HR and RHR orderings of extremes of dependent variables under Archimedean copula

Abstract

In this article, we discuss sufficient conditions for the hazard rate order on smallest order statistics for variables with Archimedean survival copula and having modified proportional hazard rates (modified scale) model. We also establish the reversed hazard rate order on largest order statistics from variables with Archimedean copula and having modified proportional reversed hazard rates model. The results established here extend the recent results of Li and Li (2019).

KEYWORDS:

• Archimedean copula
• hazard rate order
• reversed hazard rate order
• modified proportional hazard model
• modified proportional reversed hazard model

Acknowledgements

Our sincere thanks go to the reviewers for his/her useful comments and suggestions on an earlier version of this manuscript which led to this improved version.

Additional information

Funding

The fourth author thanks University of Zabol for supporting of this work, Grant Number: UOZ-GR: 3566.