A characterization of Exponential Distribution and the Sukhatme-Renyi Decomposition of Exponential Maxima

TL;DR

This paper establishes a new characterization of the exponential distribution and proves that the Sukhatme-Renyi condition is both necessary and sufficient for exponentiality, using a Maclaurin series expansion method.

Contribution

It introduces a new characterization of the exponential distribution and confirms the Sukhatme-Renyi condition as a complete criterion for exponentiality.

Findings

Sukhatme-Renyi condition is sufficient for exponentiality

A new proof method using Maclaurin series expansion is demonstrated

The characterization enhances understanding of exponential distribution properties

Abstract

A new characterization of the exponential distribution is established. It is proven that the well-known Sukhatme-Renyi necessary condition is also sufficient for exponentiality. A method of proof due to Arnold and Villasenor based on the Maclaurin series expansion of the density is utilized.