B Z@sdZddlmZddlZddlmZddZddd Zd d Z d d Z ddZ ddZ ddZ ddZddZd ddZddZddZdS)!zhelper functions conversion between moments contains: * conversion between central and non-central moments, skew, kurtosis and cummulants * cov2corr : convert covariance matrix to correlation matrix Author: Josef Perktold License: BSD-3 )rangeN)combc Cst|}|d}dgt|}d|d<d|g}xrt|ddD]^\}}|d}|dxBt|dD]2}||t||dd|||||7<qhWq@W|ddS)zwconvert central to non-central moments, uses recursive formula optionally adjusts first moment to return mean rN)exact)lenlist enumerateappendrr)mcnmeanmncnnmkr?lib/python3.7/site-packages/statsmodels/stats/moment_helpers.pymc2mncs 6rTc Cst|}|d}dgt|}g}xnt|D]b\}}|dxNt|dD]>}||d||t||dd|||||7<qLWq,W|r||d<|ddS)zwconvert non-central to central moments, uses recursive formula optionally adjusts first moment to return mean rr)rN)rrr r rr)rZwmeanr r murrrrrmnc2mc)s Brc Csddg}|d}dgt|}xvt|ddD]b\}}|d}|dxFt|dD]6}||t|d|dd|||||7<qXWq0W||d<|ddS)aconvert non-central moments to cumulants recursive formula produces as many cumulants as moments References ---------- Kenneth Lange: Numerical Analysis for Statisticians, page 40 (http://books.google.ca/books?id=gm7kwttyRT0C&pg=PA40&lpg=PA40&dq=convert+cumulants+to+moments&source=web&ots=qyIaY6oaWH&sig=cShTDWl-YrWAzV7NlcMTRQV6y0A&hl=en&sa=X&oi=book_result&resnum=1&ct=result) rgrrN)r)rr r rr)kappar Zkappa0rrr rrrrcum2mc<s  :rc Csdgt|}dg}xxt|ddD]d\}}|d}||xHtd|D]:}||t|d|ddd|||||8<qLWq&W|ddS)zconvert non-central moments to cumulants recursive formula produces as many cumulants as moments http://en.wikipedia.org/wiki/Cumulant#Cumulants_and_moments rN)r)rr r rr)rrrrr rrrrmnc2cumTs >rcCs tt|S)z4just chained because I have still the test case )rr)r rrrmc2cumesrcCsR|\}}}}dgd}||d<||d<||d|d<|d|d|d <t|S) z9convert mean, variance, skew, kurtosis to central momentsNrrg?rg@g@)tuple)argsrZsig2ZskZkurZcntrrrmvsk2mcks  r c Cs|\}}}}|}|||}||d}|d|||d}|d|d} | d||d||||d} |||| fS)z=convert mean, variance, skew, kurtosis to non-central momentsg?rg@g@rr) rr mc2skewkurtrmnc2mc3mnc3mc4mnc4rrrmvsk2mncws   (r*cCs<|\}}}}t||d}t||dd}||||fS)z>convert central moments to mean, variance, skew, kurtosis g?g@g@)npZdivide)rr r"r&r(r#r$rrrmc2mvsks r,c Csl|\}}}}|}|||}|d|||d}|d||d||||d}t||||fS)z>convert central moments to mean, variance, skew, kurtosis rrr!)r,) rrr%r'r)r r"r&r(rrrmnc2mvsks   (r-FcCs>t|}tt|}|t||}|r6||fS|SdS)a+convert covariance matrix to correlation matrix Parameters ---------- cov : array_like, 2d covariance matrix, see Notes Returns ------- corr : ndarray (subclass) correlation matrix return_std : bool If this is true then the standard deviation is also returned. By default only the correlation matrix is returned. Notes ----- This function does not convert subclasses of ndarrays. This requires that division is defined elementwise. np.ma.array and np.matrix are allowed. N)r+ asanyarraysqrtdiagouter)covZ return_stdstd_corrrrrcov2corrs  r5cCs(t|}t|}|t||}|S)aconvert correlation matrix to covariance matrix given standard deviation Parameters ---------- corr : array_like, 2d correlation matrix, see Notes std : array_like, 1d standard deviation Returns ------- cov : ndarray (subclass) covariance matrix Notes ----- This function does not convert subclasses of ndarrays. This requires that multiplication is defined elementwise. np.ma.array are allowed, but not matrices. )r+r.r1)r4Zstdr3r2rrrcorr2covs  r6cCstt|S)aget standard deviation from covariance matrix just a shorthand function np.sqrt(np.diag(cov)) Parameters ---------- cov : array_like, square covariance matrix Returns ------- std : ndarray standard deviation from diagonal of cov )r+r/r0)r2rrrse_covsr7)T)F)__doc__Zstatsmodels.compat.pythonrZnumpyr+Z scipy.miscrrrrrrr r*r,r-r5r6r7rrrr s