Regular vine copula provides rich models for dependence structure modeling.It combines vine structures and families of bivariate copulas to construct a number of multivariate distributions that can model a wide range ...Regular vine copula provides rich models for dependence structure modeling.It combines vine structures and families of bivariate copulas to construct a number of multivariate distributions that can model a wide range dependence patterns with different tail dependence for different pairs.Two special cases of regular vine copulas,C-vine and D-vine copulas,have been extensively investigated in the literature.We propose the Python package,pyvine,for modeling,sampling and testing a more generalized regular vine copula(R-vine for short).R-vine modeling algorithm searches for the R-vine structure which maximizes the vine tree dependence in a sequential way.The maximum likelihood estimation algorithm takes the sequential estimations as initial values and uses L-BFGS-B algorithm for the likelihood value optimization.R-vine sampling algorithm traverses all edges of the vine structure from the last tree in a recursive way and generates the marginal samples on each edge according to some nested conditions.Goodness-of-fit testing algorithm first generates Rosenblatt’s transformed data E and then tests the hypothesis H^(∗)_(0):E∼C_(⊥)by using Anderson–Darling statistic,where C_(⊥)is the independence copula.Bootstrap method is used to compute an adjusted p-value of the empirical distribution of replications of Anderson–Darling statistic.The computing of related functions of copulas such as cumulative distribution functions,Hfunctions and inverse H-functions often meets with the problem of overflow.We solve this problem by reinvestigating the following six families of bivariate copulas:Normal,Student t,Clayton,Gumbel,Frank and Joe’s copulas.Approximations of the above related functions of copulas are given when the overflow occurs in the computation.All these are implemented in a subpackage bvcopula,in which subroutines are written in Fortran and wrapped into Python and,hence,good performance is guaranteed.展开更多
As wind farms are commonly installed in areas with abundant wind resources,spatial dependence of wind speed among nearby wind farms should be considered when modeling a power system with large-scale wind power.In this...As wind farms are commonly installed in areas with abundant wind resources,spatial dependence of wind speed among nearby wind farms should be considered when modeling a power system with large-scale wind power.In this paper,a novel bivariate non-parametric copula,and a bivariate diffusive kernel(BDK)copula are proposed to formulate the dependence between random variables.BDK copula is then applied to higher dimension using the pair-copula method and is named as pair diffusive kernel(PDK)copula,offering flexibility to formulate the complicated dependent structure of multiple random variables.Also,a quasi-Monte Carlo method is elaborated in the sampling procedure based on the combination of the Sobol sequence and the Rosen-blatt transformation of the PDK copula,to generate correlated wind speed samples.The proposed method is applied to solve probabilistic optimal power flow(POPF)problems.The effectiveness of the BDK copula is validated in copula definitions.Then,three different data sets are used in various goodness-of-fit tests to verify the superior performance of the PDK copula,which facilitates in formulating the dependence structure of wind speeds at different wind farms.Furthermore,samples obtained from the PDK copula are used to solve POPF problems,which are modeled on three modified IEEE 57-bus power systems.Compared to the Gaussian,T,and parametric-pair copulas,the results obtained from the PDK copula are superior in formulating the complicated dependence,thus solving POPF problems.展开更多
In this paper, we consider the statistical analysis for the dependent competing risks model in theconstant stress accelerated life testing (CSALT) with Type-II progressive censoring. It is focusedon two competing risk...In this paper, we consider the statistical analysis for the dependent competing risks model in theconstant stress accelerated life testing (CSALT) with Type-II progressive censoring. It is focusedon two competing risks from Lomax distribution. The maximum likelihood estimators of theunknown parameters, the acceleration coefficients and the reliability of unit are obtained by usingthe Bivariate Pareto Copula function and the measure of dependence known as Kendall’s tau.In addition, the 95% confidence intervals as well as the coverage percentages are obtained byusing Bootstrap-p and Bootstrap-t method. Then, a simulation study is carried out by the MonteCarlo method for different measures of Kendall’s tau and different testing schemes. Finally, a realcompeting risks data is analysed for illustrative purposes. The results indicate that using copulafunction to deal with the dependent competing risks problems is effective and feasible.展开更多
For the class of(partially specified)internal risk factor models we establish strongly simplified supermodular ordering results in comparison to the case of general risk factor models.This allows us to derive meaningf...For the class of(partially specified)internal risk factor models we establish strongly simplified supermodular ordering results in comparison to the case of general risk factor models.This allows us to derive meaningful and improved risk bounds for the joint portfolio in risk factor models with dependence information given by constrained specification sets for the copulas of the risk components and the systemic risk factor.The proof of our main comparison result is not standard.It is based on grid copula approximation of upper products of copulas and on the theory of mass transfers.An application to real market data shows considerable improvement over the standard method.展开更多
基金This work was supported by the NNSF of China(Nos.11371340,71871208).
