Title: Archimedean Copula Parameter Estimation with Kendall Distribution Function
Abstract:In the literature, up to now, it is common that for Gumbel, Clayton and Frank calculated Kendall Distribution function ( ) K u and to the extent those applications have been made.Kendall distribution ...In the literature, up to now, it is common that for Gumbel, Clayton and Frank calculated Kendall Distribution function ( ) K u and to the extent those applications have been made.Kendall distribution functions show stochastic orderings of random vectors.The aim of Kendall distribution function is selected suitable copula function for using data set.For dependence structures of the data set, we calculated Kendall Tau and Spearman Rho values which are nonparametric.Based on this method, parameters of copula are obtained.In this paper, we are made Kendall Distribution function which obtained with the help of generator function of Archimedean copula calculation for Ali Mikhail Haq and Joe and in relation with that simulation study.We used data set which generated dependent generalized pareto distribution (Gp(3,3,3)) for this study.For dependency among these variables, we used Archimedean copula.In connection with this, we define basic properties of copulas and nonparametric methods Kendall Tau, Spearman Rho are given.In this study, to explain the relationship among the variables, five Archimedean copula are selected; Gumbel, Clayton, Frank Joe and Ali Mikhail Haq.Afterwards, we are obtained nonparametric estimation of parameters of these copulas with the help of Kendall Tau.With Kendall distribution function values, we found the suitable Archimedean copula family for this data set.Read More