Probability models characterized by generalized reversed lack of memory property

TL;DR

This paper characterizes a subclass of the reversed generalized Pareto distribution and related probability models using a generalized reversed lack of memory property, extending to bivariate cases.

Contribution

It introduces a new characterization of probability distributions via a generalized reversed lack of memory property using an associative binary operator.

Findings

Characterization of a subclass of reversed generalized Pareto distribution

Extension of the property to bivariate distributions

Generalization of probability models using the binary operator

Abstract

A binary operator * over real numbers is said to be associative if $(x*y)*z=x*(y*z)$ and is said to be reducible if $x*y=x*z$ or $y*w=z*w$ if and only if $z=y$. The operation is said to have an identity element $\tilde{e}$ if $x*\tilde{e}=x$. In this paper a characterization of a subclass of the reversed generalized Pareto distribution (Castillo and Hadi (1995)) in terms of the reversed lack of memory property (Asha and Rejeesh (2007)) is generalized using this binary operation and probability distributions are characterized using the same. This idea is further generalized to the bivariate case.