文摘Regular vine copula provides rich models for dependence structure modeling.It combines vine structures and families of bivariate copulas to construct a number of multivariate distributions that can model a wide range dependence patterns with different tail dependence for different pairs.Two special cases of regular vine copulas,C-vine and D-vine copulas,have been extensively investigated in the literature.We propose the Python package,pyvine,for modeling,sampling and testing a more generalized regular vine copula(R-vine for short).R-vine modeling algorithm searches for the R-vine structure which maximizes the vine tree dependence in a sequential way.The maximum likelihood estimation algorithm takes the sequential estimations as initial values and uses L-BFGS-B algorithm for the likelihood value optimization.R-vine sampling algorithm traverses all edges of the vine structure from the last tree in a recursive way and generates the marginal samples on each edge according to some nested conditions.Goodness-of-fit testing algorithm first generates Rosenblatt’s transformed data E and then tests the hypothesis H^(∗)_(0):E∼C_(⊥)by using Anderson–Darling statistic,where C_(⊥)is the independence copula.Bootstrap method is used to compute an adjusted p-value of the empirical distribution of replications of Anderson–Darling statistic.The computing of related functions of copulas such as cumulative distribution functions,Hfunctions and inverse H-functions often meets with the problem of overflow.We solve this problem by reinvestigating the following six families of bivariate copulas:Normal,Student t,Clayton,Gumbel,Frank and Joe’s copulas.Approximations of the above related functions of copulas are given when the overflow occurs in the computation.All these are implemented in a subpackage bvcopula,in which subroutines are written in Fortran and wrapped into Python and,hence,good performance is guaranteed.
基金supported by Key-Area Research and Development Program of Guangdong Province(No.2020B010166004)the National Natural Science Foundation of China(No.52077081).
文摘As wind farms are commonly installed in areas with abundant wind resources,spatial dependence of wind speed among nearby wind farms should be considered when modeling a power system with large-scale wind power.In this paper,a novel bivariate non-parametric copula,and a bivariate diffusive kernel(BDK)copula are proposed to formulate the dependence between random variables.BDK copula is then applied to higher dimension using the pair-copula method and is named as pair diffusive kernel(PDK)copula,offering flexibility to formulate the complicated dependent structure of multiple random variables.Also,a quasi-Monte Carlo method is elaborated in the sampling procedure based on the combination of the Sobol sequence and the Rosen-blatt transformation of the PDK copula,to generate correlated wind speed samples.The proposed method is applied to solve probabilistic optimal power flow(POPF)problems.The effectiveness of the BDK copula is validated in copula definitions.Then,three different data sets are used in various goodness-of-fit tests to verify the superior performance of the PDK copula,which facilitates in formulating the dependence structure of wind speeds at different wind farms.Furthermore,samples obtained from the PDK copula are used to solve POPF problems,which are modeled on three modified IEEE 57-bus power systems.Compared to the Gaussian,T,and parametric-pair copulas,the results obtained from the PDK copula are superior in formulating the complicated dependence,thus solving POPF problems.
基金This work is supported by the National Natural Science Foundation of China[grant number 71571144],[grant number 71401134],[grant number 71171164],[grant number 11701406]Natural Science Basic Research Program of Shaanxi Province[grant number 2015JM1003]Program of International Cooperation and Exchanges in Science and Technology Funded by Shaanxi Province[grant number 2016KW-033].
文摘In this paper, we consider the statistical analysis for the dependent competing risks model in theconstant stress accelerated life testing (CSALT) with Type-II progressive censoring. It is focusedon two competing risks from Lomax distribution. The maximum likelihood estimators of theunknown parameters, the acceleration coefficients and the reliability of unit are obtained by usingthe Bivariate Pareto Copula function and the measure of dependence known as Kendall’s tau.In addition, the 95% confidence intervals as well as the coverage percentages are obtained byusing Bootstrap-p and Bootstrap-t method. Then, a simulation study is carried out by the MonteCarlo method for different measures of Kendall’s tau and different testing schemes. Finally, a realcompeting risks data is analysed for illustrative purposes. The results indicate that using copulafunction to deal with the dependent competing risks problems is effective and feasible.
文摘For the class of(partially specified)internal risk factor models we establish strongly simplified supermodular ordering results in comparison to the case of general risk factor models.This allows us to derive meaningful and improved risk bounds for the joint portfolio in risk factor models with dependence information given by constrained specification sets for the copulas of the risk components and the systemic risk factor.The proof of our main comparison result is not standard.It is based on grid copula approximation of upper products of copulas and on the theory of mass transfers.An application to real market data shows considerable improvement over the standard method.
