In this paper, the composite hypothesis that lifetimes follow an exponential distribution is tested based on observed randomly right censored data. Testing this hypothesis is complicated by the presence of this censoring, due to the fact that not all lifetimes are observed. To account for this complication, we propose modifications to tests based on the empirical characteristic function and Laplace transform. In the full sample case, these empirical functions can be expressed as integrals with respect to the empirical distribution function of the lifetimes. We propose replacing this estimate of the distribution function by the Kaplan–Meier estimate. The resulting test statistics can be expressed in easily calculable forms in terms of summations of functionals of the observed data. Additionally, a general framework for goodness-of-fit testing, in the presence of random right censoring, is outlined. A Monte Carlo study is performed, the results of which indicate that the newly modified tests generally outperform the existing tests. A practical application, concerning initial remission times of leukaemia patients, is discussed along with some concluding remarks and avenues for future research.

中文翻译：

---

存在随机右删失的特征函数和基于拉普拉斯变换的指数检验

在本文中，基于观察到的随机右删失数据检验了寿命服从指数分布的复合假设。由于并非所有生命周期都被观察到，这种审查的存在使测试这个假设变得复杂。为了解决这种复杂性，我们建议对基于经验特征函数和拉普拉斯变换的测试进行修改。在完整样本的情况下，这些经验函数可以表示为关于寿命经验分布函数的积分。我们建议用 Kaplan-Meier 估计代替这个分布函数估计。根据观察数据的泛函总和，可以以易于计算的形式表示得到的测试统计量。此外，拟合优度测试的一般框架，在随机右删失的情况下，概述了。执行蒙特卡罗研究，其结果表明新修改的测试通常优于现有测试。讨论了关于白血病患者初始缓解时间的实际应用，以及一些结论和未来研究的途径。