+
    i                        ^ RI Ht ^ RIHt ^ RIH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HtHtHt ^ R	IHtHtHtHtHtHtH t  ^ R
I!H"t" ]	! RRR./R7      t#]R 4       t$]$PK                  ]4      R R l4       t&]$PK                  ]4      R R l4       t&]$PK                  ]4      R R l4       t&]$PK                  ]4      R R l4       t&]$PK                  ]4      R R l4       t&]$PK                  ]4      R R l4       t&]$PK                  ]4      R R l4       t&]$PK                  ]4      R R l4       t&]$PK                  ]4      R  R! l4       t&]$PK                  ]4      R" R# l4       t&]$PK                  ]4      R$ R% l4       t&]$PK                  ]4      R& R' l4       t&]$PK                  ]4      R( R) l4       t&]$PK                  ]4      R* R+ l4       t&]$PK                  ]4      R, R- l4       t&]$PK                  ]4      R. R/ l4       t&]$PK                  ]4      R0 R1 l4       t&]$PK                  ]4      R2 R3 l4       t&]$PK                  ] 4      R4 R5 l4       t&]$PK                  ]"4      R6 R7 l4       t&R8# )9    )singledispatch)Dummy)exp)lambdify)import_moduleDiscreteDistributionHandmadeSingleContinuousDistribution)
ChiSquaredDistributionExponentialDistributionGammaDistributionLogNormalDistributionNormalDistributionParetoDistributionUniformDistributionBetaDistributionStudentTDistributionCauchyDistribution)GeometricDistributionLogarithmicDistributionNegativeBinomialDistributionPoissonDistributionSkellamDistributionYuleSimonDistributionZetaDistributionSingleFiniteDistributionscipyfromliststats)import_kwargsc                     R # N distsizeseeds   &&&_/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/stats/sampling/sample_scipy.pydo_sample_scipyr+      s        c                $    V ^8  d   QhR\         /#    r'   r
   )formats   "r*   __annotate__r1      s     6 6( 6r,   c                 N  a ^ RI p\        R4      p\        W@P                  V4      RR.4      o ! V3R lRVP                  P
                  4      pV! \        V P                  P                  4      \        V P                  P                  4      RR7      pVP                  WR7      # )	r   Nznumpyr   c                   .   <a  ] tR t^#t o V3R ltRtV tR# )_.<locals>.scipy_pdfc                   < S! V4      # r$   r%   )r'   xhandmade_pdfs   &&r*   _pdf_.<locals>.scipy_pdf._pdf$       ?"r,   r%   N)__name__
__module____qualname____firstlineno__r:   __static_attributes____classdictcell__)__classdict__r9   s   @r*   	scipy_pdfr6   #        	# 	#r,   rD   abnamer(   random_state)scipy.statsr   r   pdfr!   rv_continuousfloatset_inf_suprvs)r'   r(   r)   r   r3   rD   scipy_rvr9   s   &&&    @r*   _rU      s     c
AAxx{Wg,>?L#EKK-- # 5/ /kCH<<T<55r,   c                $    V ^8  d   QhR\         /# r.   )r   )r0   s   "r*   r1   r1   -   s     P P" Pr,   c                 ~    \         P                  P                  P                  \	        V P
                  4      WR 7      # )dfr(   rK   )r   r!   chi2rS   rO   kr&   s   &&&r*   rU   rU   ,   s,     ;;5=tOOr,   c                $    V ^8  d   QhR\         /# r.   )r   )r0   s   "r*   r1   r1   3   s     [ [# [r,   c                     \         P                  P                  P                  ^\	        V P
                  4      ,          WR7      # )   )scaler(   rK   )r   r!   exponrS   rO   rater&   s   &&&r*   rU   rU   2   s2     ;;  q5+;';$ ZZr,   c                $    V ^8  d   QhR\         /# r.   )r   )r0   s   "r*   r1   r1   9   s     i i ir,   c                     \         P                  P                  P                  \	        V P
