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.