On Generalized Reversed Aging Intensity Functions

TL;DR

This paper introduces a family of generalized reversed aging intensity functions that depend on a parameter, providing new tools to analyze aging properties of distributions and defining related orderings.

Contribution

It proposes a novel family of reversed aging intensity functions parameterized by a real number, extending the analysis of aging properties and distribution characterization.

Findings

Characterizes distribution functions for positive absolutely continuous variables when parameter is positive.

Defines and studies generalized reversed aging intensity orders.

Provides numerical examples illustrating the theoretical concepts.

Abstract

The reversed aging intensity function is defined as the ratio of the instantaneous reversed hazard rate to the baseline value of the reversed hazard rate. It analyzes the aging property quantitatively, the higher the reversed aging intensity, the weaker the tendency of aging. In this paper, a family of generalized reversed aging intensity functions is introduced and studied. Those functions depend on a real parameter. If the parameter is positive they characterize uniquely the distribution functions of univariate positive absolutely continuous random variables, in the opposite case they characterize families of distributions. Furthermore, the generalized reversed aging intensity orders are defined and studied. Finally, several numerical examples are given.