Some More Results on Characterization of the Exponential Distribution

TL;DR

This paper explores new characterizations of the exponential distribution through properties of independence in linear forms with random coefficients and regression constancy, expanding understanding of its statistical properties.

Contribution

It introduces novel characterizations of the exponential distribution based on independence and regression properties, extending previous theoretical results.

Findings

Characterizations via independence of linear forms with random coefficients

Results based on regression constancy of statistics

Enhanced understanding of exponential distribution properties

Abstract

There are given characterizations of the exponential distribution by the properties of the independence of linear forms with random coefficients. Related results based on the constancy of regression of one statistic on a linear form are obtained.