Orderings of the finite mixture with modified proportional hazard rate model

TL;DR

This paper investigates stochastic orderings in finite mixture models with modified proportional hazard rates, establishing conditions under various majorization and transformation settings, supported by numerical examples.

Contribution

It provides new sufficient conditions for stochastic and hazard orderings in finite mixture models with modified proportional hazard rates, extending existing theory.

Findings

Established conditions for stochastic orderings under chain majorization.

Derived criteria for hazard rate, star, and Lorenz orders using supermajorization.

Numerical examples illustrate the theoretical results.

Abstract

In this paper, we consider finite mixture models with modified proportional hazard rates. Sufficient conditions for the usual stochastic order and the hazard order are established under chain majorization. We study stochastic comparisons under different settings of T-transform for various values of chain majorization. We establish usual stochastic order and hazard rate order between two mixture random variables when a matrix of model parameters and mixing proportions changes to another matrix in some mathematical sense. Sufficient conditions for the star order and Lorenz order are established under weakly supermajorization. The results of this paper are illustrated with numerical examples.