Nonparametric Estimation of Extropy, Rényi Extropy, and Tsallis Extropy: Almost Sure Convergence and Asymptotic Normality

Abstract

This paper proposes a nonparametric estimation procedure for extropy and its extensions, namely the α-Rényi and α-Tsallis extropies, for finite discrete random variables. We establish almost sure rates of convergence and asymptotic normality for the plug-in estimators. The theoretical results are validated through a comprehensive simulation study. The findings provide a solid foundation for the use of extropy-based measures in practical applications, including forecasting, risk assessment, and decision-making under uncertainty.

19 pages, 5 figures. Submitted to a journal for publication. Companion paper on finite-sample bias correction also available