Some results on stochastic comparisons of two finite mixture models with general components

Abstract

Finite mixture (FM) models have found key applications in many fields. Recently, some discussions have been made on comparing finite mixture models. In this paper, we discuss stochastic comparison of two FM models with respect to usual stochastic order when the mixture components have a general family of distributions. This problem has been studied when there is heterogeneity in one parameter (i.e., the distributional parameter), as well as when there is heterogeneity in two parameters (i.e., the distributional parameter and the mixing proportions). The sufficient conditions considered are based on p-larger order and reciprocally majorization order. Several examples have been provided to illustrate the established results.

Keywords:

• Finite mixture models
• matrix majorization
• p-larger order
• reciprocally majorization order
• T-transform matrix
• usual stochastic order

Mathematics Subject Classification:

• 60E15

Acknowledgements

The authors express their sincere thanks to the Editor and the anonymous reviewers for their useful comments and suggestions on an earlier version of this manuscript, which led to this improved version.

Disclosure statement

All the authors state that there is no conflict of interest.

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. Suchandan Kayal gratefully acknowledges the partial financial support for this work received under the grant MTR/2018/000350, SERB, India.