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.

摘要

在本文中，我们提出了几种统计数据来对基于渐进式 II 型删失数据的瑞利分布进行拟合优度检验，其中分别使用累积熵及其上下界和样本间距，以及相应的统计量由T _E、T _U、T _L和T _{S 表示}。特别是，T _S的零分布导出检验统计量。然后将开发的方法扩展到单参数威布尔模型的情况。针对不同的替代方案探索了这些统计量的各自性能，并通过广泛的蒙特卡罗模拟研究了与一些现有拟合优度测试统计量的功效比较。结果表明，在大多数情况下，T _S比其他的更有效；所有检验统计量对于风险函数递减的备择假设都有显着的表现。最后，在一个说明性示例中应用了建议的统计数据。