ó áp7]c@s±dZddlmZddlZddlmZmZmZddl m Z ddl m Z ddlm Zdd lmZdd lmZdd lmZd „Zd „Zd„Zd„Zd„Zd„Zdddd„Zejdd„Ze dkr­ej!dddgdddgdddggƒZ"ej!dddgdddgdddggƒZ#ej!dddgdddgdddggƒZ$e$Z%ej&ej ej dgƒZ'ej&dddgƒZ'ej&dddgƒZ(ej&dddgƒZ(de'(de((dZ)ej*e)ƒZ+e,e e'e(e"dd ƒƒe,ej-j.e(de)ƒej-j.e'de)ƒdƒdZ/e,e e/e'e+e/e(e+e%ƒƒd!Z)e,ee'e(e%e)ƒƒej&ddgddggƒZ0e,edd"ge0d#d$ƒƒd%Z1edd"ge0d#e1ƒZ2e,ej3e2dd"gkj4dƒdƒde1ƒe,eej ej5d#ƒej6d#ƒe%dd#…dd#…fd#ƒƒndS(&s2Multivariate Distribution Probability of a multivariate t distribution Now also mvstnormcdf has tests against R mvtnorm Still need non-central t, extra options, and convenience function for location, scale version. Author: Josef Perktold License: BSD (3-clause) Reference: Genz and Bretz for formula iÿÿÿÿ(tprint_functionN(t integratetstatstspecial(tchii(t mvstdnormcdf(texp(tlog(tgamma(tgammalncCsK||ddtj| dƒ}|tj|dƒd|d:}|S(spdf of chi-square distributiong@ii(tnpRRR(tselftxtdftPx((sMlib/python2.7/site-packages/statsmodels/sandbox/distributions/multivariate.pytchi2_pdfs$#cCsO|dt|ƒ| |d|ddtdƒt|dƒ}t|ƒS(Ngð?gà?ig@(tnp_logt sps_gammalntnp_exp(R R ttmp((sMlib/python2.7/site-packages/statsmodels/sandbox/distributions/multivariate.pytchi_pdf$sEcCsI|dt|ƒ| |d|ddtdƒt|dƒ}|S(Ngð?gà?ig@(RR(R R R((sMlib/python2.7/site-packages/statsmodels/sandbox/distributions/multivariate.pyt chi_logpdf*sEc Csjtj|dƒ}t||ƒ}|tt|||||||ddddƒƒ7}t|ƒ}|S(Ngà?tmaxptsi@Btabsepsgíµ ÷Æ°>(R tsqrtRRRR(tstatbtRR tsqrt_dftret((sMlib/python2.7/site-packages/statsmodels/sandbox/distributions/multivariate.pytfunbgh/s % c Cs{t|ƒ}tj|ƒ}t|dt|ƒ||dƒt|||||||tj|dƒddddƒS(Nigà?iÿÿÿÿRi@BRg-Cëâ6?(tlenR RRRRt tril_indices(RRRRR tnR((sMlib/python2.7/site-packages/statsmodels/sandbox/distributions/multivariate.pytfunbgh27s  #/cCs&tjdd|dƒt|dƒS(Ng@igà?(R tpowert sps_gamma(R ((sMlib/python2.7/site-packages/statsmodels/sandbox/distributions/multivariate.pyt bghfactor?sgñh㈵øä>c Cstd||||fddddddƒ}|d k rI|j|ƒntj|d|g|ƒ\}} tjt|| |\} } | t|ƒ} | S( s8 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. targstepsabsg-Cëâ6?tepsrelg{®Gáz„?tlimiti–iN( tdicttNonetupdateRtppfRtquadR#R&( RRRR tiepstquadkwdstmvstkwdstkwdstlowertuppertresterrtprob((sMlib/python2.7/site-packages/statsmodels/sandbox/distributions/multivariate.pyt mvstdtprobCs - "cCs•tj|ƒ}t|ƒ}|tjkr3d}ntjj||ƒ|}tjjtj|ƒ||fƒ}||tj|ƒdd…dfS(sgenerate 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 gð?N( R tasarrayR tinftrandomt chisquaretmultivariate_normaltzerosRR,(tmtSR R"tdR tz((sMlib/python2.7/site-packages/statsmodels/sandbox/distributions/multivariate.pytmultivariate_t_rvsYs  $t__main__gð?igà?gYÀg¸…ëQ¸î¿gg¸…ëQ¸î?ig$@Rgíµ ÷Æ°>ig4@iii'(7t__doc__t __future__RtnumpyR tscipyRRRt scipy.statsRtextrasRRRRRt scipy.specialRR%R RRRRRR#R&R,R9R;RDt__name__R:tcorrt corr_indept corr_equalRtarrayRRR RRtprinttttcdfRRAtnobstrvsttsumtalltonesR?(((sMlib/python2.7/site-packages/statsmodels/sandbox/distributions/multivariate.pytsV       " 333 8&!3I