ó áp7]c@sldZddlmZddlmZddlmZddlmZddl Z d„Z dej fd „ƒYZ d „ZdH\ZZdI\ZZd„Zd„Zd„Ze ejeededdddddddƒZe eje je jddddddddddƒZe eje je jdd ƒZd!ej fd"„ƒYZd#ej fd$„ƒYZd%„Zd&ej fd'„ƒYZd(e fd)„ƒYZ!e!ƒZ"eeje"j#e"j$e"j%e"j&e"j'd*d+dd,d-e j(dddd.dd/dd0d1ƒZ)eej*e"j#e"j$e"j%e"j&e"j'd*d+dd,d-e j(dd dd.dd2dd3d4ƒZ+d5„Z$d6„Z%d7„Z&d8„Z'd9„Z,eeje,e$e%e&e'd*d:de j( d-d,dddd;dd<dd=d>ƒZ-d?„Z$d@„Z%dA„Z&dB„Z'dC„Z.eeje j/e$e%e&e'd*d+dd,d-e j(ddddDddEddFdGƒZ0dS(Js{ A class for the distribution of a non-linear monotonic transformation of a continuous random variable simplest usage: example: create log-gamma distribution, i.e. y = log(x), where x is gamma distributed (also available in scipy.stats) loggammaexpg = Transf_gen(stats.gamma, np.log, np.exp) example: what is the distribution of the discount factor y=1/(1+x) where interest rate x is normally distributed with N(mux,stdx**2)')? (just to come up with a story that implies a nice transformation) invnormalg = Transf_gen(stats.norm, inversew, inversew_inv, decr=True, a=-np.inf) This class does not work well for distributions with difficult shapes, e.g. 1/x where x is standard normal, because of the singularity and jump at zero. Note: I'm working from my version of scipy.stats.distribution. But this script runs under scipy 0.6.0 (checked with numpy: 1.2.0rc2 and python 2.4) This is not yet thoroughly tested, polished or optimized TODO: * numargs handling is not yet working properly, numargs needs to be specified (default = 0 or 1) * feeding args and kwargs to underlying distribution is untested and incomplete * distinguish args and kwargs for the transformed and the underlying distribution - currently all args and no kwargs are transmitted to underlying distribution - loc and scale only work for transformed, but not for underlying distribution - possible to separate args for transformation and underlying distribution parameters * add _rvs as method, will be faster in many cases Created on Tuesday, October 28, 2008, 12:40:37 PM Author: josef-pktd License: BSD iÿÿÿÿ(tprint_function(t iteritems(tstats(t distributionsNcKs8td„t|ƒDƒƒ}|jddƒ}||fS(Ncss?|]5\}}|jdƒr|jdddƒ|fVqdS(tu_tiN(t startswithtreplace(t.0tktv((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pys 3s tu_args(tdictRtpoptNone(tkwargstu_kwargsR ((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pytget_u_argskwargs1st Transf_gencBs)eZdZd„Zd„Zd„ZRS(sUa class for non-linear monotonic transformation of a continuous random variable c Osü||_||_|jddƒ|_|jddƒ}|jddƒ}|jddƒ}|jdtj ƒ} |jd tjƒ} |jd tƒ|_t |\|_ |_ ||_ t t|ƒjd| d | d|d |jd|d|ƒdS( Ntnumargsitnamet transfdisttlongnames#Non-linear transformed distributiontextradoctatbtdecrtshapes(tfunctfuncinvR RRtnptinftFalseRRR RtklstsuperRt__init__R( tselfR!RRtargsRRRRRR((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyR#<s   $ cOsO|js(|jj|j|ƒ||ŽSd|jj|j|ƒ||ŽSdS(Ngð?(RR!t_cdfR(R$txR%R((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyR&Ys cOsO|js(|j|jj|||ŽƒS|j|jjd|||ŽƒSdS(Ni(RRR!t_ppf(R$tqR%R((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyR(`s (t__name__t __module__t__doc__R#R&R((((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyR8s  cCstjd|ƒS(Ngð?(Rtdivide(R'((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pytinversegsgš™™™™™©?gš™™™™™¹?g"@gð?cCsddt|tS(Ngð?i(tmuxtstdx(R'((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pytinversewlscCsd|dttS(Ngð?(R/R0(R'((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyt inversew_invnscCs|S(N((R'((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pytidentitqsRRiRtdiscfRsnormal-based discount factorRsA distribution of discount factor y=1/(1+x)) with x N(0.05,0.1**2)iRtlnnormsExp 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|ƒjd|d|ƒ||_dS(NRiRsLog transformed distributionRi(RR"R6R#R!(R$R!R%RRR((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyR#s      cGs|jjtj|ƒ|ŒS(N(R!R&Rtlog(R$R'R%((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyR&¡scGstj|jj||ŒƒS(N(RtexpR!R((R$R)R%((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyR(¤s(R*R+R,R#R&R((((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyR6ˆs  t LogTransf_gencBs)eZdZd„Zd„Zd„ZRS(sµDistribution based on log/exp transformation the constructor can be called with a distribution class and generates the distribution of the transformed random variable cOsd|kr|d|_n d|_d|kr>|d}nd}d|kr]|d}nd}tt|ƒjd|d|ƒ||_dS(NRiRsLog transformed distributionRi(RR"R9R#R!