Abstract

In this article we derive the exact null distribution of a class of Hollander-Proschan type statistics for testing exponentiality against NWBUE alternatives. The exact null distribution of a previously established statistic is obtained as a special case. Critical values are tabulated for different combinations of parameter values. Performance of the tests for small sample sizes has also been studied in various alternative scenarios. We analyse two wellknown data sets in the light of our result.

中文翻译：

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关于广义 Hollander-Proschan 类型统计量的精确分布

摘要

在本文中，我们推导出了一类 Hollander-Proschan 类型统计量的精确零分布，用于测试 NWBUE 替代方案的指数。先前建立的统计量的精确零分布是作为特例获得的。针对参数值的不同组合列出了临界值。在各种替代方案中也研究了小样本量的测试性能。我们根据我们的结果分析了两个众所周知的数据集。