The Generalized Marshall–Olkin Type Multivariate Pareto Distributions
Abstract In this paper, two generalized Marshall–Olkin type multivariate Pareto distributions are developed. They are generated by two different methods and are denoted respectively by the notations GMOP(I), (II), (III), (IV) and the reduction multivariate Pareto, RMP(I), (II), (III), (IV). All of them have univariate Pareto as marginals. Several distributional properties of these two alternative multivariate Pareto distributions are studied and two characterization properties of GMOP(I) distribution are thoroughly verified. One special subset of GMOP(IV) family can be generated by a fatal shock model of an m-component system. The multivariate Pareto RMP family is a subclass of GMOP.