ó áp7]c@s‰dZddlmZddlZddlmZmZmZddlZddlm Z m Z ddl m Z ddl mZmZddlmZmZd e jfd „ƒYZeƒZd e jfd „ƒYZed dddddƒZde jfd„ƒYZd„Zd„Zd„Zd„Zde jfd„ƒYZd„Zde jfd„ƒYZd„Z d^\Z!Z"d_\Z!Z"d#„Z#d$„Z$d%„Z%ee j&e#e$d&e'd'd(d d)d*d+dd,ƒZ(ee j&ejej)d'd-d.d(d d/d*d0dd1ƒZ*ee j+ej)ejd'd2ƒZ,d3e jfd4„ƒYZ-d5e jfd6„ƒYZ.d7e jfd8„ƒYZ/d9e0fd:„ƒYZ1e1ƒZ2e/e j&e2j3e2j4e2j5e2j6e2j7d;d<d.d=d>ej8d'd(d d?d*d@ddAdBƒZ9e/e j:e2j3e2j4e2j5e2j6e2j7d;d<d.d=d>ej8d'd2d d?d*dCddDdEƒZ;dF„Z4dG„Z5dH„Z6dI„Z7dJ„Z<e/e j&e<e4e5e6e7d;dKd.ej8 d>d=d'd(d dLd*dMddNdOƒZ=dP„Z4dQ„Z5dR„Z6dS„Z7dT„Z>e/e j&ej?e4e5e6e7d;d<d.d=d>ej8d'd(d dUd*dVddWdXƒZ@idYd(6dZd26d[d-6ZAd\„ZBdd]„ZDdS(`sàVarious extensions to distributions * skew normal and skew t distribution by Azzalini, A. & Capitanio, A. * Gram-Charlier expansion distribution (using 4 moments), * distributions based on non-linear transformation - Transf_gen - ExpTransf_gen, LogTransf_gen - TransfTwo_gen (defines as examples: square, negative square and abs transformations) - this versions are without __new__ * mnvormcdf, mvstdnormcdf : cdf, rectangular integral for multivariate normal distribution TODO: * Where is Transf_gen for general monotonic transformation ? found and added it * write some docstrings, some parts I don't remember * add Box-Cox transformation, parameterized ? this is only partially cleaned, still includes test examples as functions main changes * add transf_gen (2010-05-09) * added separate example and tests (2010-05-09) * collect transformation function into classes Example ------- >>> logtg = Transf_gen(stats.t, np.exp, np.log, numargs = 1, a=0, name = 'lnnorm', longname = 'Exp transformed normal', extradoc = ' distribution of y = exp(x), with x standard normal' 'precision for moment andstats is not very high, 2-3 decimals') >>> logtg.cdf(5, 6) 0.92067704211191848 >>> stats.t.cdf(np.log(5), 6) 0.92067704211191848 >>> logtg.pdf(5, 6) 0.021798547904239293 >>> stats.t.pdf(np.log(5), 6) 0.10899273954837908 >>> stats.t.pdf(np.log(5), 6)/5. #derivative 0.021798547909675815 Author: josef-pktd License: BSD iÿÿÿÿ(tprint_functionN(tpoly1dtsqrttexp(tstatstspecial(t distributions(tranget iteritems(tmvsk2mctmc2mvskt SkewNorm_gencBsGeZdZd„Zd„Zd„Zd„Zd„Zdd„ZRS(sunivariate Skew-Normal distribution of Azzalini class follows scipy.stats.distributions pattern but with __init__ cCs&tjj|ddddddƒdS(NtnamesSkew Normal distributiontshapestalphatextradoct (Rt rv_continuoust__init__(tself((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyRLs cCsdS(Ni((RR((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyt _argcheckRscCs‚|tjd|dƒ}tjjd|jƒ}||tjd|dƒtjjd|jƒ}tj|dk|| ƒS(Niitsizei(tnpRRtnormtrvst_sizetwhere(RRtdeltatu0tu1((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyt_rvsUs5cCs|j||ƒS(N(t_mom0_sc(RtnR((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyt_munp\scCs?dtjdtjƒtj|d dƒtj||ƒS(Ng@i(RRtpiRRtndtr(RtxR((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyt_pdfastmvskcCsdS(N((RR$Rtmoments((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyt _stats_skipes( t__name__t __module__t__doc__RRRR!R%R((((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR Ds     t SkewNorm2_gencBs eZdZd„Zd„ZRS(sjunivariate Skew-Normal distribution of Azzalini class follows scipy.stats.distributions pattern cCsdS(Ni((RR((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyRsscCs?dtjdtjƒtj|d dƒtj||ƒS(Ng@i(RRR"RRR#(RR$R((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR%vs(R)R*R+RR%(((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR,ms R sSkew Normal distributionR RRs -inf < alpha < inft ACSkewT_gencBs;eZdZd„Zd„Zd„Zd„Zd„ZRS(szunivariate Skew-T distribution of Azzalini class follows scipy.stats.distributions pattern but with __init__ cCs&tjj|ddddddƒdS(NR sSkew T distributionR s df, alphaRs¼ Skewed T distribution by Azzalini, A. & Capitanio, A. (2003)_ the pdf is given by: pdf(x) = 2.0 * t.pdf(x, df) * t.cdf(df+1, alpha*x*np.sqrt((1+df)/(x**2+df))) with alpha >=0 Note: different from skewed t distribution by Hansen 1999 .._ Azzalini, A. & Capitanio, A. (2003), Distributions generated by perturbation of symmetry with emphasis on a multivariate skew-t distribution, appears in J.Roy.Statist.Soc, series B, vol.65, pp.367-389 (RRR(R((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR…s cCs||k|dkS(Ni((RtdfR((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR™scCsHtjj|d|jƒ}tj|d|jƒ}|tj||ƒS(NR(Rtchi2RRtskewnormRR(RR.RtVtz((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR¡scCs|j|||ƒS(N(R(RR R.R((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR!¨scCsLdtjj||ƒtj|d||tjd||d|ƒƒS(Ng@ii(RttR%RtstdtrRR(RR$R.R((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR%­s(R)R*R+RRRR!R%(((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR-s     cCsodg|}tdƒ|d((R;R<R=sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pytpdf_moments_stås,      '"  c s»t|ƒ}|dkr'tdƒ‚n|\‰}}}tdƒ‰t|ƒ‰|dkr¢t|dƒ}|d}|d}ˆ||d||d‰n‡‡‡fd†}|S( s:Return the Gaussian expanded pdf function given the list of 1st, 2nd moment and skew and Fisher (excess) kurtosis. Parameters ---------- mvsk : list of mu, mc2, skew, kurt distribution is matched to these four moments Returns ------- pdffunc : function function that evaluates the pdf(x), where x is the non-standardized random variable. Notes ----- Changed so it works only if four arguments are given. Uses explicit formula, not loop. This implements a Gram-Charlier expansion of the normal distribution where the first 2 moments coincide with those of the normal distribution but skew and kurtosis can deviate from it. In the Gram-Charlier distribution it is possible that the density becomes negative. This is the case when the deviation from the normal distribution is too large. References ---------- http://en.wikipedia.org/wiki/Edgeworth_series Johnson N.L., S. Kotz, N. Balakrishnan: Continuous Univariate Distributions, Volume 1, 2nd ed., p.30 is2Four moments must be given to approximate the pdf.iig@g8@icsF|ˆˆ}ˆ|ƒtj| |dƒtjdtjƒˆS(Ng@i(RRRR"(R$R:(R;R<R=(sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pytpdffuncFs(R?R@RRR9( R&R7tmc2tskewtkurtRFtC3tC4RL((R;R<R=sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pytpdf_mvsk s(       !c sét|ƒ}|dkr'tdƒ‚n|\}}}}||d}||dd}tdƒ‰t|dƒ‰|d‰|dkrÐt|dƒ}|d} |d } ˆ| |d | |d ‰n‡‡‡fd †} | S( sReturn the Gaussian expanded pdf function given the list of central moments (first one is mean). Changed so it works only if four arguments are given. Uses explicit formula, not loop. Notes ----- This implements a Gram-Charlier expansion of the normal distribution where the first 2 moments coincide with those of the normal distribution but skew and kurtosis can deviate from it. In the Gram-Charlier distribution it is possible that the density becomes negative. This is the case when the deviation from the normal distribution is too large. References ---------- http://en.wikipedia.org/wiki/Edgeworth_series Johnson N.L., S. Kotz, N. Balakrishnan: Continuous Univariate Distributions, Volume 1, 2nd ed., p.30 is:At least two moments must be given to approximate the pdf.gø?g@g@iig@g8@iicsF|ˆˆ}ˆ|ƒtj| |dƒtjdtjƒˆS(Ng@i(RRRR"(R$R:(R;R<R=(sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR>ˆs(R?R@RRR9( RER7tmcRMtmc3tmc4RNRORFRPRQR>((R;R<R=sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyt pdf_momentsKs        !t NormExpan_gencBs)eZdZd„Zd„Zd„ZRS(sGram-Charlier Expansion of Normal distribution class follows scipy.stats.distributions