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Recently, Di Crescenzo and Paolillo [Di Crescenzo A, Paolillo L. Analysis and applications of the residual varentropy of random lifetimes. Probab Eng Informational Sci. 2021;35(3):680–698] and Maadani et al. [Maadani S, Mohtashami Borzadaran GR, Rezaei Roknabadi AH. Varentropy of order statistics and some stochastic comparisons. Commun Stat - Theory Methods. 2021;51(18):6447–6460.] presented the applications of varentropy in reliability theory. The present article introduces some estimators of the varentropy of a continuous random variable. Properties of the proposed estimators are stated, and comparisons are made in terms of the mean squared error. Then, the proposed estimators are applied and some tests for uniformity are constructed. Percentage points and power values of the tests against seven alternatives are reported. The results of a simulation study show that the tests have good performance in terms of power.

Varentropy estimators with applications in testing uniformity