On new goodness-of-fit tests for the Rayleigh distribution

Abstract

The Rayleigh distribution has been observed in numerous processes across multiple research disciplines. It has therefore become increasingly important to test if a specific data set originated from this distribution. Goodness-of-fit tests developed specifically for the Rayleigh distribution have become more researched over the past 10 years and there is no consensus on which test performs best in certain situations. The primary aim of this thesis is to develop new goodness-of-fit tests for the Rayleigh distribution. We propose several novel tests based on diff erent approaches, the first of which is a conditional expectation characterization. The second approach deals with a differential equation that has the Rayleigh density function as the unique solution and the third approach is based on the Mellin transform. The asymptotic theory of some of the newly proposed tests are developed and the finite-sample performance of the new tests are compared to that of existing tests in an extensive Monte Carlo simulation study. In the simulation study, the tests are compared against several alternative distributions that are commonly used as alternatives for the Rayleigh distribution, as well as against two mixture distributions to assess the power performance with respect to local alternatives. When the power estimates of the goodness-of-fit tests are considered, it is clear that the newly developed tests are very competitive and tend to outperform or match the competitor tests that are considered in this study.