Multivariate distributions generated from mixtures of convolution and product families
Albert W. Marshall, Ingram Olkin · Lecture notes-monograph series · 1990
A number of standard univariate distributions can be represented as mixtures of other standard distributions.In this paper such mixture representations are exploited to generate families of multivariate distributions with given marginals.Attention is confined to mixtures of parametric families where the parameter appears as the order of a convolution or as a power of the distribution or survival function.The mixture structure yields properties of the generated multivariate distributions such as total positivity, association and infinite divisibility.Examples obtained include the bivariate Poisson, binomial, negative binomial, normal, chi-square, logistic and Pareto distributions.