A Class of Multivariate New Better Than Used Distributions

Abstract

A class of multivariate distributions with new better than used (NBU) marginals is introduced. A number of necessary and sufficient conditions for a distribution to be a member in the class are given. Closure results, which are useful for the identification or construction of members in the class, are derived. In particular, simple proofs of some well known preservation properties of the class of the univariate NBU distributions are obtained. Two examples of replacement models, that give rise to multivariate NBU distributions in the class, are discussed.