U md$@sdZddlZddlmZddlmZmZGdddZGdddeZ e Z Gd d d eZ e Z Gd d d eZ e ZGd ddeZeZGdddeZeZGdddeZeZdS)z Pickand's dependence functions as generators for EV-copulas Created on Wed Jan 27 14:33:40 2021 Author: Josef Perktold License: BSD-3 N)stats)_approx_fprime_cs_scalar approx_hessc@s,eZdZddZddZddZddZd S) PickandDependencecOs |j||SN)evaluate)selfargskwargsr d/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/statsmodels/distributions/copula/depfunc_ev.py__call__szPickandDependence.__call__cGstdSr)NotImplementedErrorrtr r r r rszPickandDependence.evaluatecGst|}t||jS)zkFirst derivative of the dependence function implemented through numerical differentiation )npZ atleast_1drrrr r r derivs zPickandDependence.derivcsDt|dkr&t|gjdd}ntfdd|D}|S)zlSecond derivative of the dependence function implemented through numerical differentiation r rcs"g|]}t|gjddqS)r)rr)rr).0tir rr r )sz,PickandDependence.deriv2..)rsizerrarray)rrr d2r rr deriv2!s zPickandDependence.deriv2N)__name__ __module__ __qualname__r rrrr r r r rsrc@s4eZdZdZdZddZddZddZd d Zd S) AsymLogisticzasymmetric logistic model of Tawn 1988 special case: a1=a2=1 : Gumbel restrictions: - theta in (0,1] - a1, a2 in [0,1] cCs<|dko|dk}|dko|dk}|dko.|dk}|o:|o:|SNrrr ra1a2thetacondthZconda1Zconda2r r r _check_args9szAsymLogistic._check_argscCsPd|d|}|d||7}|||d||d|d||7}|S)Nr?r rrr$r%r&transfr r r r?s,zAsymLogistic.evaluatecCsp|}|||d|d||d|d|d||d||d|d||d||}|SNrr )rrr$r%r&bd1r r r rJs2*zAsymLogistic.derivcCsx|}d|||d||d|d|||d||d|d||d|d|d|d}|S)Nrr )rrr$r%r&r-rr r r rQs**zAsymLogistic.deriv2N rrr__doc__k_argsr(rrrr r r r r .s  r c@s4eZdZdZdZddZddZddZd d Zd S) AsymNegLogisticzasymmetric negative logistic model of Joe 1990 special case: a1=a2=1 : symmetric negative logistic of Galambos 1978 restrictions: - theta in (0,inf) - a1, a2 in (0,1] r!cCs4|dk}|dko|dk}|dko&|dk}|o2|o2|Sr"r r#r r r r(gszAsymNegLogistic._check_argscCs<||}}d|d|d|||d|| }|S)Nrgr r*r r r rms zAsymNegLogistic.evaluatecCsh||}}d|}|d}||d|||||||d|||||| d}|S)Nrr )rrr$r%r&m1m2r.r r r rvs "zAsymNegLogistic.derivc Cs|}||}}|d|d|}||d|}|d|d|}||d|} |d|||| | } |d|d|d||d} | | } | S)Nrr4r/r ) rrr$r%r&r-Za1tpZa2tpZa1tnZa2tnt1t2rr r r rs $zAsymNegLogistic.deriv2Nr0r r r r r3\s   r3c@s4eZdZdZdZddZddZddZd d Zd S) AsymMixedzasymmetric mixed model of Tawn 1988 special case: k=0, theta in [0,1] : symmetric mixed model of Tiago de Oliveira 1980 restrictions: - theta > 0 - theta + 3*k > 0 - theta + k <= 1 - theta + 2*k <= 1 r/cCs<|dk}|d|dko2||dko2|d|dk}||@S)Nrr!rr/r )rr&kr'cond1r r r r(s,zAsymMixed._check_argscCs,d||||||||d}|S)Nrr!r )rrr&r:r+r r r rs(zAsymMixed.evaluatecCs*|| d||d||d}|S)Nr/r!r )rrr&r:Zd_dtr r r rs&zAsymMixed.derivcCsd|d||}|S)Nr/r )rrr&r:Zd2_dt2r r r rszAsymMixed.deriv2Nr0r r r r r9s  r9c@s$eZdZdZdZddZddZdS)AsymBiLogisticzbilogistic model of Coles and Tawn 1994, Joe, Smith and Weissman 1992 restrictions: - (beta, delta) in (0,1)^2 or - (beta, delta) in (-inf,0)^2 not vectorized because of numerical integration r/cCs8|dko|dko|dko|dk}|dko.|dk}||BSr"r )rbetadeltar;cond2r r r r(s zAsymBiLogistic._check_argscs0fdd}ddlm}||ddd}|S)NcsHdt| d}dtd| }t||Sr,)rpowermaximum)wterm1term2r>r?rr r _integrantsz+AsymBiLogistic.evaluate.._integrantr)quadr)Zscipy.integraterH)rrr>r?rGrHr+r rFr rs zAsymBiLogistic.evaluateNrrrr1r2r(rr r r r r=sr=c@s>eZdZdZdZddZddZddd Zd d Zd d Z dS)HRzmodel of Huesler Reiss 1989 special case: a1=a2=1 : symmetric negative logistic of Galambos 1978 restrictions: - lambda in (0,inf) rcCs |dk}|S)Nrr )rlamdaZcondr r r r(szHR._check_argscCsRtd||d|}ddlm}d||||||||}|S)Nr)?r)normr)rlog scipy.statsrM_cdf)rrrKtermrMr+r r r rs  z HR.evaluaterr/cCst|ttjfs.d|kr&d|kr&d}ntddtdtj}|}td||d|}dd||d|}d||d||d}||} tj | } t | d d|} | | } ||} tj | }t | d d|}| | }|dkr,|| ||d| || }|dkr|d|||d| |d |d|| ||d||}|dkr|S|dkr|S|dkr||fSdS) Nrr/r4zorder should be 1, 2, or (1,2)r)rL)rr4)r/r4) isinstanceintrinteger ValueErrorsqrtpirNrrMZcdfexp)rrrKorderdnagZgd1Zgd2tpfpZfd1pZfd2ptnfnZfd1nZfd2nr.rr r r _derivss>     "    z HR._derivscCs|||dSr,rbrrrKr r r rszHR.derivcCs|||dS)Nr/rcrdr r r r!sz HR.deriv2N)rR) rrrr1r2r(rrbrrr r r r rJs ,rJc@s$eZdZdZdZddZddZdS)TEVz_t-EV model of Demarta and McNeil 2005 restrictions: - rho in (-1,1) - x > 0 r/cCs$|}|dk}|dko|dk}|o"|Sr"r )rrhodfxr;r@r r r r(2szTEV._check_argsc Cs|}ddlm}t|d|d||}td||d||}td|td||}||} ||} ||| |dd||| |d} | S)Nr)rr)r)rOrrrArWrP) rrrfrgrhZstats_trDrEZterm0Zz1Zz2r+r r r r8s  ,z TEV.evaluateNrIr r r r re)sre)r1numpyrZscipyrZstatsmodels.tools.numdiffrrrr Ztransform_tawnr3Z transform_joer9Ztransform_tawn2r=Ztransform_bilogisticrJZ transform_hrreZ transform_tevr r r r s   +4!M