Abstract

Kaplan and Meier’s 1958 article developed a nonparametric estimator of the survivor function from a right-censored dataset. Determining the size of the support of the estimator as a function of the sample size provides a challenging exercise for students in an advanced course in mathematical statistics. We devise two algorithms for calculating the support size and calculate the associated probability mass function for small sample sizes and particular probability distributions for the failure and censoring times.

中文翻译：

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Kaplan–Meier 乘积极限估计器的概率质量函数

摘要

Kaplan 和 Meier 在1958 年的文章中开发了一个来自右删失数据集的幸存者函数的非参数估计量。确定作为样本大小函数的估计量的支持大小为数理统计高级课程的学生提供了一项具有挑战性的练习。我们设计了两种算法来计算支持大小，并计算小样本的相关概率质量函数和失败和审查时间的特定概率分布。