Lack-of-partial-memory and aging properties of multivariate generalized Marshall-Olkin distributions

Abstract

This article finds that multivariate generalized Marshall-Olkin distributions are of the lack-of-partial-memory property in the sense of residual lifetimes of elder components being independent of those younger ones’ ages. Also, we further investigate aging behavior and stochastic dependence of the multivariate residual lifetime of this family of random vectors.

Keywords:

• Dependence function
• IHR
• lack-of-partial-memory
• residual lifetime
• upper orthant order

Acknowledgments

The authors are indebt to the two anonymous reviewers. They read through the original version with great patience and bring forth insightful comments and pertinent suggestions, which substantially improved the presentation of this article.

Funding

Dr. Jianhua Lin’s research is financially supported by Fundamental Research Funds for the Central Universities of China (20720170003).