New results on stochastic comparisons of finite mixtures for some families of distributions

Abstract

The classical finite mixture model is an effective tool to describe the lifetimes of the items existing in a random sample which are selected from some heterogeneous populations. This paper carries out stochastic comparisons between two classical finite mixture models in the sense of the usual stochastic order, when the subpopulations follow a wide class of distributions including the scale model, the proportional hazard rate model and the proportional reversed hazard rate model. Next, we consider the hazard rate and dispersive orders when the subpopulations follow the proportional hazard rate model and also the reversed hazard rate order in the case that the subpopulations follow the proportional reversed hazard rate model. Finally, the likelihood ratio order between two finite mixtures is characterized when the subpopulations belong to the transmuted-G model.

Keywords:

• Finite mixture model
• majorization
• proportional hazard rate model
• proportional reversed hazard rate model
• stochastic order

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E15

Acknowledgement

We would like to thank and express our deep gratitude to referees for their useful suggestions and comments, which led to the improved presentation of the manuscript.