pattern but with __init__ c Kstjj|ddddddƒ|jddƒ}|dkrtj|ƒd \}}}}||||f|_t||||fƒ}nT|d kr³t|ƒ}||_n0|d kr×|}t|ƒ|_n t d ƒ‚||_ t |jƒ|_ dS( NR sNormal Expansion distributionR RRs The distribution is defined as the Gram-Charlier expansion of the normal distribution using the first four moments. The pdf is given by pdf(x) = (1+ skew/6.0 * H(xc,3) + kurt/24.0 * H(xc,4))*normpdf(xc) where xc = (x-mu)/sig is the standardized value of the random variable and H(xc,3) and H(xc,4) are Hermite polynomials Note: This distribution has to be parameterized during initialization and instantiation, and does not have a shape parameter after instantiation (similar to frozen distribution except for location and scale.) Location and scale can be used as with other distributions, however note, that they are relative to the initialized distribution. tmodetsampleiR&tcentmomsmode must be 'mvsk' or centmom( RRRtgetRtdescribeR&R R R@RERRR%( RtargstkwdsRXR;R<tsktkurRE((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR”s"        cCs |j|ƒS(N(R(RR ((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR!¾scCs|jS(N(R&(R((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR(Ãs(R)R*R+RR!R((((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyRWs * cKs8td„t|ƒDƒƒ}|jddƒ}||fS(Ncss?|]5\}}|jdƒr|jdddƒ|fVqdS(tu_tiN(t startswithtreplace(t.0RGtv((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pys òs tu_args(tdictRtpopR5(tkwargstu_kwargsRg((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pytget_u_argskwargsðst Transf_gencBs2eZdZd„Zd„Zd„Zd„ZRS(sUa class for non-linear monotonic transformation of a continuous random variable c Osó||_||_|jddƒ|_|jddƒ}|jddƒ}|jddƒ}|jdtj ƒ} |jd tjƒ} |jd tƒ|_t |\|_ |_ ||_ t t|ƒjd| d | d|d|d|ƒdS( NtnumargsiR t transfdisttlongnames#Non-linear transformed distributionRtatbtdecr(tfunctfuncinvRiRnR5RtinftFalseRsRlRgRktklstsuperRmR( RRxRtRuR]RjR RpRRqRr((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyRûs   $cOs(|j|j_|j|jj|ŒƒS(N(RRxRuR(RR]Rj((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyRscOsO|js(|jj|j|ƒ||ŽSd|jj|j|ƒ||ŽSdS(Ngð?(RsRxt_cdfRu(RR$R]Rj((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyRzs cOsO|js(|j|jj|||ŽƒS|j|jjd|||ŽƒSdS(Ni(RsRtRxt_ppf(RtqR]Rj((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR{"s (R)R*R+RRRzR{(((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyRm÷s    cCstjd|ƒS(Ngð?(Rtdivide(R$((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pytinverse)sgš™™™™™©?gš™™™™™¹?g"@gð?cCsddt|tS(Ngð?i(tmuxtstdx(R$((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pytinversew.scCsd|dttS(Ngð?(RR€(R$((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyt inversew_inv0scCs|S(N((R$((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pytidentit3sRsRnitdiscfRpsnormal-based discount factorsA distribution of discount factor y=1/(1+x)) with x N(0.05,0.1**2)iRqtlnnormsExp transformed normalso distribution of y = exp(x), with x standard normalprecision for moment andstats is not very high, 2-3 decimalsit ExpTransf_gencBs)eZdZd„Zd„Zd„ZRS(sµDistribution based on log/exp transformation the constructor can be called with a distribution class and generates the distribution of the transformed random variable cOsd|kr|d|_n d|_d|kr>|d}nd}d|kr]|d}nd}tt|ƒjddd|ƒ||_dS(NRniR sLog transformed distributionRqi(RnRyR†RRx(RRxR]RjR Rq((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyRQs      cGs|jjtj|ƒ|ŒS(N(RxtcdfRtlog(RR$R]((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyRzcscGstj|jj||ŒƒS(N(RRRxtppf(RR|R]((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR{gs(R)R*R+RRzR{(((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR†Js  t LogTransf_gencBs)eZdZd„Zd„Zd„ZRS(sµDistribution based on log/exp