaC GOOAaC$87??13q5;Q$QR 	 q,,wqsQB/GGGr'   c               0    \         P                  ! WV4      # r   )r  
_binom_cdfr  s   &&$$,r%   r=   Binomial._cdf_formula  r  r'   c               f    V P                  R W#R7      p\        P                  ! W8  WV3R R 4      # )r   r  r_  c                  R    \         P                  ! \        P                  ! V !  4      # r   )r2   r3   r  r  argss   *r%   <lambda>*Binomial._logcdf_formula.<locals>.<lambda>  s    "&&!67r'   c                  T    \         P                  ! \        P                  ! V !  ) 4      # r   )r2   r   r  	_binom_sfr  s   *r%   r  r    s    "((CMM4$8#89r'   rF   xpxapply_wherer.   r   r  r_  r#   medians   &&$$, r%   r:   Binomial._logcdf_formula  s:     ##C1#2qzA!979
 	
r'   c               0    \         P                  ! WV4      # r   )r  r  r  s   &&$$,r%   rC   Binomial._ccdf_formula  s    }}Q1%%r'   c               f    V P                  R W#R7      p\        P                  ! W8  WV3R R 4      # )r   r  c                  T    \         P                  ! \        P                  ! V !  ) 4      # r   )r2   r   r  r  r  s   *r%   r  +Binomial._logccdf_formula.<locals>.<lambda>  s    "((CNND$9#9:r'   c                  R    \         P                  ! \        P                  ! V !  4      # r   )r2   r3   r  r  r  s   *r%   r  r    s    "&&!56r'   r  r  s   &&$$, r%   r@   Binomial._logccdf_formula  s8    ##C1#2qzA!9:6
 	
r'   c               0    \         P                  ! WV4      # r   )r  
_binom_ppfr  s   &&$$,r%   rF   Binomial._icdf_formula  r  r'   c               0    \         P                  ! WV4      # r   )r  
_binom_isfr  s   &&$$,r%   rL   Binomial._iccdf_formula  r  r'   c                   \         P                  ! V^,           V,          4      p\         P                  ! V^8H  V^,
          V4      pVR,          # )r   r+   )r2   floorrH  )r.   r  r_  r#   modes   &$$, r%   rh   Binomial._mode_formula  s;    xx1a xxQq$/Bxr'   c               x    V^8X  d	   W#,          # V^8X  d$   W#,          ^V,
          W#,          ,           ,          # R# r   Nr+   r.   rn   r  r_  r#   s   &&$$,r%   ro   Binomial._moment_raw_formula   s1    A:3JA:3A$$r'   c               z   V^8X  d   \         P                  ! V4      # V^8X  d   W#,          ^V,
          ,          # V^8X  d,   W#,          ^V,
          ,          ^^V,          ,
          ,          # V^8X  dH   W#,          ^V,
          ,          ^^V,          ^,
          V,          ^V,
          ,          ,           ,          # R# r  )r2   rs   r  s   &&$$,r%   rv    Binomial._moment_central_formula	  s    A:==##A:3A;A:3A;AaC((A:3A;QqS1WaKQ$7 788r'   r+   ry  )r   r   )r   r  r0  )rz     )g      ?g      ?)r   rz  )r   r   r5     )"r   r   r   r   r   r
   r   	_n_domainr	   	_p_domainr   r   _n_param_p_paramr   r   r   r   r-   r  r  r=   r:   rC   r@   rF   rL   rh   ro   r   rv   r   r   r   r   s   @@r%   r   r     s      !As8~NI.II!HMJc)XFHc)\JHc*gFH+Hh?@I-'H'
&
'' #$Q
 &2""r'   )r   r   r   r   )#sysnumpyr2   r   
scipy._libr   r  scipyr   scipy.specialr   r  (scipy.stats._distribution_infrastructurer   r   r	   r
   r   r   r   __all__r   r   r!   r   r  r   ru  r   modulesr   __dict___module	dist_namer   r+   r'   r%   <module>r     s    
   -  (6 6 6 8hD# hDV>K/V K/\C1% C1N?( ?DR=$ R=j<# <Z2# Z2@ ++h

(
(I!.wy/A!BGI r'   