A Mixture Model of Proportional Reversed Hazard Rate

Abstract

This article investigates properties of mixture model of proportional reversed hazard rate. Firstly, the mixing random variable and the overall population variable are proved to be positively likelihood dependent. Secondly, lower bounds for the distribution function as well as the conditional distribution are established in the case that the mixing variable belongs to certain nonparametric classes. Finally, some stochastic orders on the mixing (baseline) variables are proved to be translated to the corresponding overall population variables.

Keywords:

• DRHR
• Hazard rate order
• HNBUE
• Likelihood ratio order
• Positively likelihood ratio dependent

Mathematics Subject Classification:

• Primary 60E15
• Secondary 60K10, 62N05

Acknowledgments

The authors would like to thank the two anonymous referees as well as the Associate Editor for their insightful comments which greatly improve the presentation of this manuscript and brought our attention to the more interesting topic in this line of research.

The authors were supported by National Natural Science Foundation of China (10771090).