Construction of multivariate distributions: a review of some recent results

Abstract

The construction of multivariate distributions is an active field of research in theoretical and applied statistics. In this paper some recent developments in this field are reviewed. Specifically, we study and review the following set of methods: (a) Construction of multivariate distributions based on order statistics, (b) Methods based on mixtures, (c) Conditionally specified distributions, (d) Multivariate skew distributions, (e) Distributions based on the method of the variables in common and (f) Other methods, which include multivariate weighted distributions, vines and multivariate Zipf distributions.