A characterization of uniform distribution using varextropy with application in testing uniformity

TL;DR

This paper introduces a new characterization of the uniform distribution using varextropy, develops a uniformity test based on this characterization, and evaluates its performance through theoretical derivations and real-world data application.

Contribution

It provides the first characterization of uniform distribution via varextropy and proposes a new statistical test for uniformity based on this property.

Findings

The test effectively distinguishes uniform from non-uniform distributions.

Critical values and power of the test are analytically derived.

Application to real data demonstrates the test's practical utility.

Abstract

In statistical analysis, quantifying uncertainties through measures such as entropy, extropy, varentropy, and varextropy is of fundamental importance for understanding distribution functions. This paper investigates several properties of varextropy and give a new characterization of uniform distribution using varextropy. The alredy proposed estimators are used as a test statistics. Building on the characterization of the uniform distribution using varextropy, we give a uniformity test. The critical value and power of the test statistics are derived. The proposed test procedure is applied to a real-world dataset to assess its performance and effectiveness.