                  4      \	        V P                  4      WR 7      # ))rG   r_   r(   rK   )r   r!   gammarS   rO   r[   thetar&   s   &&&r*   rU   rU   8   s8     ;;  5=djj8IPT hhr,   c                $    V ^8  d   QhR\         /# r.   )r   )r0   s   "r*   r1   r1   ?   s     q q! qr,   c                     \         P                  P                  P                  \	        \        V P                  4      4      \	        V P                  4      WR 7      # ))r_   sr(   rK   )r   r!   lognormrS   rO   r   meanstdr&   s   &&&r*   rU   rU   >   s<     ;;""s499~)>%/X\"ppr,   c                $    V ^8  d   QhR\         /# r.   )r   )r0   s   "r*   r1   r1   E   s     k k kr,   c                     \         P                  P                  P                  \	        V P
                  4      \	        V P                  4      WR 7      # )locr_   r(   rK   )r   r!   normrS   rO   rj   rk   r&   s   &&&r*   rU   rU   D   s6    ;;E$))$4E$((ORVjjr,   c                $    V ^8  d   QhR\         /# r.   )r   )r0   s   "r*   r1   r1   J   s     k k kr,   c                     \         P                  P                  P                  \	        V P
                  4      \	        V P                  4      WR 7      # ))rH   r_   r(   rK   )r   r!   paretorS   rO   alphaxmr&   s   &&&r*   rU   rU   I   s8     ;;!!E$**$5U477^RV!jjr,   c                $    V ^8  d   QhR\         /# r.   )r   )r0   s   "r*   r1   r1   P   s     N N  Nr,   c                 ~    \         P                  P                  P                  \	        V P
                  4      WR 7      # rX   )r   r!   trS   rO   nur&   s   &&&r*   rU   rU   O   s(    ;;==dggTMMr,   c                $    V ^8  d   QhR\         /# r.   )r   )r0   s   "r*   r1   r1   U   s     | | |r,   c                     \         P                  P                  P                  \	        V P
                  4      \	        V P                  V P
                  ,
          4      WR 7      # rn   )r   r!   uniformrS   rO   leftrightr&   s   &&&r*   rU   rU   T   sE     ;;""uTYY'7uTZZRVR[R[E[?\cg"{{r,   c                $    V ^8  d   QhR\         /# r.   )r   )r0   s   "r*   r1   r1   [   s     g g gr,   c                     \         P                  P                  P                  \	        V P
                  4      \	        V P                  4      WR 7      # ))rG   rH   r(   rK   )r   r!   betarS   rO   rt   r&   s   &&&r*   rU   rU   Z   s8     ;;%

"3uTYY7Gdffr,   c                $    V ^8  d   QhR\         /# r.   )r   )r0   s   "r*   r1   r1   a   s     m m mr,   c                     \         P                  P                  P                  \	        V P
                  4      \	        V P                  4      WR 7      # rn   )r   r!   cauchyrS   rO   x0rd   r&   s   &&&r*   rU   rU   `   s6    ;;!!eDGGnE$**<MTX!llr,   c                $    V ^8  d   QhR\         /# r.   r   )r0   s   "r*   r1   r1   h   s     6 6( 6r,   c                 *  a ^ RI Hp \        R4      p\        W@P	                  V4      RR.4      o ! V3R lRV4      pV! \        V P                  P                  4      \        V P                  P                  4      RR7      pVP                  WR7      # )	r   rv_discreter3   r4   r   c                   .   <a  ] tR t^nt o V3R ltRtV tR# )_.<locals>.scipy_pmfc                   < S! V4      # r$   r%   )r'   r8   handmade_pmfs   &&r*   _pmf_.<locals>.scipy_pmf._pmfo   r<   r,   r%   N)r=   r>   r?   r@   r   rA   rB   )rC   r   s   @r*   	scipy_pmfr   n   rE   r,   r   rF   rJ   )
