On a new positive dependence concept based on the conditional mean inactivity time order

Abstract

In this paper, we introduce a new positive dependence concept between two non negative random variables which is related to a conditional version of the mean inactivity time order. A number of properties and relationship between the new notion and the concept of positive likelihood ratio dependence (PLRD) is discussed. Some results in terms of proposed notions for the Archimedean family of copulas are provided.

KEYWORDS:

• Mean inactivity time (MIT)
• positive likelihood ratio dependence (PLRD)
• stochastic order
• totally positive of order 2 (TP₂)

MATHEMATICS SUBJECT CLASSIFICATION:

• 62H20
• 62N05

Acknowledgments

The authors would like to thank two anonymous referees and Ali Dolati at the department of Statistics of Yazd university for useful comments and suggestions that lead to this improved version of the paper.