Vfd(dZddlZddlmZddlmZddlmZGddeZ Gdd e Z Gd d e Z dS) zb Created on Fri Jan 29 19:19:45 2021 Author: Josef Perktold Author: Pamphile Roy License: BSD-3 N)stats)multivariate_t)CopulacDeZdZdZdZd dZd dZd dZdd Zd Z d Z dS)EllipticalCopulaa3Base class for elliptical copula This class requires subclassing and currently does not have generic methods based on an elliptical generator. Notes ----- Elliptical copulas require that copula parameters are set when the instance is created. Those parameters currently cannot be provided in the call to methods. (This will most likely change in future versions.) If non-empty ``args`` are provided in methods, then a ValueError is raised. The ``args`` keyword is provided for a consistent interface across copulas. c8|dkr|d}t||S)NzaMethods in elliptical copulas use copula parameters in attributes. `arg` in the method is ignored) ValueError)selfargsmsgs Klib/python3.11/site-packages/statsmodels/distributions/copula/elliptical.py _handle_argszEllipticalCopula._handle_args"s) 2::$*ACS// !Kr Nc|||j||}|j|S)N)size random_state)rdistr_mvrvsdistr_uvcdf)r nobsr rxs rrzEllipticalCopula.rvs*sF $ M  4l  C C}  ###rc|||j|}|j|}|t j|j|dz S)N)axis)rrppfrpdfnpprod)r ur r mv_pdf_ppfs rrzEllipticalCopula.pdf/sj $m""]&&s++ BGDM$5$5c$:$:DDDDDrc|||j|}|j|SN)rrrrr)r r"r rs rrzEllipticalCopula.cdf6sA $m""}  %%%rc||j}|jdkr|d}dtj|ztjz }|S)aBivariate kendall's tau based on correlation coefficient. Parameters ---------- corr : None or float Pearson correlation. If corr is None, then the correlation will be taken from the copula attribute. Returns ------- Kendall's tau that corresponds to pearson correlation in the elliptical copula. Nr(rrr(corrshaper arcsinpi)r r+rhos rtauzEllipticalCopula.tau;sD <9D :  :D")D//!BE) rcNtj|tjzdz }|S)aPPearson correlation from kendall's tau. Parameters ---------- tau : array_like Kendall's tau correlation coefficient. Returns ------- Pearson correlation coefficient for given tau in elliptical copula. This can be used as parameter for an elliptical copula. r()r sinr.)r r0r+s r corr_from_tauzEllipticalCopula.corr_from_tauPs"vcBEkAo&& rctj|}|jddkr0tj|dddf|dddfd}n||j}tj|}t|D]Q}t|dz|D];}tj|d|f|d|fd}|x|||f<|||f< 2, then average tau is used. rr(Nr.) r asarrayr,r kendalltauk_dimeyerange _arg_from_tau)r datarr0kijtau_ijs rfit_corr_paramzEllipticalCopula.fit_corr_param`s Jt   71:??"1QQQT7AaaadG44Q7CC A&))C1XX 3 3qsA33A"-aQi36CCAFF,22C1IAqD 3!!#&&&r)rr Nr r%) __name__ __module__ __qualname____doc__rrrrr0r3r@r rrrrs$$$$ EEEE&&&& * '''''rrc2eZdZdZdfd Zd dZdZxZS) GaussianCopulaaGaussian copula. It is constructed from a multivariate normal distribution over :math:`\mathbb{R}^d` by using the probability integral transform. For a given correlation matrix :math:`R \in[-1, 1]^{d \times d}`, the Gaussian copula with parameter matrix :math:`R` can be written as: .. math:: C_R^{\text{Gauss}}(u) = \Phi_R\left(\Phi^{-1}(u_1),\dots, \Phi^{-1}(u_d) \right), where :math:`\Phi^{-1}` is the inverse cumulative distribution function of a standard normal and :math:`\Phi_R` is the joint cumulative distribution function of a multivariate normal distribution with mean vector zero and covariance matrix equal to the correlation matrix :math:`R`. Parameters ---------- corr : scalar or array_like Correlation or scatter matrix for the elliptical copula. In the bivariate case, ``corr` can be a scalar and is then considered as the correlation coefficient. If ``corr`` is None, then the scatter matrix is the identity matrix. k_dim : int Dimension, number of components in the multivariate random variable. allow_singular : bool Allow singular correlation matrix. The behavior when the correlation matrix is singular is determined by `scipy.stats.multivariate_normal`` and might not be appropriate for all copula