Tail Dependence of Multivariate Pareto Distributions

Abstract Various multivariate Pareto distributions are known to exhibit the heavy tail behaviors. This paper examines the tail dependence properties of a general class of multivariate Pareto distributions with the Pareto index and some common scale parameters. The multivariate tail dependence describes the amount of dependence in the upper-orthant tail or lower-orthant tail of a multivariate distribution and can be used in the study of dependence among extreme values. We derive the explicit expressions of tail dependencies of the multivariate Pareto distributions and related copulas of Archimedean type. Properties of the tail dependence coefficients are discussed and some examples are presented to illustrate our results