transformation the constructor can be called with a distribution class and generates the distribution of the transformed random variable cOsd|kr|d|_n d|_d|kr>|d}nd}d|kr]|d}nd}tt|ƒjd|d|ƒ||_dS(NRniR sLog transformed distributionRqi(RnRyRŠRRx(RRxR]RjR Rq((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyRqs      cGs|jjtj|ƒ|ŒS(N(RxRzRR(RR$R]((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyRzƒscGstj|jj||ŒƒS(N(RRˆRxR{(RR|R]((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR{†s(R)R*R+RRzR{(((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyRŠjs  t TransfTwo_gencBsDeZdZd„Zd„Zd„Zd„Zd„Zd„ZRS(sODistribution based on a non-monotonic (u- or hump-shaped transformation) the constructor can be called with a distribution class, and functions that define the non-linear transformation. and generates the distribution of the transformed random variable Note: the transformation, it's inverse and derivatives need to be fully specified: func, funcinvplus, funcinvminus, derivplus, derivminus. Currently no numerical derivatives or inverse are calculated This can be used to generate distribution instances similar to the distributions in scipy.stats. cOso||_||_||_||_||_|jddƒ|_|jddƒ} |jddƒ} |jddƒ} |jdtj ƒ} |jd tj ƒ} |jd t ƒ|_ t |\|_ |_||_tt|ƒjd| d | d| d |jd| d| ƒyD|jjtd |d |d|d|d|d|d |j ƒƒWntk rjnXdS(NRniR RoRps#Non-linear transformed distributionRRqRrtshapeR RxRtt funcinvplust funcinvminust derivplust derivminus(RtRRŽRRRiRnR5RRvRwRŒRlRgRkRxRyR‹RR t _ctor_paramtupdateRhtAttributeError(RRxRtRRŽRRR]RjR RpRRqRr((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyRÁs0      $     cGs(|j|j_|j|jj|ŒƒS(N(RRxRtR(RR]((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyRëscOs˜|jdkrd}n$|jdkr0d}n tdƒ‚||j|ƒ|jj|j|ƒ||Ž|j|ƒ|jj|j|ƒ||ŽS(Ntuithumpiÿÿÿÿsshape can only be `u` or `hump`(RŒR@RRxR%RRRŽ(RR$R]Rjtsignpdf((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR%ïs   .cOsh|jdkrM|jj|j|ƒ||Ž|jj|j|ƒ||ŽSd|j|||ŽSdS(NR”gð?(RŒRxRzRRŽt_sf(RR$R]Rj((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyRzüs cOsh|jdkrM|jj|j|ƒ||Ž|jj|j|ƒ||ŽSd|j|||ŽSdS(NR•gð?(RŒRxRzRRŽ(RR$R]Rj((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR—s cOs|j||ŒS(N(R(RR R]Rj((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR!s( R)R*R+RRR%RzR—R!(((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR‹±s *  t SquareFunccBs;eZdZd„Zd„Zd„Zd„Zd„ZRS(s³class to hold quadratic function with inverse function and derivative using instance methods instead of class methods, if we want extension to parameterized function cCs tj|ƒS(N(RR(RR$((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyt inverseplus scCsdtj|ƒS(Ng(RR(RR$((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyt inverseminus#scCsdtj|ƒS(Ngà?(RR(RR$((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR&scCsddtj|ƒS(Nggà?(RR(RR$((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR)scCstj|dƒS(Ni(Rtpower(RR$((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyt squarefunc,s(R)R*R+R™RšRRRœ(((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR˜s     RŒR”gRrt squarenormssquared normal distributions7 distribution of the square of a normal random variables y=x**2 with x N(0.0,1)ssquared t distributions2 distribution of the square of a t random variables y=x**2 with x t(dof,0.0,1)cCstj| ƒS(N(RR(R$((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR™?scCsdtj| ƒS(Ng(RR(R$((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyRšBscCsddtj| ƒS(Nggà?(RR(R$((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyREscCsdtj| ƒS(Ngà?