or copula distribution metnods. Behavior might change in future versions. Notes ----- Elliptical copulas require that copula parameters are set when the instance is created. Those parameters currently cannot be provided in the call to methods. (This will most likely change in future versions.) If non-empty ``args`` are provided in methods, then a ValueError is raised. The ``args`` keyword is provided for a consistent interface across copulas. References ---------- .. [1] Joe, Harry, 2014, Dependence modeling with copulas. CRC press. p. 163 Nr(Fct||tj|}n8|dkr2tj|dkrtjd|g|dgg}tj||_|jf|_tj |_ tj |||_ dS)Nr7r(r?)covallow_singular)super__init__r r8rarrayr5r+r rnormrmultivariate_normalr)r r+r7rL __class__s rrNzGaussianCopula.__init__s u%%% <6%==DD aZZBGDMMQ..8b$Z$455DJt$$ YL   1^555 rcdS)a Bivariate tail dependence parameter. Joe (2014) p. 182 Parameters ---------- corr : any Tail dependence for Gaussian copulas is always zero. Argument will be ignored Returns ------- Lower and upper tail dependence coefficients of the copula with given Pearson correlation coefficient. )rrr )r r+s rdependence_tailzGaussianCopula.dependence_tails $trc,||Sr%r3r r0s rr:zGaussianCopula._arg_from_taus!!#&&&r)Nr(Fr%)rBrCrDrErNrTr: __classcell__rRs@rrGrG~sk22h 5 5 5 5 5 5('''''''rrGcBeZdZdZd fd Zd dZd dZd dZd ZxZ S) StudentTCopulaaStudent t copula. Parameters ---------- corr : scalar or array_like Correlation or scatter matrix for the elliptical copula. In the bivariate case, ``corr` can be a scalar and is then considered as the correlation coefficient. If ``corr`` is None, then the scatter matrix is the identity matrix. df : float (optional) Degrees of freedom of the multivariate t distribution. k_dim : int Dimension, number of components in the multivariate random variable. Notes ----- Elliptical copulas require that copula parameters are set when the instance is created. Those parameters currently cannot be provided in the call to methods. (This will most likely change in future versions.) If non-empty ``args`` are provided in methods, then a ValueError is raised. The ``args`` keyword is provided for a consistent interface across copulas. References ---------- .. [1] Joe, Harry, 2014, Dependence modeling with copulas. CRC press. p. 181 Nr(ct||tj|}n8|dkr2tj|dkrtjd|g|dgg}||_tj||_||f|_ tj ||_ t|||_dS)NrIr(rrJ)df)r,r])rMrNr r8rrOr]r5r+r rtrrr)r r+r]r7rRs rrNzStudentTCopula.__init__s u%%% <6%==DD aZZBGDMMQ..8b$Z$455DJt$$ 2J 2 &Tb999 rr c td)Nz!CDF not available in closed form.)NotImplementedError)r r"r s rrzStudentTCopula.cdfs!"EFFFrc||j}|jdkr|d}dtj|dz ztjz }|S)a Bivariate Spearman's rho based on correlation coefficient. Joe (2014) p. 182 Parameters ---------- corr : None or float Pearson correlation. If corr is None, then the correlation will be taken from the copula attribute. Returns ------- Spearman's rho that corresponds to pearson correlation in the elliptical copula. Nr'r)r(r*)r r+r0s r spearmans_rhozStudentTCopula.spearmans_rho sJ" <9D :  :D")D1H%%%- rc||j}|jdkr|d}|j}tj|dzd|z zdz |z }dt j||dzz}||fS)a Bivariate tail dependence parameter. Joe (2014) p. 182 Parameters ---------- corr : None or float Pearson correlation. If corr is None, then the correlation will be taken from the copula attribute. Returns ------- Lower and upper tail dependence coefficients of the copula with given Pearson correlation coefficient. Nr'r)rr()r+r,r]r sqrtrr^r)r r+r]r^lams rrTzStudentTCopula.dependence_tail$s}" <9D :  :D WgrAv!d(+a/$677 7%'++aa(((Cxrc,||Sr%rVrWs rr:zStudentTCopula._arg_from_tau@s!!#&&&r)NNr(rAr%) rBrCrDrErNrrcrTr:rXrYs@rr[r[s: : : : : : :GGGG 28'''''''rr[) rEnumpyr scipyrstatsmodels.compat.scipyr(statsmodels.distributions.copula.copulasrrrGr[r rrrls333333;;;;;;i'i'i'i'i'vi'i'i'XX'X'X'X'X'%X'X'X'vj'j'j'j'j'%j'j'j'j'j'r