(R$R!R%RRR((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyR#®s      cGs|jjtj|ƒ|ŒS(N(R!R&RR8(R$R'R%((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyR&ÀscGstj|jj||ŒƒS(N(RR7R!R((R$R)R%((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyR(Ãs(R*R+R,R#R&R((((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyR9§s  cCsutdƒttjddddƒ}t|jdƒƒttjjddƒƒt|jƒƒttjjdƒƒt|jddƒƒtd ƒttjƒ}t|j dd ƒƒttj jdd ƒƒt|j d d ƒƒttj jd d ƒƒtd ƒttj ƒ}t|j d d ƒƒttj jd d ƒƒttj ƒ}t|j d d ƒƒdS(NsResults for lognormalRiRsLog transformed normal generalitsizeisResults for expgammai iisResults for loglaplace( tprintR6RtnormtcdftlognormtrvsR9tgammaR&tloggammatlaplacet loglaplace(t lognormalgt loggammaexpgt loglaplacegtloglaplaceexpg((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pytexamples_transfÆs&   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. c Os||_||_||_||_||_|jddƒ|_|jddƒ} |jddƒ} |jddƒ} |jdtj ƒ} |jd tj ƒ} |jd t ƒ|_ t |\|_ |_||_tt|ƒjd| d | d| d |jd| d| ƒdS( NRiRRRs#Non-linear transformed distributionRRRtshapeR(Rt funcinvplust funcinvminust derivplust derivminusR RRRRR RJRR RR!R"RIR#R(R$R!RRKRLRMRNR%RRRRRR((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyR#'s&       cGs(|j|j_|j|jj|ŒƒS(N(t_sizeR!Rt_rvs(R$R%((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyRPIscOs˜|jdkrd}n$|jdkr0d}n tdƒ‚||j|ƒ|jj|j|ƒ||Ž|j|ƒ|jj|j|ƒ||ŽS(Ntuithumpiÿÿÿÿsshape can only be `u` or `hump`(RJt ValueErrorRMR!t_pdfRKRNRL(R$R'R%Rtsignpdf((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyRTMs   .cOsh|jdkrM|jj|j|ƒ||Ž|jj|j|ƒ||ŽSd|j|||ŽSdS(NRQgð?(RJR!R&RKRLt_sf(R$R'R%R((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyR&Zs cOsh|jdkrM|jj|j|ƒ||Ž|jj|j|ƒ||ŽSd|j|||ŽSdS(NRRgð?(RJR!R&RKRL(R$R'R%R((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyRVcs cOs|j||ŒS(N(t_mom0_sc(R$tnR%R((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyt_munpls( R*R+R,R#RPRTR&RVRY(((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyRIs "  t SquareFunccBs;eZdZd„Zd„Zd„Zd„Zd„ZRS(s³class to hold quadratic function with inverse function and derivative using instance methods instead of class methods, if we want extension to parameterized function cCs tj|ƒS(N(Rtsqrt(R$R'((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyt inverseplus~scCsdtj|ƒS(Ng(RR[(R$R'((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyt inverseminusscCsdtj|ƒS(Ngà?(RR[(R$R'((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyRM„scCsddtj|ƒS(Nggà?(RR[(R$R'((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyRN‡scCstj|dƒS(Ni(Rtpower(R$R'((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyt squarefuncŠs(R*R+R,R\R]RMRNR_(((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyRZxs     RJRQgRt 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'((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyR\scCsdtj| ƒS(Ng(RR[(R'((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyR] scCsddtj| ƒS(Nggà?(RR[(R'((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyRM£scCsdtj| ƒS(Ngà?(RR[(R'((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyRN¦scCstj|dƒ S(Ni(RR^(R'((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyt negsquarefunc©sRRt 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'((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyR\´scCsd|S(Ng((R'((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyR]·scCsdS(Ngð?((R'((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyRMºscCsdS(Nggð?gð¿((R'((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyRN½scCs tj|ƒS(N(Rtabs(R'((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pytabsfuncÀstabsnormsabsolute of normal distributions? distribution of the absolute value of a normal random variables y=abs(x) with x N(0,1)(gš™™™™™©?gš™™™™™¹?(g"@gð?(1R,t __future__Rtstatsmodels.compat.pythonRtscipyRt scipy.statsRtnumpyRRt rv_continuousRR.R/R0R1R2R3R<tTruet invdnormalgR8R7RDR@RER6R9RHRItobjectRZtsqfuncR_R\R]RMRNRt squarenormalgtttsquaretgRatnegsquarenormalgRdRct absnormalg(((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/transformed.pyt(sv  /        !  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