Ordering results on extremes of scaled random variables with dependence and proportional hazards

ABSTRACT

This study deals with random variables equipped with Archimedean copulas and following scale proportional hazards (SPHs) or revered hazards models. We build the usual stochastic order both between minimums of two SPHs samples with Archimedean survival copulas and between maximums from two scale proportional reversed hazards (PRHs) samples with Archimedean copulas. The hazard rate order between minimums of independent SPHs samples and the reversed hazard rate order between maximums of independent scale PRHs samples are both derived. Also we have a discussion on the dispersive order between minimums from samples with a common Archimedean survival copula. The present results either generalize or improve some related ones in the recent literature.

KEYWORDS:

• Archimedean copula
• dispersive order
• DRHR
• hazard rate order
• IHR
• majorization
• proportional hazards model

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 60E15
• Secondary: 62G30

Acknowledgments

The authors would like to thank the two anonymous reviewers for their valuable comments, which help improve the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Rui Fang http://orcid.org/0000-0001-6569-5462

Additional information

Funding

Dr Fang's research is supported by National Natural Science Foundation of China [11601303] and Guangdong Natural Science Foundation [2016A030310076].