Deriving CDF of Kolmogorov-Smirnov Test Statistic  

作　　者：Jan Vrbik 

机构地区：[1]Department of Mathematics and Statistics, Brock University, St. Catharines, Ontario, Canada

出　　处：《Applied Mathematics》2020年第3期227-246,共20页应用数学（英文）

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.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.

关 键 词：KOLMOGOROV-SMIRNOV Test ASYMPTOTIC DISTRIBUTIONS GENERATING Functions JACOBI THETA 

分 类 号：O17[理学—数学]