Inactivity stochastic precedence order

Abstract

The aim of this article is to extend the inactivity probability order, defined by Abouelmagd et al. (Communications in Statistics-Theory and Methods 47, 3293–3304, 2018), to the case of non independent random variables. It is done by defining a new stochastic order based on the inactivity times of two non negative dependent random variables and the stochastic precedence order. Some characterizations and preservation properties of the new stochastic order have been developed. Also, some of its reliability properties and its relation with the other existing well known stochastic orders have been studied. We also discuss some applications of the derived results.

Keywords:

• Inactivity time
• univariate stochastic orders
• inactivity probability order
• stochastic precedence order
• joint weak reversed hazard rate order

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E15
• 62N05
• 60E05

Acknowledgment

We wish to express our thanks to Prof. Neeraj Misra for suggesting the idea of the inactivity stochastic precedence order. The authors are very thankful to the anonymous referees for their fruitful comments and suggestions which have resulted in a significant improvement of the article. The second author acknowledges the financial support received from the UGC, India and the third author also acknowledges the financial assistance from the RGNF, India.