U Kv fïã@s°dZddlZddlmZmZmZddlmZddl m Z ddlm Z ddlm Zdd lmZdd lmZd d „Zd d„Zdd„Zdd„Zdd„Zdd„Zd-dd„Zejdfdd„Zedkr¬e dddgdddgdddgg¡Ze dddgdddgdddgg¡Z e dddgdddgdddgg¡Z!e!Z"e #ej ej dg¡Z$e #d d d g¡Z$e #d!d!d!g¡Z%e #d"d"d"g¡Z%d#e$dd…<d$e%dd…<d%Z&e 'e&¡Z(e)e e$e%ed&d'ƒe)ej* +e%de&¡ej* +e$de&¡d$ƒdZ,e)e e,e$e(e,e%e(e"ƒƒd(Z&e)ee$e%e"e&ƒƒe #ddgddgg¡Z-e)ed%d)ge-d*d+ƒƒd,Z.ed%d)ge-d*e.ƒZ/e)e 0e/d%d)gk 1d¡d¡de.ƒe)eej e 2d*¡e 3d*¡e"dd*…dd*…fd*ƒƒdS).a2Multivariate Distribution Probability of a multivariate t distribution Now also mvstnormcdf has tests against R mvtnorm Still need non-central t, extra options, and convenience function for location, scale version. Author: Josef Perktold License: BSD (3-clause) Reference: Genz and Bretz for formula éN)Ú integrateÚstatsÚspecial)Úchié)Ú mvstdnormcdf)Úexp)Úlog)Úgamma)ÚgammalncCsB||ddt | d¡}|t |d¡d|d}|S)zpdf of chi-square distributionç@ré)Únprrr )ÚselfÚxÚdfZPx©rúR/tmp/pip-unpacked-wheel-2v6byqio/statsmodels/sandbox/distributions/multivariate.pyÚchi2_pdfs rcCsF|dt|ƒ| |d|ddtdƒt|dƒ}t|ƒS©Nçð?çà?rr )Únp_logÚ sps_gammalnÚnp_exp©rrÚtmprrrÚchi_pdf#s0 ÿrcCsB|dt|ƒ| |d|ddtdƒt|dƒ}|Sr)rrrrrrÚ chi_logpdf)s0 ÿrc CsNt |d¡}t||ƒ}|tt|||||||dddƒ7}t|ƒ}|S)Nré@Bçíµ ÷Æ°>©ZmaxptsÚabseps)rÚsqrtrrrr)ÚsÚaÚbÚRrÚsqrt_dfÚretrrrÚfunbgh.s ÿ r*c Cs`t|ƒ}t |¡}t|dt|ƒ||dƒt|||||||t |d¡dddS)Nrréÿÿÿÿrç-Cëâ6?r!)Úlenrr#rrrZ tril_indices)r$r%r&r'rÚnr(rrrÚfunbgh26s $ÿÿr/cCs t dd|d¡t|dƒS)Nr rr)rÚpowerÚ sps_gamma)rrrrÚ bghfactor>sr2çñh㈵øä>c Csht||||fdddd}|dk r*| |¡t |d|g|¡\}} tjt|| f|Ž\} } | t|ƒ} | S)a8 Probability of rectangular area of standard t distribution assumes mean is zero and R is correlation matrix Notes ----- This function does not calculate the estimate of the combined error between the underlying multivariate normal probability calculations and the integration. r,g{®Gáz„?é–)ÚargsZepsabsZepsrelÚlimitNr)ÚdictÚupdaterZppfrZquadr/r2) r%r&r'rZiepsZquadkwdsZmvstkwdsÚkwdsÚlowerÚupperÚresÚerrZprobrrrÚ mvstdtprobBs   r>cCspt |¡}t|ƒ}|tjkr(t |¡}ntj ||¡|}tj t |¡||f¡}||t  |¡dd…dfS)agenerate random variables of multivariate t distribution Parameters ---------- m : array_like mean of random variable, length determines dimension of random variable S : array_like square array of covariance matrix df : int or float degrees of freedom n : int number of observations, return random array will be (n, len(m)) Returns ------- rvs : ndarray, (n, len(m)) each row is an independent draw of a multivariate t distributed random variable N) rÚasarrayr-ÚinfÚonesÚrandomZ chisquareZmultivariate_normalÚzerosr#)ÚmÚSrr.ÚdrÚzrrrÚmultivariate_t_rvsXs   rHÚ__main__rrgYÀg¸…ëQ¸î¿gg¸…ëQ¸î?r+ég$@r )r"ég4@r éi')r3NN)4Ú__doc__ZnumpyrZscipyrrrZ scipy.statsrÚextrasrrrr rZ scipy.specialr r1r rrrrr*r/r2r>r@rHÚ__name__r?ZcorrZ corr_indepZ corr_equalr'Úarrayr%r&rr#r(ÚprintÚtZcdfr$rEZnobsZrvstÚsumÚallrArCrrrrÚsT       " """   , &6