Stochastic comparison results between two finite mixture models with generalized Weibull distributed components

Abstract

In this paper, we establish sufficient conditions for stochastic comparisons of two finite mixture models (FMMs) with respect to the usual stochastic order, hazard rate order, and likelihood ratio order when the mixing components have generalized Weibull family of distributions. The established (sufficient) conditions are mainly based on the majorization order, weak supermajorization order, and weak submajorization order. The stochastic comparisons are studied when there is heterogeneity in one (model) parameter, and then in two parameters (model parameter and mixing proportion). Further, the concept of unordered majorization order is employed to establish the usual stochastic order between two FMMs. To illustrate the theoretical results established here, several numerical examples and counterexamples are presented. Finally, we have generalized some of the results to the case of τ-mixture models.

Keywords:

• FMMs
• stochastic orders
• vector majorization
• unordered majorization order
• τ-mixture model

Mathematics Subject Classifications:

• 60E15
• 90B25

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The financial support (vide D.O. No. F. 14-34/2011 (CPP-II) dated 11.01.2013, F. No. 16-9(June 2019)/2019(NET/CSIR), UGC-Ref.No.:1238/(CSIR-UGC NET JUNE 2019)) from the University Grants Commission (UGC), Government of India, is sincerely acknowledged with thanks by Raju Bhakta. The authors also express their sincere thanks to the Editor-in-Chief, Associate Editor and the anonymous reviewers for their incisive comments and observations on an earlier version of this manuscript which led to this much improved version.