M/Ph@dZddlZddlmZmZmZddlZddlmZmZddl m Z ddl m Z m Z  ddlmZn#e$r ddlmZYnwxYwGdd e jZeZGd d e jZed d ZGdde jZdZdZdZdZGdde jZ dZGdde jZdZd\Z Z!d\Z Z!dZ"dZ#dZ$eej%e"e#d dd!d"d#$Z&eej%ejej'd%dd&d'(Z(eej)ej'ejd)*Z* Gd+d,e jZ+Gd-d.e jZ, Gd/d0e jZ-Gd1d2Z.e.Z/e-ej%e/j0e/j1e/j2e/j3e/j4d3d4ej5dd5d67 Z6e-ej7e/j0e/j1e/j2e/j3e/j4d3d4ej5d)d5d87 Z8d9Z1d:Z2d;Z3d<Z4d=Z9e-ej%e9e1e2e3e4d>ej5 d4dd?d@7 Z:dAZ1dBZ2dCZ3dDZ4dEZ;e-ej%ej<e1e2e3e4d3d4ej5ddFdG7 Z= dHdIdJdKZ>dLZ?dNdMZ@dS)OaVarious 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 do not remember * add Box-Cox transformation, parametrized ? 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 N)poly1dsqrtexp)statsspecial) distributions)mvsk2mcmc2mvsk)mvndstc8eZdZdZdZdZdZdZdZd dZ d S) SkewNorm_genzunivariate Skew-Normal distribution of Azzalini class follows scipy.stats.distributions pattern but with __init__ cJtj|dddS)NSkew Normal distributionalphanameshapesr rv_continuous__init__selfs h/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/sandbox/distributions/extras.pyrzSkewNorm_gen.__init__Rs5#,, + -     cdSNrrs r _argcheckzSkewNorm_gen._argcheckZqrcH|tjd|dzzz }tj|j}||ztjd|dzz tj|jzz}tj|dk|| S)Nrsizer)nprrnormrvs_sizewhere)rrdeltau0u1s r_rvszSkewNorm_gen._rvs]sEQJ/// Z^^^ , , RZ"'!eqj.11EJNN N4S4SS SxQRC(((rc.|||SN_mom0_sc)rnrs r_munpzSkewNorm_gen._munpds}}Q&&&rcdtjdtjzz tj|dz dz zt j||zzSN@r#r&rpirrndtrrxrs r_pdfzSkewNorm_gen._pdfiJRWQY'''"&!q&3*?*??',uWXyBYBYYYrmvskcdSr0r)rr<rmomentss r _stats_skipzSkewNorm_gen._stats_skipms rNr?) __name__ __module__ __qualname____doc__rr r.r4r=rBrrrr r Is   )))''' ZZZ      rr ceZdZdZdZdZdS) SkewNorm2_genzjunivariate Skew-Normal distribution of Azzalini class follows scipy.stats.distributions pattern cdSrrrs rr zSkewNorm2_gen._argcheck}r!rcdtjdtjzz tj|dz dz zt j||zzSr6r8r;s rr=zSkewNorm2_gen._pdfr>rN)rDrErFrGr r=rrrrIrIvsA ZZZZZrrIrrrc0eZdZdZdZdZdZdZdZdS) ACSkewT_genzzunivariate Skew-T distribution of Azzalini class follows scipy.stats.distributions pattern but with __init__ cJtj|dddS)NzSkew T distributionz df, alpharrrs rrzACSkewT_gen.__init__s5#,, & -     rc||k|dkzS)Nrr)rdfrs rr zACSkewT_gen._argchecks26**rctj||j}t||j}|t j||z z S)Nr$)rchi2r(r)skewnormr&r)rrPrVzs rr.zACSkewT_gen._rvssK JNN2DJN / / LLTZL 0 0271r6??""rc0||||Sr0r1)rr3rPrs rr4zACSkewT_gen._munps}}QE***rc dtj||ztj|dz||zt jd|z|dz|zz zzS)Nr7rr#)rtr=rstdtrr&r)rr<rPrs rr=zACSkewT_gen._pdfsm]_))!R0007=aQRUWU\ VQ $V&V&J&4'4'' 'rN) rDrErFrGrr r.r4r=rrrrMrMsi    0+++###+++ '''''rrMcdg|z}td|d<td|D]@}||dz tddg||dz zz ||<A|S)Nrr)rrangederiv)Nplistr3s r _hermnormr_sw FQJEayyE!H 1a[[HHQ<%%''&!Q..5Q<*GGa Lrc t|}|dkrtdtd t|d |d |dkrt |dz}t d|dzD]~}d}t |dz dz D]^}|d|zz }|dzr ||dz }n)||dz  zt j|dz zz }|||| |zz |zz }_t fd}| fS)zReturn the Gaussian expanded pdf function given the list of central moments (first one is mean). version of scipy.stats, any changes ? the scipy.stats version has a bug and returns normal distribution r#:At least two moments must be given to approximate the pdf.rrc|z z }|t| |zdz ztdtjzz z Sr6)rrr&r9r<xnmusigtotps rthisfuncz pdf_moments_st..thisfuncsK"f^tBxx#rcBhn---QY?