Testing for the Rayleigh Distribution: A New Test with Comparisons to Tests for Exponentiality Based on Transformed Data

Mathematics

Elzanie Bothma¹  James Samuel Allison¹  Gerrit Lodewicus Grobler¹ 

[1] School of Mathematical and Statistical Sciences, Faculty of Natural and Agricultural Sciences, North-West University, Potchefstroom 2531, South Africa;

关键词: asymptotics;    goodness-of-fit;    Monte Carlo simulation;    Rayleigh distribution;    Stein characterization;   

DOI  :  10.3390/math10081316

来源: DOAJ

【 摘 要 】

We propose a new goodness-of-fit test for the Rayleigh distribution which is based on a distributional fixed-point property of the Stein characterization. The limiting null distribution of the test is derived and the consistency against fixed alternatives is also shown. The results of a finite-sample comparison is presented, where we compare the power performance of the new test to a variety of other tests. In addition to existing tests for the Rayleigh distribution we also exploit the link between the exponential and Rayleigh distributions. This allows us to include some powerful tests developed specifically for the exponential distribution in the comparison. It is found that the new test outperforms competing tests for many of the alternative distributions. Interestingly, the highest estimated power, against all alternative distributions considered, is obtained by one of the tests specifically developed for the Rayleigh distribution and not by any of the exponentiality tests based on the transformed data. The use of the new test is illustrated on a real-world COVID-19 data set.

【 授权许可】

Unknown