U md@sdZddlZddlmZmZmZddlmZddl m Z ddlm Z ddlm Zdd lmZdd lmZd d Zd dZddZddZddZddZd-ddZejdfddZedkredddgdddgdddggZedddgdddgdddggZ edddgdddgdddggZ!e!Z"e#ej ej dgZ$e#d d d gZ$e#d!d!d!gZ%e#d"d"d"gZ%d#e$dd<d$e%dd<d%Z&e'e&Z(e)e e$e%ed&d'e)ej*+e%de&ej*+e$de&d$dZ,e)e e,e$e(e,e%e(e"d(Z&e)ee$e%e"e&e#ddgddggZ-e)ed%d)ge-d*d+d,Z.ed%d)ge-d*e.Z/e)e0e/d%d)gk1ddde.e)eej e2d*e3d*e"dd*dd*fd*dS).a2Multivariate Distribution Probability of a multivariate t distribution Now also mvstnormcdf has tests against R mvtnorm Still need non-central t, extra options, and convenience function for location, scale version. Author: Josef Perktold License: BSD (3-clause) Reference: Genz and Bretz for formula N) integratestatsspecial)chi) mvstdnormcdf)exp)log)gamma)gammalncCsB||ddt| d}|t|dd|d}|S)zpdf of chi-square distribution@r)nprrr )selfxdfZPxrg/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/statsmodels/sandbox/distributions/multivariate.pychi2_pdfs rcCsF|dt|| |d|ddtdt|d}t|SN??rr )np_log sps_gammalnnp_exprrtmprrrchi_pdf#s0 rcCsB|dt|| |d|ddtdt|d}|Sr)rrrrrr chi_logpdf)s0 rc CsNt|d}t||}|tt|||||||ddd7}t|}|S)Nr@Bư>Zmaxptsabseps)rsqrtrrrr)sabRrsqrt_dfretrrrfunbgh.s  r*c Cs`t|}t|}t|dt|||dt|||||||t|ddddS)Nrrr-C6?r!)lenrr#rrrZ tril_indices)r$r%r&r'rnr(rrrfunbgh26s $r/cCs tdd|dt|dS)Nr rr)rpower sps_gamma)rrrr bghfactor>sr2h㈵>c Csht||||fdddd}|dk r*||t|d|g|\}} tjt|| f|\} } | t|} | S)a8 Probability of rectangular area of standard t distribution assumes mean is zero and R is correlation matrix Notes ----- This function does not calculate the estimate of the combined error between the underlying multivariate normal probability calculations and the integration. r,g{Gz?)argsZepsabsZepsrellimitNr)dictupdaterZppfrquadr/r2) r%r&r'rZiepsZquadkwdsZmvstkwdskwdslowerupperreserrZprobrrr mvstdtprobBs   r?cCspt|}t|}|tjkr(t|}ntj|||}tjt|||f}||t |dddfS)agenerate random variables of multivariate t distribution Parameters ---------- m : array_like mean of random variable, length determines dimension of random variable S : array_like square array of covariance matrix df : int or float degrees of freedom n : int number of observations, return random array will be (n, len(m)) Returns ------- rvs : ndarray, (n, len(m)) each row is an independent draw of a multivariate t distributed random variable N) rasarrayr-infonesrandomZ chisquareZmultivariate_normalzerosr#)mSrr.drzrrrmultivariate_t_rvsXs   rI__main__rrgYgQggQ?r+g$@r )r"g4@r i')r3NN)4__doc__numpyrZscipyrrrZ scipy.statsrextrasrrrr rZ scipy.specialr r1r rrrrr*r/r2r?rArI__name__r@ZcorrZ corr_indepZ corr_equalr'arrayr%r&rr#r(printtZcdfr$rFZnobsZrvstsumallrBrDrrrrsT       " """   , &6