#EEr) len ValueErrorrrr_r[scipy factorial2 SystemErrorprint) cntr]DvalskCkr3mmomdiffrjrgrhris @@@rpdf_moments_strwsa CA1uu011 1 !99D s1v,,C QB1uu!a%   1a!e__$$ A{## 3 3AAE A1u Ka!e*a!e*sSy53CAE3J3J'JJ %(1+q(72 2BB FFFFFFF T>rc$ t|}|dkrtd|\ }}}td t| |dkr6t |dz}|dz }|dz } ||dzz ||dzz fd}|S) a;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 ---------- https://en.wikipedia.org/wiki/Edgeworth_series Johnson N.L., S. Kotz, N. Balakrishnan: Continuous Univariate Distributions, Volume 1, 2nd ed., p.30 z2Four moments must be given to approximate the pdf.rr#@8@rbc|z z }|tj| |zdz ztjdtjzz z Sr6r&rrr9res rpdffunczpdf_mvsk..pdffuncYQ"f^tBxx"&"rC000271ru93E3EEKKrrkrlrrr_) r?r]mc2skewkurtrrC3C4r~rgrhris @@@rpdf_mvskr sP D A1uu011 1BT4 !99D s))C1uu!a%   CZ D[b58m#b58m3LLLLLLL Nrcf t|}|dkrtd|\}}}}||dzz }||dzz dz }tdt|d |d |dkr6t |dz}|dz } |d z } | |d zz | |d zz fd } | S) aReturn 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 ---------- https://en.wikipedia.org/wiki/Edgeworth_series Johnson N.L., S. Kotz, N. Balakrishnan: Continuous Univariate Distributions, Volume 1, 2nd ed., p.30 r#rag?r7g@rrrzr{rbryc|z z }|tj| |zdz ztjdtjzz z Sr6r}res rrjzpdf_moments..thisfuncrrr)rqr]mcrmc3mc4rrrrrrrjrgrhris @@@r pdf_momentsr`s4 CA1uu011 1BS#  D  c !D !99D s1v,,C QB1uu!a%   CZ D[b58m#b58m3LLLLLLL Orc$eZdZdZdZdZdZdS) NormExpan_genzGram-Charlier Expansion of Normal distribution class follows scipy.stats.distributions pattern but with __init__ c tj|dd|dd}|dkr@t j|dd\}}}}||||f|_t||||f}nI|dkrt|}||_n,|dkr|}t||_ntd ||_ t|j|_ dS) NzNormal Expansion distribution rmodesampler#r?centmomzmode must be 'mvsk' or centmom) rrrgetrdescriber?r r rlrqrr=) rargskwdsrrgrhskkurrqs rrzNormExpan_gen.__init__s#,, 0 -   .xx)) 8  $~d33ABB7 BRS"c*DI2sB,--CC V^^$--CDII Y  C DII=>> >TY'' rc,||Sr0r1)rr3s rr4zNormExpan_gen._munps}}Qrc|jSr0rCrs rrBzNormExpan_gen._stats_skips yrN)rDrErFrGrr4rBrrrrrsL+(+(+(Z   rrc rd|D}|dd}||fS)Ncni|]2\}}|d|ddd|3S)u_r) startswithreplace).0rsvs r z$get_u_argskwargs.. sN+++da||D))+ $A&&+++ru_args)itemspop)kwargsu_kwargsrs rget_u_argskwargsr sE++fllnn+++H \\(D ) )F 8 rc4eZdZdZfdZdZdZdZxZS) Transf_genzUa class for non-linear monotonic transformation of a continuous random variable c ||_||_|dd|_|dd}|dd}|dd}|dtj } |d tj} |d d |_td i|\|_|_ ||_ t | | || dS)Nnumargsrr transfdistlongname#Non-linear transformed distributionextradocabdecrF)rrrrr) funcfuncinvrrr&infrrrrklssuperr) rrrrrrrrrrr __class__s rrzTransf_gen.__init__s  zz)Q// zz&,//::j*OPP::j$// JJsRVG $ $ JJsBF # #JJvu-- &6%?%?%?