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On a new test of fit to the beta distribution. Stat. 2021; 10:e341. https://doi.org/10.1002/sta4.341, .
The beta distribution is a key distribution for modeling data in the unit interval as relative frequency data or random probabilities. Due to its two shape parameters it is a versatile distribution and therefore it is found in a variety of research areas such as meteorology, geology and communication theory. Prior to serious statistical inference by a beta model, one should check the goodness-of-fit of the data to this parametric probability law. In the present paper the authors propose a new goodness-of-fit test for the composite hypothesis of the data belonging to the family of beta distributions based on a conditional moment characterization of the beta law. The authors theoretically derive that the test statistic converges to an asymptotic null distribution and that the testing procedure is consistent against general alternatives. Since the null distribution depends on both of the unknown shape parameters, a bootstrap procedure is proposed to simulate appropriate critical values. A Monte Carlo simulation study shows the performances of the new test statistic in competition to classical and recent tests for the beta distribution. It is found that the newly proposed test is a strong competitor to the existing procedures and even outperforms most of the other tests for the considered alternatives. Finally, the test is applied to a real data set related to air humidity and it is shown that the new test successfully identifies the data that is beta distributed.More Details