Goodness-of-fit test for Rayleigh distribution based on progressively type-II censored sample

Junru Ren and Wenhao Gui

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 16, 3851-3874

Abstract: In this article, we propose several statistics to conduct goodness-of-fit tests for Rayleigh distribution based on progressively Type-II censored data, where a cumulative entropy and its upper and lower bounds as well as the sample spacings are used respectively, and the corresponding statistics are denoted by TE, TU, TL and TS. Especially, the null distribution of TS test statistic is derived. Then the developed methods are extended to the case of one-parameter Weibull model. The respective performance of these statistics is explored against different alternatives, and the power comparisons with some existing goodness-of-fit test statistics are studied via a wide range of Monte Carlo simulations. The results reveal that TS is more effective than the others in most cases; all test statistics have a remarkable performance for the alternative hypothesis with decreasing hazard function. Finally, the proposed statistics are applied in an illustrative example.

Date: 2021
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DOI: 10.1080/03610926.2020.1869988

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