%?" T] 1x@@@@@rch|j|j_||jj|Sr0)r)rrr.)rrrs rr.zTransf_gen._rvs0s*||MDHM40111rc|js)|jj||g|Ri|Sd|jj||g|Ri|z SN?)rr_cdfrrr<rrs rrzTransf_gen._cdf4spy I 48=aB4BBB6BB Bt||AHHHHHHH Hrc|js)||jj|g|Ri|S||jjd|z g|Ri|Sr)rrr_ppf)rqrrs rrzTransf_gen._ppf<sqy D99]TX]1>t>>>v>>?? ?99]TX]1q5B4BBB6BBCC Cr) rDrErFrGrr.rr __classcell__rs@rrrs~AAAAA4222IIIDDDDDDDrrc,tjd|Sr)r&divider<s rinverserCs 9S!  r)g?g?)g"@rc2ddtz|tzzz S)Nrrmuxstdxrs rinversewrKs !c'AH$ %%rc2d|z dz tz tz Srrrs r inversew_invrOs !GcMC 4 ''rc|Sr0rrs ridentitrS HrTdiscfznormal-based discount factorzA distribution of discount factor y=1/(1+x)) with x N(0.05,0.1**2))rrrrrr#lnnormzExp transformed normal)rrrrr)rc.eZdZdZfdZdZdZxZS) ExpTransf_genDistribution based on log/exp transformation the constructor can be called with a distribution class and generates the distribution of the transformed random variable cd|vr|d|_nd|_d|vr |d}nd}d|vr |d}nd}td|||_dSNrrrzLog transformed distributionrr)rrrrrrrrrrrrrs rrzExpTransf_gen.__init__ts   !),DLLDL V  &>DD1D &==s AAA 14(((rcN |jjtj|g|RSr0)rcdfr&logrr<rs rrzExpTransf_gen._cdfs) tx|BF1II-----rcLtj|jj|g|RSr0)r&rrppfrrrs rrzExpTransf_gen._ppfs(vldhl1,t,,,---rrDrErFrGrrrrrs@rrrls`&... .......rrc.eZdZdZfdZdZdZxZS) LogTransf_genrcd|vr|d|_nd|_d|vr |d}nd}d|vr |d}nd}t||||_dSrrrs rrzLogTransf_gen.__init__s   !),DLLDL V  &>DD1D &==s AAA 14(((rcL|jjtj|g|RSr0)rrr&rrs rrzLogTransf_gen._cdfs&tx}RVAYY.....rcLtj|jj|g|RSr0)r&rrrrs rrzLogTransf_gen._ppfs(vmdhmA----...rrrs@rrrs`$//////////rrc@eZdZdZfdZdZdZdZdZdZ xZ S) TransfTwo_genaODistribution 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. c ||_||_||_||_||_|dd|_|dd} |dd} |dd} |dtj } |d tj} |d d |_ tdi|\|_ |_ ||_ t| | | |j| |jt'|||||||j dS)NrrrrrrrrrshapeF)rrrrr)rr funcinvplus funcinvminus derivplus derivminusrr)rrrrrrrr&rrrrrrrrr _ctor_paramupdatedict)rrrrrrrrrrrrrrrs rrzTransfTwo_gen.__init__s\  &("$zz)Q// zz&,//::j*OPP::j$// JJsRVG $ $ JJsBF # #ZZ// &6%?%?%?%?" T] 14 X     St*i&dj : : :     rch|j|j_||jj|Sr0)r)rrr.)rrs rr.zTransfTwo_gen._rvss*yy-...rc\|jdkrd}n|jdkrd}ntd||||jj||g|Ri|z|||jj||g|Ri|zz zS)Nurhumpzshape can only be `u` or `hump`)rrlrrr=rrr)rr<rrsignpdfs rr=zTransfTwo_gen._pdfs :  GG Z6 ! !GG>?? ?$..++mdhmDz'TransfTwo_gen._munp..5s 000C 3000r)r&rr2isscalarfloat)rr3rrouts rr4zTransfTwo_gen._munp4s[004000jq0400011 ;s   ::  r) rDrErFrGrr.r=rrr4rrs@rrrs   $ $ $ $ $ L/// H H H666777rrc0eZdZdZdZdZdZdZdZdS) SquareFunczclass to hold quadratic function with inverse function and derivative using instance methods instead of class methods, if we want extension to parametrized function c*tj|Sr0r&rrr<s r inversepluszSquareFunc.inverseplusMswqzzrc0dtj|z SNrcr r s r inverseminuszSquareFunc.inverseminusPRWQZZrc0dtj|z SN?r r s rrzSquareFunc.derivplusSrrc6ddtj|z z SNrcrr r s rrzSquareFunc.derivminusVsS271::%%%rc,tj|dSNr#r&powerr s r squarefunczSquareFunc.squarefuncYsx1~~rN) rDrErFrGr rrrrrrrrrFsi       &&&rrrrc squarenormzsquared normal distribution)rrrrrrzsquared t distributionc,tj| Sr0r rs rr r ps 7A2;;rc2dtj| z Srr rs rrrt ! rc8ddtj| z z Srr rs rrrxs rwr{{" ""rc2dtj| z Srr rs rrr|rrc.tj|d Srrrs r negsquarefuncr"s HQNN?rr negsquarenormz$negative squared normal distributionc|Sr0rrs rr r rrc d|z Srrrs rrrs 7NrcdSrrrs rrrs 3rcdS)Ngrrs rrrs 9rc*tj|Sr0)r&absrs rabsfuncr*s 6!99rabsnormzabsolute of normal