Ordering results between two finite arithmetic mixture models with multiple-outlier location-scale distributed components

TL;DR

This paper develops methods for comparing two finite mixture models with multiple-outlier location-scale components, providing conditions under which one model stochastically dominates another, aiding in understanding population heterogeneity.

Contribution

It introduces stochastic comparison techniques for finite mixture models with multiple-outlier components using vector majorization and univariate orders.

Findings

Derived sufficient conditions for stochastic ordering of mixture models.

Established comparison framework within multiple-outlier location-scale models.

Enhanced understanding of population heterogeneity in mixture models.

Abstract

In this article, we introduce finite mixture models (FMMs) renowned for capturing population heterogeneity. Our focus lies in establishing stochastic comparisons between two arithmetic (finite) mixture models, employing the vector majorization concept in the context of various univariate orders of magnitude, transform, and variability. These comparisons are conducted within the framework of multiple-outlier location-scale models. Specifically, we derive sufficient conditions for comparing two finite arithmetic mixture models with components distributed in a multiple-outlier location-scale model.