Stochastic Comparisons of Weighted Distributions and Their Mixtures

Abstract

In this paper, various stochastic ordering properties of a parametric family of weighted distributions and the associated mixture model are developed. The effect of stochastic variation of the output random variable with respect to the parameter and/or the underlying random variable is specifically investigated. Special weighted distributions are considered to scrutinize the consistency as well as the usefulness of the results. Stochastic comparisons of coherent systems made of identical but dependent components are made and also a result for comparison of Shannon entropies of weighted distributions is developed.