Dj dZddlZddlmZmZmZddlmZddl m Z ddlm Z ddlm Zdd lmZdd lmZd Zd Zd ZdZdZdZd,dZej6dfdZedk(rej<gdgdgdgZej<gdgdgdgZ ej<gdgdgdgZ!e!Z"ejFej6 ej6 dgZ$ejFgdZ$ejFgdZ%ejFgdZ%d e$ddd!e%ddd"Z&ejNe&Z(e)e e$e%ed#$e)ejTjWe%de&ejTjWe$de&z d!zdZ,e)e e,e$ze(z e,e%ze(z e"d%Z&e)ee$e%e"e&ejFd&d'gd'd&ggZ-e)ed"d(ge-d)d*d+Z.ed"d(ge-d)e.Z/e)ej`e/d"d(gkjcddd&ze.z e)eej6 ejdd)zejfd)e"dd)dd)fd)yy)-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 rC:\Crop_Prediction\Backend\crop-ai-system\venv\Lib\site-packages\statsmodels/sandbox/distributions/multivariate.pychi2_pdfrsQ RVAXrvvqbf~ %B'--3 RV ,,B Ic|dz t|z| |zdzz|dzdz tdzz t|dzz }t|SN??rr)np_log sps_gammalnnp_exprrtmps rchi_pdfr!#sT b5&) r!tCx (BsF1HfSk+A A 3  C #;rc|dz t|z| |zdzz|dzdz tdzz t|dzz }|Sr)rrrs r chi_logpdfr#)sO b5&) r!tCx (BsF1HfSk+A A 3  C Jrc tj|dz}t||}|tt ||z|z ||z|z |ddz }t |}|S)Nr@Bư>maxptsabseps)rsqrtr#rrr)sabRrsqrt_dfrets rfunbghr1.scggbfoG Qr C6,qs7{AaCK07F 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 rfunbgh2r86sw AAggbkG 2a4"1Q3s7* + !A#g+qs7{Abooa6L4M!(7 77rcXtjdd|dzz t|dzz S)Nrrr)rpower sps_gamma)rs r bghfactorr<>s) 88C2c6 "Yr#v%6 66rct||||fddd}||j|tj|d|z g|\}} t j t || 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?)argsepsabsepsrellimitr)dictupdaterppfrquadr8r<) r,r-r.riepsquadkwdsmvstkwdskwdslowerupperreserrprobs r mvstdtprobrPBsy aAr]4C HD H77D!d(+R0LE5~~gueNN)4__doc__numpyrscipyrrr scipy.statsrextrasrr rr r scipy.specialr r;r rrr!r#r1r8r<rPrSr]__name__rRcorr corr_indep corr_equalr.arrayr,r-rr*r/printtcdfr+rZnobsrvstsumallrTrXrrrxs ++ ,0  77,!#!$D z 2::}WY7 8D[9:J_[EFJA266'266'&)*A$%AA"#A AaD AaD BbggbkG ,q!T$ /0 577;;qtR 577;;qtR#8 81 <= A ,qs7{AaCK 34 B *Q1b !"2b'2b'"#A c#Y1a 01 D s3iAt 4D &"&&$Cy.%%a( +b 04 78 *bffWWRWWQZ'!a2A2h BCEr