Stochastic Orderings between Two Finite Mixtures with Inverted-Kumaraswamy Distributed Components

Abstract

In this paper, we consider two finite mixture models (FMMs) with inverted-Kumaraswamy distributed components’ lifetimes. Several stochastic ordering results between the FMMs are obtained. Mainly, we focus on three different cases in terms of the heterogeneity of parameters. The usual stochastic order between the FMMs is established when heterogeneity presents in one parameter as well as two parameters. In addition, we also study ageing faster order in terms of the reversed hazard rate between two FMMs when heterogeneity is in two parameters. For the case of heterogeneity in three parameters, we obtain the comparison results based on reversed hazard rate and likelihood ratio orders. The theoretical developments are illustrated using several examples and counterexamples.

Keywords

• FMMs
• stochastic orders
• weak supermajorization
• weak submajorization
• matrix majorization