We propose a new L2‐type goodness‐of‐fit test for the family of beta distributions based on a conditional moment characterization. The asymptotic null distribution is identified, and since it depends on the underlying parameters, a parametric bootstrap procedure is proposed. Consistency against all alternatives that satisfy a convergence criterion is shown, and a Monte Carlo simulation study indicates that the new procedure outperforms most of the classical tests. Finally, the procedure is applied to a real data set related to air humidity.

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We propose a new L 2 -type goodness-of-fit test for the family of beta distributions based on a conditional moment characterisation. The asymptotic null distribution is identified, and since it depends on the underlying parameters, a parametric bootstrap procedure is proposed. Consistency against all alternatives that satisfy a convergence criterion is shown, and a Monte Carlo simulation study indicates that the new procedure outperforms most of the classical tests. Finally, the procedure is applied to a real data set related to air humidity.

The Rayleigh distribution has recently become popular as a model for a range of phenomena. As a result, a number of goodness-of-fit tests have been developed for this distribution. In this paper, we provide the first overview of goodness-of-fit tests for the Rayleigh distribution and compare these tests in a Monte-Carlo study to identify the tests that provide the highest powers against a wide range of alternatives. Our findings suggest that two recently developed tests as well as a test based on the Laplace transform and a test based on the Hellinger distance are the better performing tests.

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