On Arnold-Villasenor Conjectures for Characterizing Exponential Distribution Based on Sample of Size Three

TL;DR

This paper extends previous characterizations of the exponential distribution from samples of size two to size three, providing new theoretical results and an example with simulated data.

Contribution

It proves some of Arnold and Villasenor's conjectures for sample size three, advancing the understanding of exponential distribution characterizations.

Findings

Proved new characterizations for sample size three

Extended previous results from size two to size three

Included an example with simulated data

Abstract

Arnold and Villasenor (2013) obtain a series of characterizations of the exponential distribution based on random samples of size two. These results were already applied in constructing goodness-of-fit tests. Extending the techniques from Arnold and Villasenor (2013), we prove some of the conjectures for samples of size three. An example with simulated data is discussed.