Testing uniformity based on new entropy estimators

Abstract

In this paper, we first introduce new entropy estimators for distributions with known and bounded supports. Our estimators are obtained by using constrained maximum likelihood estimation of cumulative distribution function for absolutely continuous distributions with known and bounded supports. We prove the consistency of our estimators. Then, we propose uniformity tests based on the proposed entropy estimators and compare their powers with the powers of other tests of uniformity. Our simulation results show that the proposed entropy estimators perform well in estimating entropy and testing uniformity.