M/Ph6@dZddlmZddlmZddlZdZGddejZ dZ d \Z Z d \Z Z d Z d Zd Ze eje eddddZe ejejejddddZe ejejejdZ GddejZGddejZdZ GddejZGdd ZeZeejejejejej ej!d!d"ej"dd#d$% Z#eej$ejejejej ej!d!d"ej"dd#d&% Z%d'Zd(Zd)Z d*Z!d+Z&eeje&eee e!d,ej" d"dd-d.% Z'd/Zd0Zd1Z d2Z!d3Z(eejej)eee e!d!d"ej"dd4d5% Z*dS)6a{ 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 )stats) distributionsNc rd|D}|dd}||fS)Ncni|]2\}}|d|ddd|3S)u_) startswithreplace).0kvs m/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/sandbox/distributions/transformed.py z$get_u_argskwargs...sN+++da||D))+ $A&&+++u_args)itemspop)kwargsu_kwargsrs rget_u_argskwargsr,sE++fllnn+++H \\(D ) )F 8 rc.eZdZdZfdZdZdZxZS) Transf_genzUa class for non-linear monotonic transformation of a continuous random variable c,||_||_|dd|_|dd}|dd}|dd}|dtj } |d tj} |d d |_td i|\|_|_ ||_ t | | ||j | dS)Nnumargsrname transfdistlongname#Non-linear transformed distributionextradocabdecrFr!r"rshapesr)funcfuncinvrrnpinfr#rrrklssuper__init__r%) selfr+r'r(argsrrrr r!r" __class__s rr-zTransf_gen.__init__9s  zz)Q// zz&,//::j*OPP::j$// JJsRVG $ $ JJsBF # #JJvu-- &6%?%?%?%?" T] 14 X      rc|js)|jj||g|Ri|Sd|jj||g|Ri|z SN?)r#r+_cdfr(r.xr/rs rr4zTransf_gen._cdfTspy I 48=aB4BBB6BB Bt||AHHHHHHH Hrc|js)||jj|g|Ri|S||jjd|z g|Ri|S)Nr )r#r'r+_ppf)r.qr/rs rr8zTransf_gen._ppf\sqy D99]TX]1>t>>>v>>?? ?99]TX]1q5B4BBB6BBCC Cr__name__ __module__ __qualname____doc__r-r4r8 __classcell__r0s@rrr4sj     6IIIDDDDDDDrrc,tjd|Sr2)r)divider6s rinverserDcs 9S!  r)g?g?)g"@r3c2ddtz|tzzz S)Nr3r muxstdxrCs rinversewrIks !c'AH$ %%rc2d|z dz tz tz Sr2rFrCs r inversew_invrKos !GcMC 4 ''rc|SNr&rCs ridentitrNs HrTdiscfznormal-based discount factor)r#rrrlnnormzExp transformed normal)rr!rrr )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}t||||_dSNrr rzLog transformed distributionr!rr!rrr,r-r+r.r+r/rrr!r0s rr-zExpTransf_gen.__init__s   !),DLLDL V  &>DD1D &==s AAA 14(((rcL|jjtj|g|RSrM)r+r4r)logr.r6r/s rr4zExpTransf_gen._cdf&tx}RVAYY.....rcLtj|jj|g|RSrM)r)expr+r8r.r9r/s rr8zExpTransf_gen._ppf(vmdhmA----...rr:r@s@rrTrTs`&//////////rrTc.eZdZdZfdZdZdZxZS) LogTransf_genrUcd|vr|d|_nd|_d|vr |d}nd}d|vr |d}nd}t||||_dSrWrYrZs rr-zLogTransf_gen.__init__s   !),DLLDL V  &>DD1D &==s AAA 14(((rcL|jjtj|g|RSrM)r+r4r)r`r]s rr4zLogTransf_gen._cdfr^rcLtj|jj|g|RSrM)r)r\r+r8ras rr8zLogTransf_gen._ppfrbrr:r@s@rrdrds`$//////////rrdctdttjdd}t|dttjddt|ttjdt|dtdttj}t| dd ttj dd t| d d ttj d d td ttj }t| d d ttj d d ttj }t| d d dS) NzResults for lognormalrzLog transformed normal generalrXr )sizezResults for expgamma rQzResults for loglaplace) printrTrnormcdflognormrvsrdgammar4loggammalaplace loglaplace) lognormalg loggammaexpg loglaplacegloglaplaceexpgs rexamples_transfrzs !"""uzQ5UVVVJ *..   %-  Aq ! !""" *     %-  a !!! *..a. !!! !!! --L ,  Ar " "### %.  Q # #$$$ ,  Ar " "### %.  Q # #$$$  "### ..K +  1b ! !""" %   q" % %&&&"5=11N .  a $ $%%%%%rc@eZdZdZfdZdZdZdZdZdZ xZ S) TransfTwo_genaODistribution based on a non-monotonic (u- or hump-shaped transformation) the constructor can be called with a distribution class, and functions that define the non-linear transformation. and generates the distribution of the transformed random variable Note: the transformation, it's inverse and derivatives need to be fully specified: func, funcinvplus, funcinvminus, derivplus, derivminus. Currently no numerical derivatives or inverse are calculated This can be used to generate distribution instances similar to the distributions in scipy.stats. cV||_||_||_||_||_|dd|_|dd} |dd} |dd} |dtj } |d tj} |d d |_ td i|\|_ |_ ||_ t| | | |j| dS)Nrrrrrrr r!r"shapeFr$r&)r' funcinvplus funcinvminus derivplus derivminusrrr)r*r~rrrr+r,r-r%)r.r+r'rrrrr/rrrr r!r"r0s rr-zTransfTwo_gen.__init__1s  &("$zz)Q// zz&,//::j*OPP::j$// JJsRVG $ $ JJsBF # #ZZ// &6%?%?%?%?" T] 14 X      rch|j|j_||jj|SrM)_sizer+r'_rvs)r.r/s rrzTransfTwo_gen._rvsPs*yy-...rc\|jdkrd}n|jdkrd}ntd||||jj||g|Ri|z|||jj||g|Ri|zz zS)Nur humpzshape can only be `u` or `hump`)r~ ValueErrorrr+_pdfrrr)r.r6r/rsignpdfs rrzTransfTwo_gen._pdfTs :  GG Z6 ! !GG>?? ?$..++mdhmDr-rrr4rrr?r@s@rr|r| s        >/// H H H666777'''''''rr|c0eZdZdZdZdZdZdZdZdS) SquareFunczclass to hold quadratic function with inverse function and derivative using instance methods instead of class methods, if we want extension to parametrized function c*tj|SrMr)sqrtr.r6s r inversepluszSquareFunc.inverseplusswqzzrc0dtj|z SNrrs r inverseminuszSquareFunc.inverseminusRWQZZrc0dtj|z SN?rrs rrzSquareFunc.derivplusrrc6ddtj|z z SNrrrrs rrzSquareFunc.derivminussS271::%%%rc,tj|dSNrQr)powerrs r squarefunczSquareFunc.squarefuncsx1~~rN) r;r<r=r>rrrrrr&rrrrsi       &&&rrrr squarenormzsquared normal distribution)r~r!r"rrrzsquared t distributionc,tj| SrMrrCs rrrs 7A2;;rc2dtj| z SrrrCs rrr ! rc8ddtj| z z SrrrCs rrrs rwr{{" ""rc2dtj| z SrrrCs rrrrrc.tj|d SrrrCs r negsquarefuncrs HQNN?rr negsquarenormz$negative squared normal distributionc|SrMr&rCs rrrrOrc d|z Srr&rCs rrrs 7NrcdSr2r&rCs rrrs 3rcdS)Ngr&rCs rrrs 9rc*tj|SrM)r)absrCs rabsfuncrs 6!99rabsnormzabsolute of normal distribution)+r>scipyr scipy.statsrnumpyr)r rv_continuousrrDrGrHrIrKrNrn invdnormalgr`r\rvrrrwrTrdrzr|rsqfuncrrrrrr* squarenormalgtsquaretgrnegsquarenormalgrr absnormalgr&rrrs##H%%%%%%,D,D,D,D,D,,D,D,D^  T  T&&&(((   jX|$!";Y Z BFBF !QX!9 z%+rvrvqAAA  / / / / /M/ / / /F/////M////D$&$&$&R >U'U'U'U'U'M/U'U'U'D.  ej&*;V=O$163CVEV$'3"&&'lEb    =&"3V5G,f.>@Q"cRV!"@X   ###!=]K!*JfSV)**P###   ]5:rv{L$jsbf#$9?` r