Varextropy measure with application

Document Type : Original Article

Author

• Santosh Kumar Chaudhary

Department of Statistics‎, ‎Central University of Jharkhand‎, ‎Cheri-Manatu‎, ‎Ranchi‎, ‎Jharkhand‎, ‎835222‎, ‎India

10.22067/smps.2025.92576.1044

Abstract

‎‎In statistical analysis, understanding and quantifying uncertainty is fundamental. Measures such as entropy, extropy, varentropy, and varextropy provide valuable insights into the characteristics of probability distributions. ‎ This paper focuses on the concept of varextropy and presents a novel characterization of the uniform distribution, showing that the varextropy of a random variable is zero if and only if the variable is uniformly distributed on the unit interval. Building on this property, we propose a new goodness-of-fit test for uniformity based on a nonparametric estimator of varextropy, denoted by \( \widehat{\Delta} \)‎, as introduced by Noughabi and Noughabi (2024). ‎‎‎The test statistic is shown to be consistent‎, ‎and its distribution under the null hypothesis is explored via Monte Carlo simulations‎. ‎Critical values are tabulated for various sample sizes and tuning parameters, and the test’s power is empirically evaluated against alternatives such as the Beta(1,2) distribution, demonstrating superior performance in detecting departures from uniformity. The proposed method is further applied to a real-world environmental dataset of vinyl chloride concentrations, where the transformed data, via the probability integral transform, are shown to conform to a uniform distribution. ‎Overall‎, ‎this study not only extends the theoretical understanding of varextropy but also introduces a practical and effective tool for uniformity testing in both simulated and real data contexts‎.

Keywords

• ‎Entropy
• Extropy
• ‎Goodness-of-fit
• ‎Monte Carlo simulation‎
• ‎Nonparametric estimator
• ‎Order statistics
• ‎Uniformity test
• ‎Varextropy

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