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

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 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.

Keywords:

• Goodness-of-fit
• Rayleigh distribution
• progressively Type-II censored sample
• cumulative residual Kullback-Leibler divergence
• spacings
• one-parameter Weibull distribution

Additional information

Funding

This article has been funded by National Statistical Science Research Project of China (No. 2019LZ32).