rL   r   r   r   rM   rO   rP   rQ   rR   rS   )r'   r(   r)   r   r3   r   rT   r   s   &&&    @r*   rU   rU   g   sr    'c
AAxx{Wg,>?L#K # 5/53G)+H<<T<55r,   c                $    V ^8  d   QhR\         /# r.   )r   )r0   s   "r*   r1   r1   x   s     O O! Or,   c                 ~    \         P                  P                  P                  \	        V P
                  4      WR 7      # )pr(   rK   )r   r!   geomrS   rO   r   r&   s   &&&r*   rU   rU   w   *    ;;%-dNNr,   c                $    V ^8  d   QhR\         /# r.   )r   )r0   s   "r*   r1   r1   }   s     Q Q# Qr,   c                 ~    \         P                  P                  P                  \	        V P
                  4      WR 7      # r   )r   r!   logserrS   rO   r   r&   s   &&&r*   rU   rU   |   s*    ;;!!E$&&M!PPr,   c                $    V ^8  d   QhR\         /# r.   )r   )r0   s   "r*   r1   r1      s     b b( br,   c                     \         P                  P                  P                  \	        V P
                  4      \	        V P                  4      WR 7      # ))nr   r(   rK   )r   r!   nbinomrS   rO   rr   r&   s   &&&r*   rU   rU      s4    ;;!!E$&&MU466]!aar,   c                $    V ^8  d   QhR\         /# r.   )r   )r0   s   "r*   r1   r1      s     W W Wr,   c                 ~    \         P                  P                  P                  \	        V P
                  4      WR 7      # ))mur(   rK   )r   r!   poissonrS   rO   lamdar&   s   &&&r*   rU   rU      s+    ;;""eDJJ&7d"VVr,   c                $    V ^8  d   QhR\         /# r.   )r   )r0   s   "r*   r1   r1      s     k k kr,   c                     \         P                  P                  P                  \	        V P
                  4      \	        V P                  4      WR 7      # ))mu1mu2r(   rK   )r   r!   skellamrS   rO   r   r   r&   s   &&&r*   rU   rU      s5    ;;""uTXXE$((ORV"jjr,   c                $    V ^8  d   QhR\         /# r.   )r   )r0   s   "r*   r1   r1      s     Z Z! Zr,   c                 ~    \         P                  P                  P                  \	        V P
                  4      WR 7      # ))rt   r(   rK   )r   r!   	yulesimonrS   rO   rhor&   s   &&&r*   rU   rU      s*    ;;  $$5?$YYr,   c                $    V ^8  d   QhR\         /# r.   )r   )r0   s   "r*   r1   r1      s     O O Or,   c                 ~    \         P                  P                  P                  \	        V P
                  4      WR 7      # ))rG   r(   rK   )r   r!   zipfrS   rO   rh   r&   s   &&&r*   rU   rU      r   r,   c                $    V ^8  d   QhR\         /# r.   r   )r0   s   "r*   r1   r1      s     
6 
6$ 
6r,   c                     ^ RI Hp V P                  p. . reVP                  4        F9  w  rxVP	                  \        V4      4       VP	                  \        V4      4       K;  	  V! RWV3R7      p	V	P                  WR7      # )r   r   rT   )rI   valuesrJ   )rL   r   dictitemsappendintrO   rS   )
r'   r(   r)   r   density_r8   yr[   vrT   s
   &&&       r*   rU   rU      sk     (yyHrq 	Q	q ! 
A6:H<<T<55r,   N)'	functoolsr   sympy.core.symbolr   &sympy.functions.elementary.exponentialr   sympy.utilities.lambdifyr   sympy.externalr   sympy.statsr	   sympy.stats.crvr   sympy.stats.crv_typesr   r   r   r   r   r   r   r   r   r   sympy.stats.drv_typesr   r   r   r   r   r   r   sympy.stats.frvr   r   r+   registerrU   r%   r,   r*   <module>r      s	   $ # 6 - ( 4 8- - -V V V 4 	gj'-CD   676 86  01P 2P
 12[ 3[
 +,i -i
 /0q 1q
 ,-k .k ,-k .k
 ./N 0N -.| /|
 *+g ,g
 ,-m .m 676 86 /0O 1O 12Q 3Q 67b 8b -.W /W -.k /k /0Z 1Z *+O ,O 23
6 4
6r,   