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

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  • Gerrit Lodewicus Grobler

    (School of Mathematical and Statistical Sciences, Faculty of Natural and Agricultural Sciences, North-West University, Potchefstroom 2531, South Africa)

  • Elzanie Bothma

    (School of Mathematical and Statistical Sciences, Faculty of Natural and Agricultural Sciences, North-West University, Potchefstroom 2531, South Africa)

  • James Samuel Allison

    (School of Mathematical and Statistical Sciences, Faculty of Natural and Agricultural Sciences, North-West University, Potchefstroom 2531, South Africa)

Abstract

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.

Suggested Citation

  • Gerrit Lodewicus Grobler & Elzanie Bothma & James Samuel Allison, 2022. "Testing for the Rayleigh Distribution: A New Test with Comparisons to Tests for Exponentiality Based on Transformed Data," Mathematics, MDPI, vol. 10(8), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1316-:d:794439
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    References listed on IDEAS

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    1. Ludwig Baringhaus & Norbert Henze, 1991. "A class of consistent tests for exponentiality based on the empirical Laplace transform," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(3), pages 551-564, September.
    2. Simos Meintanis & George Iliopoulos, 2003. "Tests of fit for the Rayleigh distribution based on the empirical Laplace transform," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(1), pages 137-151, March.
    3. Norbert Henze & Simos G. Meintanis, 2005. "Recent and classical tests for exponentiality: a partial review with comparisons," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(1), pages 29-45, February.
    4. Hadi Alizadeh Noughabi, 2015. "Empirical likelihood ratio-based goodness-of-fit test for the logistic distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(9), pages 1973-1983, September.
    5. James S. Allison & Charl Pretorius, 2017. "A Monte Carlo evaluation of the performance of two new tests for symmetry," Computational Statistics, Springer, vol. 32(4), pages 1323-1338, December.
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