Inequalities involving expectations of selected functions in reliability theory to characterize distributions

TL;DR

This paper explores inequalities involving expectations of functions like reversed hazard rate and expected inactivity time for right truncated variables, aiding in distribution characterization in reliability theory.

Contribution

It introduces new inequalities involving reversed time functions for right truncated variables, expanding distribution characterization methods in reliability analysis.

Findings

Derived inequalities for reversed hazard rate and related functions.

Characterized several distributions using these inequalities.

Extended previous work from left to right truncated variables.

Abstract

Recently, authors have studied inequalities involving expectations of selected functions viz. failure rate, mean residual life, aging intensity function and log-odds rate which are defined for left truncated random variables in reliability theory to characterize some well-known distributions. However, there has been growing interest in the study of these functions in reversed time and their applications. In the present work we consider reversed hazard rate, expected inactivity time and reversed aging intensity function to deal with right truncated random variables and characterize a few statistical distributions.