论文标题
基于Kaplan-Meier的测试在审查的存在下指数性
Kaplan-Meier based tests for exponentiality in the presence of censoring
论文作者
论文摘要
在本文中，我们检验了综合假说，即生命值遵循基于观察到的随机右审查数据的指数分布。由于观察到并非所有的生命，因此，该假设对此假设的存在变得复杂。为了解决这一复杂性，我们提出了基于经验特征功能和拉普拉斯变换的测试修改。在完整的样本情况下，这些经验函数可以表示为相对于生命的经验分布功能的积分。我们建议通过Kaplan-Meier估计来替换分布函数的估计值。可以根据观察到的数据的功能总结以易于计算的形式以易于计算的形式表示。此外，在存在随机右审查的情况下，概述了一个通用拟合测试的一般框架。进行了一项蒙特卡洛研究，其结果表明新修饰的测试通常比现有测试的表现优于现有测试。讨论了关于白血病患者初步缓解时间的实际应用，并进行了一些结论性的评论和未来研究的途径。
In this paper we test the composite hypothesis that lifetimes follow an exponential distribution 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 leukemia patients, is discussed along with some concluding remarks and avenues for future research.
