We derive the efficiencies of two new tests for exponentiality which are based on a recent characterization that uses the idea of a random shift. The finite-sample performance of the newly proposed tests is evaluated and compared to other existing tests by means of Monte Carlo simulations. It is found that the new tests perform favourably when compared to the other tests. Overall the best performing tests seem to be our new Kolmogorov-Smirnov type test, the score function based test by Cox and Oakes, and the Kolmogorov-Smirnov type test based on the mean residual life. The tests are also applied to a real-world data set with i.i.d. data as well as to simulated data from a Cox-proportional hazards model, where we test whether the so-called Cox–Snell residuals follow a standard exponential distribution.

中文翻译：

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基于随机偏移特征的指数性新测试

我们推导出两个新的指数测试的效率，这些测试基于最近使用随机移位概念的表征。新提出的测试的有限样本性能通过蒙特卡罗模拟进行评估并与其他现有测试进行比较。发现与其他测试相比，新测试的表现良好。总体而言，性能最好的测试似乎是我们的新 Kolmogorov-Smirnov 类型测试、Cox 和 Oakes 基于评分函数的测试，以及基于平均剩余寿命的 Kolmogorov-Smirnov 类型测试。这些测试还应用于具有 iid 数据的真实世界数据集以及来自 Cox 比例风险模型的模拟数据，我们在其中测试所谓的 Cox-Snell 残差是否遵循标准指数分布。