(RR(R$((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyRHscCstj|dƒ S(Ni(RR›(R$((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyt negsquarefuncKsR•t negsquarenorms$negative squared normal distributions@ distribution of the negative square of a normal random variables y=-x**2 with x N(0.0,1)cCs|S(N((R$((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR™WscCsd|S(Ng((R$((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyRšZscCsdS(Ngð?((R$((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR]scCsdS(Nggð?gð¿((R$((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyR`scCs tj|ƒS(N(Rtabs(R$((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pytabsfunccstabsnormsabsolute of normal distributions? distribution of the absolute value of a normal random variables y=abs(x) with x N(0,1)s"normal completion with ERROR < EPSsscompletion with ERROR > EPS and MAXPTS function values used; increase MAXPTS to decrease ERROR;sN > 500 or N < 1c Ks$t|ƒ}tj|ƒ}tj|ƒ}tj|ƒ}tjt||ddƒƒ}|jdksx|jdkr‡tdƒ‚nt|ƒ|kr¨tdƒ‚n|dkrÌ|jdkrÌ|}np|jdkrt|ƒ||ddkr|}n:|j||fkr0|tj |dƒ}n tdƒ‚d|krh|dkrhd ||d>> print(mvstdnormcdf([-np.inf,-np.inf], [0.0,np.inf], 0.5)) 0.5 >>> corr = [[1.0, 0, 0.5],[0,1,0],[0.5,0,1]] >>> print(mvstdnormcdf([-np.inf,-np.inf,-100.0], [0.0,0.0,0.0], corr, abseps=1e-6)) 0.166666399198 >>> print(mvstdnormcdf([-np.inf,-np.inf,-100.0],[0.0,0.0,0.0],corr, abseps=1e-8)) something wrong completion with ERROR > EPS and MAXPTS function values used; increase MAXPTS to decrease ERROR; 1.048330348e-006 0.166666546218 >>> print(mvstdnormcdf([-np.inf,-np.inf,-100.0],[0.0,0.0,0.0], corr, maxpts=100000, abseps=1e-8)) 0.166666588293 ig@scan handle only 1D boundssbounds have different lengthsiiÿÿÿÿs corrcoef has incorrect dimensiontmaxptsi'issomething wrong(R?RtarraytzerostinttndimR@RRŒt tril_indicestisneginftisposinftonestputmaskRARtkdetmvntmvndstRDt informcode( tlowertuppertcorrcoefR^R tcorreltlowinftuppinftinfinterrortcdfvaluetinform((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyt mvstdnormcdfÅs:? ! -     -cKs½tj|ƒ}|dkr8tj|jƒ tj}ntj|ƒ}tj|ƒ}tjtj|ƒƒ}|||}|||}tj|ƒ}|||j }t ||||S(sDmultivariate normal cumulative distribution function This is a wrapper for scipy.stats.kde.mvn.mvndst which calculates a rectangular integral over a multivariate normal distribution. Parameters ---------- lower, upper : array_like, 1d lower and upper integration limits with length equal to the number of dimensions of the multivariate normal distribution. It can contain -np.inf or np.inf for open integration intervals mu : array_lik, 1d list or array of means cov : array_like, 2d specifies covariance matrix optional keyword parameters to influence integration * maxpts : int, maximum number of function values allowed. This parameter can be used to limit the time. A sensible strategy is to start with `maxpts` = 1000*N, and then increase `maxpts` if ERROR is too large. * abseps : float absolute error tolerance. * releps : float relative error tolerance. Returns ------- cdfvalue : float value of the integral Notes ----- This function normalizes the location and scale of the multivariate normal distribution and then uses `mvstdnormcdf` to call the integration. See Also -------- mvstdnormcdf : location and scale standardized multivariate normal cdf N( RR¤R5R«RŒRvRtdiagt atleast_2dtTR»(R²R;tcovR±R^tstdevtdivrowtcorr((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyt mvnormcdf:s( (gš™™™™™©?gš™™™™™¹?(g"@gð?(ER+t __future__RtnumpyRRRRRARRt scipy.statsRtstatsmodels.compat.pythonRRt statsmodels.stats.moment_helpersR R RR R0R,t skewnorm2R-R9RKRRRVRWRlRmR~RR€RR‚RƒRtTruet invdnormalgRˆt lognormalgtgammat loggammaexpgR†RŠR‹tobjectR˜tsqfuncRœR™RšRRRvt squarenormalgR3tsquaretgRžtnegsquarenormalgR¡R t absnormalgR°R»R5RÃ(((sGlib/python2.7/site-packages/statsmodels/sandbox/distributions/extras.pyt3sš  %   Z ( > Bc 2        !  Gi               U   u