Bivariate Reversed Hazard Rate, Notions, and Measures of Dependence and their Relationships

Abstract

In this article, we extend some important results existing in the reliability literature based on the bivariate hazard rate to a case in which the bivariate reversed hazard rate is considered. In particular, we prove the existence of a link between the components of a bivariate reversed hazard rate and notions of dependence based on the left tail of a distribution. Moreover, we use this link to study some properties of a local dependence measure. Finally, we propose some characterizations of bivariate distribution based on the relation between various definitions of reversed hazard.

Keywords:

• Left corner set decreasing
• Left tail decreasing
• Local dependence measure
• Mean reversed residual life

Mathematics Subject Classification:

• Primary 62E05
• Secondary 62H20

Acknowledgments

The author wishes to thank the anonymous Associate Editor and two referees for their helpful comments which improved the earlier draft of the article.