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

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 T-E, T-U, T-L and T-S. Especially, the null distribution of T-S 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 T-S 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.