distributionz"normal completion with ERROR < EPSzscompletion with ERROR > EPS and MAXPTS function values used; increase MAXPTS to decrease ERROR;zN > 500 or N < 1)rrr#c t|}tj|}tj|}tj|}tjt ||dz zdz }|jdks |jdkrt dt||krt d|dkr|jdkr|}nb|jdkrt|||dz zdz kr|}n8|j||fkr|tj |d}nt dd|vr|dkrd |z|d<tj |}tj |}dtj |z}tj ||d tj ||dtj |||zdt||||fi|\} } } | rtd t | | | S) a standardized multivariate normal cumulative distribution function This is a wrapper for scipy.stats._mvn.mvndst which calculates a rectangular integral over a standardized multivariate normal distribution. This function assumes standardized scale, that is the variance in each dimension is one, but correlation can be arbitrary, covariance = correlation matrix 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 corrcoef : float or array_like specifies correlation matrix in one of three ways, see notes 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 ----- The correlation matrix corrcoef can be given in 3 different ways If the multivariate normal is two-dimensional than only the correlation coefficient needs to be provided. For general dimension the correlation matrix can be provided either as a one-dimensional array of the upper triangular correlation coefficients stacked by rows, or as full square correlation matrix See Also -------- mvnormcdf : cdf of multivariate normal distribution without standardization Examples -------- >>> 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 rr7zcan handle only 1D boundszbounds have different lengthsr#rz corrcoef has incorrect dimensionmaxptsi'rzsomething wrong)rkr&arrayzerosintndimrlr%r tril_indicesisneginfisposinfonesputmaskr rp informcode) loweruppercorrcoefrr3correllowinfuppinfinfinerrorcdfvalueinforms r mvstdnormcdfrBs~ E A HUOOE HUOOEx!!H Xc!q1u++,, - -F aUZ1__4555 5zzQ8999Avv(-1$$ !  H a!es1B B B Aq6 ! !"/!R001 ;<<<t q55"QYDN [  F [  F "'!** EJufa   Jufa   Jufvor***%UE5&IIDIIE8V < F!3U;;; Orc tj|}|(tj|j tjz}ntj|}tj|}tjtj|}||z |z }||z |z }tj|}||z |jz }t|||fi|S)aAmultivariate normal cumulative distribution function This is a wrapper for scipy.stats._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 ) r&r.r5rrrdiag atleast_2dTrB)r9rgcovr8rstdevdivrowcorrs r mvnormcdfrKusP HUOOE }%%%. (3--C GBGCLL ! !ERZ5 E RZ5 E ]5 ! !F <&( "D ud 3 3d 3 33rr0)ArGnumpyr&rrrrmrr scipy.statsr statsmodels.stats.moment_helpersr r scipy.stats._mvnr ImportErrorscipy.stats.mvnrr rSrI skewnorm2rMr_rwrrrrrrrrrrrr' invdnormalgr lognormalggamma loggammaexpgrrrrsqfuncrr rrrr squarenormalgrXsquaretgr"negsquarenormalgr*r) absnormalgr7rBrKrrrr\s22h########## %%%%%%========''''''''''''&&&&&&&'& & & & & =.& & & R <>> Z Z Z Z ZM/ Z Z Z M9'    6'6'6'6'6'--6'6'6'@   &&&R===@???D<<<<<M/<<<B#L/D/D/D/D/D,/D/D/Dd  T  T&&&(((   jX|$!";Y"fhhh Z BFBF !QX!9 z%+rvrvqAAA  !.!.!.!.!.M/!.!.!.H/////M////H >`````M/```Z.  ej&*;V=O$163CVEV$'3"&&'lEb    =&"3V5G,f.>@Q"cRV!"@X   ###!=]K!*JfSV)**P###   ]5:rv{L$jsbf#$9?` M^6:#%% rrrj747474747474s3 AA