Article citationsMore>>

Durbin, J. (1973) Distribution Theory for Tests Based on the Sample Distribution Function. Society for Industrial and Applied Mathematics, Philadelphia.
https://doi.org/10.1137/1.9781611970586

has been cited by the following article:

• TITLE: Deriving CDF of Kolmogorov-Smirnov Test Statistic

  AUTHORS: Jan Vrbik

  KEYWORDS: Kolmogorov-Smirnov Test, Asymptotic Distributions, Generating Functions, Jacobi Theta

  JOURNAL NAME: Applied Mathematics, Vol.11 No.3, March 17, 2020

  ABSTRACT: 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.