Duality of the Multivariate Distributions of Marshall-Olkin Type and Tail Dependence

A dual class of the multivariate distributions of Marshall-Olkin type is introduced, and their copulas are presented and utilized to derive explicit expressions of the distributional tail dependencies, which describe the amount of dependence in the upperorthant tail or lower-orthant tail of a multivariate distribution and can be used in the study of dependence among extreme values. A sufficient condition under which tail dependencies of two such distributions can be compared are obtained. Some examples are also presented to illustrate our results.