On Some Generalized Orderings: In the Spirit of Relative Ageing

TL;DR

This paper introduces new generalized stochastic orderings related to relative ageing, aiding the comparison of distributions with exponential models, especially in cases of crossing hazard rates and mean residual lives.

Contribution

It presents novel generalized orderings in the context of relative ageing, with characterizations and inter-relations, enhancing understanding of positive ageing classes.

Findings

New stochastic orderings introduced and characterized.

Inter-relations among the orderings established.

Applications to crossing hazard rates and mean residual lives.

Abstract

We introduce some new generalized stochastic orderings (in the spirit of relative ageing) which compare probability distributions with the exponential distribution. These orderings are useful to understand the phenomenon of positive ageing classes and also helpful to guide the practitioners when there are crossing hazard rates and/or crossing mean residual lives. We study some characterizations of these orderings. Inter-relations among these orderings have also been discussed.