Nonparametric probability density functions of entropy estimators applied to testing the Rayleigh distribution

Abstract

The Rayleigh distribution is widely used to model right skewed data and therefore it is important to develop efficient goodness of fit tests for this distribution. In this article, we introduce some new test statistics for examining the Rayleigh goodness of fit based on correcting moments of nonparametric probability density functions of entropy estimators. Critical points and power of the tests are explored by simulation. We show that the proposed tests are more powerful than competitor tests. Finally, the proposed tests are illustrated by a real data example.