We present new goodness-of-fit tests for the exponential distribution based on equidistribution type characterizations. For the construction of the test statistics, we employ an L 2 -distance between the corresponding V-empirical distribution functions. The resulting test statistics are V-statistics, free of the scale parameter. The quality of the tests is assessed through local Bahadur efficiencies as well as the empirical power for small and moderate sample sizes. According to both criteria, for many common alternatives, our tests perform better than the integral and Kolmogorov-type tests based on the same characterizations.

中文翻译：

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基于 Puri-Rubin 和 Desu 特征的一些一致指数检验

我们提出了基于等分布类型特征的指数分布的新拟合优度检验。为了构建检验统计量，我们在相应的 V 经验分布函数之间采用 L 2 -距离。得到的测试统计量是 V 统计量，没有尺度参数。测试的质量是通过当地的 Bahadur 效率以及中小样本量的经验能力来评估的。根据这两个标准，对于许多常见的替代方案，我们的测试比基于相同特征的积分和 Kolmogorov 型测试执行得更好。