B Z@sdZddlmZddlZddlmZmZmZddl m Z m Z ddl m Z mZm Z ddlmZdd lmZdd lmZdd lmZd d ZddZddZddZddZddZd.ddZejdfddZ e!dkre"dddgdddgdddggZ#e"dddgdddgdddggZ$e"dddgdddgdddggZ%e%Z&e'ej ej d gZ(e'd!d!d!gZ(e'd"d"d"gZ)e'd#d#d#gZ)d$e(dd<d%e)dd<d&Z*e+e*Z,e-ee(e)e#d'd(e-ej./e)de*ej./e(de*d%dZ0e-ee0e(e,e0e)e,e&d)Z*e-ee(e)e&e*e'ddgddggZ1e-e d&d*ge1d+d,d-Z2e d&d*ge1d+e2Z3e-e4e3d&d*gk5ddde2e-eej e6d+e7d+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 )print_functionN) integratestatsspecial)chichi2) mvnormcdf mvstdnormcdfr )exp)log)gamma)gammalncCsB||ddt| d}|t|dd|d}|S)zpdf of chi-square distributiong@r)npr rr )selfxdfZPxrMlib/python3.7/site-packages/statsmodels/sandbox/distributions/multivariate.pychi2_pdfs rcCsF|dt|| |d|ddtdt|d}t|S)Ng?g?rg@)np_log sps_gammalnnp_exp)rrtmprrrchi_pdf$s>rcCsB|dt|| |d|ddtdt|d}|S)Ng?g?rg@)rr)rrrrrr chi_logpdf*s>rc CsNt|d}t||}|tt|||||||ddd7}t|}|S)Ng?i@Bgư>)maxptsabseps)rsqrtrrr r)sabRrsqrt_dfZretrrrfunbgh/s  r%c Cs`t|}t|}t|dt|||dt|||||||t|ddddS)Nrg?i@Bg-C6?)rr)lenrrrrr Z tril_indices)r r!r"r#rnr$rrrfunbgh27s  $r)cCs tdd|dt|dS)Ng@rg?)rZpower sps_gamma)rrrr bghfactor?sr+h㈵>c Cs`t||||fdddd}|dk r*||tjtft|d|g||\}} |t|} | S)a4probability of rectangular area of standard t distribution assumes mean is zero and R is correlation matrix Notes ----- This function does not calculate the estimate of the combined error between the underlying multivariate normal probability calculations and the integration. g-C6?g{Gz?)argsZepsabsZepsrellimitNr)dictupdaterZquadr)rZppfr+) r!r"r#rZiepsZquadkwdsZmvstkwdskwdsZreserrZprobrrr mvstdtprobCs    r4cCsjt|}t|}|tjkr"d}ntj|||}tjt|||f}||t|dddfS)agenerate random variables of multivariate t distribution Parameters ---------- m : array_like mean of random variable, length determines dimension of random variable S : array_like square array of covariance matrix df : int or float degrees of freedom n : int number of observations, return random array will be (n, len(m)) Returns ------- rvs : ndarray, (n, len(m)) each row is an independent draw of a multivariate t distributed random variable g?N) rasarrayr'infZrandomZ chisquareZmultivariate_normalzerosr)mSrr(drzrrrmultivariate_t_rvsZs  r<__main__g?g?gYgQggQ?r&g$@gư>)rg4@ri')r,NN)8__doc__Z __future__rZnumpyrZscipyrrrZ scipy.statsrrZextrasr r r rr rZ scipy.specialr r*rrrrrr%r)r+r4r6r<__name__r5ZcorrZ corr_indepZ corr_equalr#Zarrayr!r"rrr$printtZcdfr r9ZnobsZrvstsumallZonesr7rrrrsV      " """   , &6