B Z! @s"dZddlZddlmZmZddZddZdd Zd d Z d d Z ddZ ddZ Gddde ZGddde ZGddde ZGddde ZGddde Zd3ddZd4d d!Zd5d"d#Zd$d%Zd&d'Zd(d)Zd*d+Zd,d-Zd.d/Zeeeee e e e e e e d0 ZGd1d2d2e ZdS)6z Which Archimedean is Best? Extreme Value copulas formulas are based on Genest 2009 References ---------- Genest, C., 2009. Rank-based inference for bivariate extreme-value copulas. The Annals of Statistics, 37(5), pp.2990-3022. N)expm1log1pcCs||S)z!independent bivariate copula )uvrrGlib/python3.7/site-packages/statsmodels/sandbox/distributions/copula.pycopula_bv_indepsrcCs t||S)z!comonotonic bivariate copula )npminimum)rrrrr copula_bv_minsr cCst||ddS)z&countermonotonic bivariate copula r)r maximum)rrrrr copula_bv_maxsrcCs:|dkstdtt|| t|| d| S)z.Clayton or Cook, Johnson bivariate copula rz#theta needs to be strictly positiver ) ValueErrorr power)rrthetarrrcopula_bv_clayton$srcCsV|dkstdtdt| |t| |t|  |}t|d}|S)z#Cook, Johnson bivariate copula rz#theta needs to be strictly positiver )rr logrr )rrrcdfvrrrcopula_bv_frank+s 6 rcCstdS)N)NotImplementedError)rrrhorrrcopula_bv_gauss5srcCstdS)N)r)rrrZdfrrr copula_bv_t8src@seZdZddZdS) TransformscCsdS)Nr)selfrrr__init__=szTransforms.__init__N)__name__ __module__ __qualname__rrrrrr<src@seZdZddZddZdS) TransfFrankcCs*tt| | tt|   S)N)r rr)rtrrrrevaluateBszTransfFrank.evaluatecCs"tt| t|  |S)N)r rexpr)rphirrrrinverseFszTransfFrank.inverseN)rrrr"r%rrrrr @sr c@s$eZdZddZddZddZdS) TransfClaytoncCs|dkS)Nrr)rrrr _checkargsKszTransfClayton._checkargscCst|| dS)Ng?)r r)rr!rrrrr"NszTransfClayton.evaluatecCstd|| S)Nr )r r)rr$rrrrr%QszTransfClayton.inverseN)rrrr'r"r%rrrrr&Isr&c@s(eZdZdZddZddZddZdS) TransfGumbelz requires theta >=1 cCs|dkS)Nr r)rrrrr'YszTransfGumbel._checkargscCstt| |S)N)r rr)rr!rrrrr"\szTransfGumbel.evaluatecCstt|d| S)Ng?)r r#r)rr$rrrrr%_szTransfGumbel.inverseN)rrr__doc__r'r"r%rrrrr(Tsr(c@seZdZddZddZdS) TransfIndepcCs t| S)N)r r)rr!rrrr"cszTransfIndep.evaluatecCs t| S)N)r r#)rr$rrrr%fszTransfIndep.inverseN)rrrr"r%rrrrr*bsr*rcCs6|j}|j}|||f|||f|f|}|S)z )r"r%)rr transformargsr$phi_invrrrrcopula_bv_archimedeanis&r.cCs.|j}|j}|||f||f|}|S)z,generic multivariate Archimedean copula )r"r%sum)rr+r,Zaxisr$r-rrrrcopula_mv_archimedeanrsr1c Cs6tt|||t|t||f|S)z+generic bivariate extreme value copula )r r#r)rrr+r,rrr copula_bv_ev{sr2cCsrdd}t||||s"tdd|d|}|d||7}|||d||d|d||7}|S)zasymmetric logistic model of Tawn 1988 special case: a1=a2=1 : Gumbel restrictions: - theta in (0,1] - a1, a2 in [0,1] cSs<|dko|dk}|dko|dk}|dko.|dk}|o:|o:|S)Nrr r)a1a2rcondthconda1conda2rrr _check_argssz#transform_tawn.._check_argsz invalid argsr g?)r allr)r!r3r4rr8transfrrrtransform_tawns ,r;cCsTdd}t||||s"tdd|d|d|||d|| }|S)zasymmetric 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] cSs4|dk}|dko|dk}|dko&|dk}|o2|o2|S)Nrr r)r3r4rr5r6r7rrrr8sz"transform_joe.._check_argsz invalid argsr g)r r9r)r!r3r4rr8r:rrr transform_joes .r<cCsLdd}t|||s tdd||||||||d}|S)zasymmetric 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 cSs<|dk}|d|dko2||dko2|d|dk}|o:|S)Nrr r)rkr5cond1rrrr8s,z$transform_tawn2.._check_argsz invalid argsr r=)r r9r)r!rr?r8r:rrrtransform_tawn2s (rAcsLdd}t|s tdfdd}ddlm}||dd}|S) zbilogistic model of Coles and Tawn 1994, Joe, Smith and Weissman 1992 restrictions: - (beta, delta) in (0,1)^2 or - (beta, delta) in (-inf,0)^2 not vectorized because of numerical integration cSs8|dko|dko|dko|dk}|dko.|dk}||BS)Nrr r)betadeltar@cond2rrrr8s z)transform_bilogistic.._check_argsz invalid argscsLdt| d}dtd| }t||dS)Nr )r rr )wZterm1Zterm2)rBrCr!rr _integrantsz(transform_bilogistic.._integrantr)quadr )r r9rZscipy.integraterG)r!rBrCr8rFrGr:r)rBrCr!rtransform_bilogistics   rHcCspdd}t||stdtd||d|}ddlm}d||||||||}|S) zmodel of Huesler Reiss 1989 special case: a1=a2=1 : symmetric negative logistic of Galambos 1978 restrictions: - lambda in (0,inf) cSs |dk}|S)Nrr)lamdaZcondrrrr8sz!transform_hr.._check_argsz invalid argsg?g?r)normr )r r9rr scipy.statsrJ_cdf)r!rIr8ZtermrJr:rrr transform_hrs  (rMcCsdd}t|||s tdddlm}td|t|d|d||}|td||}d||||d||||d}|S)z_t-EV model of Demarta and McNeil 2005 restrictions: - rho in (-1,1) - x > 0 cSs |dk}|dko|dk}|o|S)Nrr r)rxr@rDrrrr8sz"transform_tev.._check_argsz invalid argsr)r!g?r )r r9rrKr!ZsqrtrrL)r!rrNr8Zstats_tzr:rrr transform_tevs *,rP) ZindepiminmaxZclaytonZ cookjohnsonZcjZfrankZgaussZnormalr!c@s$eZdZdZdddZd ddZdS) CopulaBivariatezjbivariate copula class Instantiation needs the arguments, cop_args, that are required for copula rcCsP|tkrt||_n,y|d|}WntdYnX||_||_||_dS)N?z,copula needs to be a copula name or callable)rUrU) copulanamescopular marginalcdfscopargs)rrXrWrYZtmprrrr"s zCopulaBivariate.__init__NcCs<|\}}|dkr|j}|j|jd||jd|f|S)zNxx needs to be iterable, instead of x,y for extension to multivariate Nrr )rYrWrX)rZxyr,rNyrrrcdf1s zCopulaBivariate.cdf)r)N)rrrr)rr[rrrrrTs rT)r)rr/)r)r)Znumpyr Z scipy.specialrrrr rrrrrobjectrr r&r(r*r.r1r2r;r<rArHrMrPrVrTrrrrsF