A characterization of uniform distribution using varextropy with application in testing uniformity
Santosh Kumar Chaudhary, Nitin Gupta
TL;DR
This paper formalizes a varextropy-based approach to characterize uniformity on $[0,1]$ by proving the equivalence $VJ(X)=0 \iff X$ is Uniform$(0,1)$. It introduces a nonparametric estimator $\widehat{VJ}$ of varextropy, proves its consistency under $n\to\infty$, $m\to\infty$, and $m/n\to0$, and uses it to construct a Monte Carlo–based uniformity test with derived critical values and power analysis. The method is evaluated through simulations against Beta-type alternatives and applied to real data after a probability integral transform, illustrating its practical utility for goodness-of-fit testing and uncertainty quantification. The results highlight varextropy as a flexible tool for distribution characterization and hypothesis testing in applied statistics.
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.