Characterizations of Exponential Distribution Based on Two-Sided Random Shifts

TL;DR

This paper introduces a novel characterization of the exponential distribution using equations involving two-sided random shifts of order statistics, without assuming specific distributions for the shifts, employing Maclaurin series expansion techniques.

Contribution

It provides a new characterization of exponential distribution based on random shifts of order statistics without distribution assumptions for the shifts.

Findings

New characterization of exponential distribution established

Technique involves Maclaurin series expansion of density functions

No assumptions on shift distributions

Abstract

A new characterization of the exponential distribution is obtained. It is based on an equation involving randomly shifted (translated) order statistics. No specific distribution is assumed for the shift random variables. The proof uses a recently developed technique including the Maclaurin series expansion of the probability density of the parent variable.