Tail Dependence Coefficient Of Multivariate Elliptical Distributions On The Copulas

The tail dependence of multivariate distribution is frequently studied by copulas. In this article, the tail dependence coefficient of the multivariate elliptical distribution and its properties are obtained. Furthermore, some specific tail dependence coefficients (TDC) and the copulas on regularly varying elliptical distribution are given. From these results, it is easy to see that the TDC is only determined by its tail index and the correlation coefficient of the multivariate elliptical distribution. Finally, for comparing with the results in Chan (2008), some simulations are presented.There are four parts in this paper:In Section 1, we introduce the source and some relational definitions of tail dependence coefficient. the copula of multivariate tail depen-dence coefficient is given, and we illustrate it with two examples. In Section 2, we give the specific forms of the tail dependence coefficient on elliptical distributions and regularly varying elliptical distributions. In Section 3, The simulations based on uniform distribu-tion examples are presented to compare with the results in Chan (2008). Finally, some future works are discussed in this Section.