A density-based empirical likelihood ratio goodness-of-fit test for the Rayleigh distribution and power comparison

Abstract

The Rayleigh distribution has been used to model right skewed data. Rayleigh [On the resultant of a large number of vibrations of the some pitch and of arbitrary phase. Philos Mag. 1880;10:73–78] derived it from the amplitude of sound resulting from many important sources. In this paper, a new goodness-of-fit test for the Rayleigh distribution is proposed. This test is based on the empirical likelihood ratio methodology proposed by Vexler and Gurevich [Empirical likelihood ratios applied to goodness-of-fit tests based on sample entropy. Comput Stat Data Anal. 2010;54:531–545]. Consistency of the proposed test is derived. It is shown that the distribution of the proposed test does not depend on scale parameter. Critical values of the test statistic are computed, through a simulation study. A Monte Carlo study for the power of the proposed test is carried out under various alternatives. The performance of the test is compared with some well-known competing tests. Finally, an illustrative example is presented and analysed.

Keywords:

• density-based empirical likelihood
• Anderson–Darling statistic
• Cramer–von Mises statistic
• Kolmogorov–Smirnov statistic
• Kuiper statistic
• Watson statistic
• goodness-of-fit test
• Rayleigh distribution

Mathematics Subject Classification:

• 62G10
• 62G20
• 62G30

Acknowledgements

The authors thank the associate editor and an anonymous referee for suggestions that helped very much to improve this article.