Inequalities for a Class of Positively Dependent Random Variables with a Common Marginal

Abstract

This paper concerns a partial ordering of positive dependence of a class of random variables which have a common marginal distribution and are not necessarily exchangeable. The main theorem is obtained by applying a moment inequality via majorization. Inequalities for exchangeable random variables, for random variables whose marginal densities possess the semigroup property and for the multivariate normal distribution are then obtained as special cases.