Deriving CDF of Kolmogorov-Smirnov Test Statistic

• 作者: Jan Vrbik
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: KOLMOGOROV-SMIRNOV Test ASYMPTOTIC DISTRIBUTIONS GENERATING Functions JACOBI THETA
• 年，卷（期）: 2020,（3）
• 页码范围: 227-246
• 页数: 20页
• 分类号: O17

摘要

In this review article, we revisit derivation of the cumulative density function (CDF) of the test statistic of the one-sample Kolmogorov-Smirnov test. Even though several such proofs already exist, they often leave out essential details necessary for proper understanding of the individual steps. Our goal is filling in these gaps, to make our presentation accessible to advanced undergraduates. We also propose a simple formula capable of approximating the exact distribution to a sufficient accuracy for any practical sample size.