On goodness-of-fit tests for the Rayleigh distribution based on the Stein characterisation

Abstract

In this mini-dissertation, two new goodness-of- t tests for the Rayleigh distribution are proposed. These tests are developed by exploiting the Stein characterisation of the Rayleigh distribution. The newly suggested tests are compared with the traditional tests as well as with some more modern tests by making use of a Monte Carlo simulation. The traditional tests include the Kolmogorov-Smirnov, Anderson-Darling and Cram er-von Mises tests. A test based on the empirical Laplace transform and a test based on the cumulative residual entropy are the two modern tests considered. When the powers of the respective tests are compared it can be seen that the newly proposed tests are not only feasible but also very competitive. The results further indicate that the new tests outperform the other tests for most of the alternatives considered in the study. We also provide a proof of the consistency of one of our new tests, as well as a theoretical justi cation for the choice of our weight function.