Three Characterizations of Exponential Distribution Involving Median of Sample of Size Three

TL;DR

This paper introduces three new theorems that characterize the exponential distribution using functions of order statistics, specifically involving the median of a sample of size three, advancing the understanding of distribution properties.

Contribution

The paper presents novel characterizations of the exponential distribution based on the median of three sample points, expanding existing distribution characterization methods.

Findings

Three new theorems characterizing exponential distribution

Characterizations involve equidistribution of functions of order statistics

Results enhance understanding of distribution properties using median of size three

Abstract

In this paper three new characterizing theorems of exponential distribution are presented. They are based on equidistribution of some functions of order statistics. All of them include the median of sample of size three.