M/Ph dZddlZddlmZmZmZddlmZddl m Z ddlm Z ddlm Zdd lmZdd lmZd Zd Zd ZdZdZdZd-dZejdfdZedkr*ejgdgdgdgZejgdgdgdgZ ejgdgdgdgZ!e!Z"ej#ej ej dgZ$ej#gdZ$ej#gdZ%ej#gd Z%d!e$dd<d"e%dd<d#Z&ej'e&Z(e)e e$e%ed$%e)ej*+e%de&ej*+e$de&z d"zdZ,e)e e,e$ze(z e,e%ze(z e"d&Z&e)ee$e%e"e&ej#d'd(gd(d'ggZ-e)ed#d)ge-d*d+d,Z.ed#d)ge-d*e.Z/e)ej0e/d#d)gk1ddd'ze.z e)eej ej2d*zej3d*e"dd*dd*fd*dSdS).a2Multivariate Distribution Probability of a multivariate t distribution Now also mvstnormcdf has tests against R mvtnorm Still need non-central t, extra options, and convenience function for location, scale version. Author: Josef Perktold License: BSD (3-clause) Reference: Genz and Bretz for formula N) integratestatsspecial)chi) mvstdnormcdf)exp)log)gamma)gammalnc||dz dz ztj| dz z}|tj|dz d|dz zzz}|S)zpdf of chi-square distribution@r)npr rr )selfxdfPxs n/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/sandbox/distributions/multivariate.pychi2_pdfrsR RVAXrvqbf~~ %B'-3  RV ,,B Ic|dz t|z| |zdzz|dzdz tdzz t|dzz }t|SN??rr)np_log sps_gammalnnp_exprrtmps rchi_pdfr!#s] b5&)) r!tCx (BsF1HfSkk+A A 3   C #;;rc|dz t|z| |zdzz|dzdz tdzz t|dzz }|Sr)rrrs r chi_logpdfr#)sV b5&)) r!tCx (BsF1HfSkk+A A 3   C Jrc tj|dz}t||}|tt ||z|z ||z|z |ddz }t |}|S)Nr@Bư>maxptsabseps)rsqrtr#rrr)sabRrsqrt_dfrets rfunbghr1.szgbfooG Qr  C6,qs7{AaCK07FFF G GGC ++C Jrc t|}tj|}t|dz t |z||zdzz t ||z|z ||z|z |tj|dddzS)Nrrr%-C6?r')lenrr*rrr tril_indices)r+r,r-r.rnr/s rfunbgh2r86s AAgbkkG 2a4"1Q3s7* + + !A#g+qs7{Aboa6L6L4M!(777 77rc^tjdd|dzz t|dzz S)Nrrr)rpower sps_gamma)rs r bghfactorr<>s- 8C2c6 " "Yr#v%6%6 66rh㈵>ct||||fddd}|||tj|d|z g|\}} t jt || fi|\} } | t|z} | S)a8 Probability of rectangular area of standard t distribution assumes mean is zero and R is correlation matrix Notes ----- This function does not calculate the estimate of the combined error between the underlying multivariate normal probability calculations and the integration. r4g{Gz?)argsepsabsepsrellimitNr)dictupdaterppfrquadr8r<) r,r-r.riepsquadkwdsmvstkwdskwdslowerupperreserrprobs r mvstdtprobrQBs aAr]4C H H HD H7D!d(+R00LE5~gue<rys ++++++++++ ,,,,,,000000  777777,!#!$$$$D z 2:}}}WWWYYY7 8 8D[[[9::J___[[[EFFJA26'26'&)**A$$$%%AA"""##A AaaaD AaaaD BbgbkkG E,,q!T$ / / /000 E57;;qtR 57;;qtR#8#8 81 <=== A E,,qs7{AaCK 3 3444 B E**Q1b ! !"""2b'2b'"##A E  c#Y1a 0 0111 D  s3iAt 4 4D E&"&$Cy.%%a(( + +b 04 7888 E**bfWWRWQZZ'!a2A2h B BCCCEr