U Kv fB@sdZddlmZddlmZddlZddZGdddejZ d d Z d \Z Z d \Z Z d dZ ddZddZe eje edddddZe ejejejdddddZe ejejejddZGdddejZGdd d ejZd!d"ZGd#d$d$ejZGd%d&d&ZeZeejejejejej ej!d'd(ej"dd)d*d+ Z#eej$ejejejej ej!d'd(ej"dd)d,d+ Z%d-d.Zd/d0Zd1d2Z d3d4Z!d5d6Z&eeje&eee e!d7ej" d(dd8d9d+ Z'd:d.Zd;d0Zdd?Z(eejej)eee e!d'd(ej"dd@dAd+ Z*dS)Ba{ 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) distributionsNcKs*tdd|D}|dd}||fS)Ncss.|]&\}}|dr|ddd|fVqdS)Zu_N) startswithreplace).0kvr Q/tmp/pip-unpacked-wheel-2v6byqio/statsmodels/sandbox/distributions/transformed.py .s z#get_u_argskwargs..u_args)dictitemspop)kwargsu_kwargsrr r r get_u_argskwargs,s rcs0eZdZdZfddZddZddZZS) Transf_genzUa class for non-linear monotonic transformation of a continuous random variable c s||_||_|dd|_|dd}|dd}|dd}|dtj } |d tj} |d d |_tf|\|_|_ ||_ t t |j | | ||j|d dS) Nnumargsrname transfdistlongname#Non-linear transformed distributionextradocabdecrFrrrshapesr)funcfuncinvrrnpinfrrrrklssuperr__init__r ) selfr%r!r"argsrrrrrr __class__r r r'9s   zTransf_gen.__init__cOsB|js |jj||f||Sd|jj||f||SdSN?)rr%_cdfr"r(xr)rr r r r.VszTransf_gen._cdfcOsB|js ||jj|f||S||jjd|f||SdS)Nr)rr!r%_ppf)r(qr)rr r r r1^szTransf_gen._ppf__name__ __module__ __qualname____doc__r'r.r1 __classcell__r r r*r r4s rcCs td|Sr,)r#divider0r r r inverseesr;)g?g?)g"@r-cCsddt|tS)Nr-rmuxstdxr:r r r inversewmsr?cCsd|dttSr,r<r:r r r inversew_invqsr@cCs|SNr r:r r r identitusrBTZdiscfznormal-based discount factor)rrrrZlnnormzExp transformed normal)rrrrr)rcs0eZdZdZfddZddZddZZS) 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 csdd|kr|d|_nd|_d|kr,|d}nd}d|krB|d}nd}tt|j||d||_dSNrrrzLog transformed distributionrrrr)rr&rDr'r%r(r%r)rrrr*r r r's   zExpTransf_gen.__init__cGs|jjt|f|SrA)r%r.r#logr(r0r)r r r r.szExpTransf_gen._cdfcGst|jj|f|SrA)r#expr%r1r(r2r)r r r r1szExpTransf_gen._ppfr3r r r*r rDs rDcs0eZdZdZfddZddZddZZS) LogTransf_genrEcsdd|kr|d|_nd|_d|kr,|d}nd}d|krB|d}nd}tt|j||d||_dSrF)rr&rMr'r%rHr*r r r's   zLogTransf_gen.__init__cGs|jjt|f|SrA)r%r.r#rKrJr r r r.szLogTransf_gen._cdfcGst|jj|f|SrA)r#rIr%r1rLr r r r1szLogTransf_gen._ppfr3r r r*r rMs rMcCs tdttjddd}t|dttjddt|ttjdt|jddtdttj}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 generalrGr)sizezResults for expgamma rCzResults for loglaplace) printrDrnormZcdfZlognormZrvsrMgammar.ZloggammaZlaplaceZ loglaplace) lognormalg loggammaexpgZ loglaplacegZloglaplaceexpgr r r examples_transfs&    rWcsHeZdZdZfddZddZddZdd Zd d Zd d Z Z 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. cs||_||_||_||_||_|dd|_|dd} |dd} |dd} |dtj } |d tj} |d d |_ t f|\|_ |_ ||_ tt|j| | | |j| d dS) NrrrrrrrrrshapeFr)r! funcinvplus funcinvminus derivplus derivminusrrr#r$rYrrrr%r&rXr'r )r(r%r!rZr[r\r]r)rrrrrrr*r r r'3s&   zTransfTwo_gen.__init__cGs|j|j_||jj|SrA)_sizer%r!_rvs)r(r)r r r r_Us zTransfTwo_gen._rvscOst|jdkrd}n|jdkr d}ntd||||jj||f|||||jj||f||S)Nurhumpzshape can only be `u` or `hump`)rY ValueErrorr\r%_pdfrZr]r[)r(r0r)rZsignpdfr r r rdYs  $zTransfTwo_gen._pdfcOsX|jdkr>|jj||f|||jj||f||Sd|j|f||SdS)Nr`r-)rYr%r.rZr[_sfr/r r r r.gs  zTransfTwo_gen._cdfcOsX|jdkr>|jj||f|||jj||f||Sd|j|f||SdS)Nrar-)rYr%r.rZr[r/r r r reps  zTransfTwo_gen._sfcOs|j|f|SrA)Z_mom0_sc)r(nr)rr r r _munpyszTransfTwo_gen._munp) r4r5r6r7r'r_rdr.rergr8r r r*r rX"s "  rXc@s8eZdZdZddZddZddZdd Zd d Zd S) SquareFunczclass to hold quadratic function with inverse function and derivative using instance methods instead of class methods, if we want extension to parametrized function cCs t|SrAr#sqrtr(r0r r r inverseplusszSquareFunc.inversepluscCsdt|SNrirkr r r inverseminusszSquareFunc.inverseminuscCsdt|SN?rirkr r r r\szSquareFunc.derivpluscCsddt|SNrnrqrirkr r r r]szSquareFunc.derivminuscCs t|dSNrCr#powerrkr r r squarefuncszSquareFunc.squarefuncN) r4r5r6r7rlror\r]rvr r r r rhs rhr`rnZ squarenormzsquared normal distribution)rYrrrrrzsquared t distributioncCs t| SrArir:r r r rlsrlcCsdt| Srmrir:r r r rosrocCsddt| Srrrir:r r r r\sr\cCsdt| Srprir:r r r r]sr]cCst|d Srsrtr:r r r negsquarefuncsrwraZ negsquarenormz$negative squared normal distributioncCs|SrAr r:r r r rlscCsd|Srmr r:r r r roscCsdSr,r r:r r r r\scCsdS)Ngr r:r r r r]scCs t|SrA)r#absr:r r r absfuncsryZabsnormzabsolute of normal distribution)+r7ZscipyrZ scipy.statsrZnumpyr#rZ rv_continuousrr;r=r>r?r@rBrSZ invdnormalgrKrIrUrTrVrDrMrWrXrhZsqfuncrvrlror\r]r$Z squarenormalgtZsquaretgrwZnegsquarenormalgryrxZ absnormalgr r r r s$  1  #"Ne