City Research Online

Abstract

We develop an efficient recurrence method for computing p-values of the two sample KS test. A similar method but for the unweighted KS test has been previously considered in the literature, without theoretical justification. We provide such justification., showing that the difference between the p-values of the permutation KS test and the KS test is asymptotically negligible; A flexible choice of the KS weight function is allowed, leading to better power; The method is extended to compute p-values of the two sample Kuiper test, thus covering the case of data with ties We also derive a closed-form expression for the asymptotic distribution of the two-sample KS test, assuming jumps in the null distribution and illustrate its efficiency in computing p-values. We provide an extensive overview of existing statistical software for computing KS and Kuiper p-values and compare with our proposed R functions KS2sample and Kuiper2sample, demonstrating their superior performance.

Publication Type:	Article
Additional Information:	© 2026 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent.
Publisher Keywords:	Kolmogorov-Smirnov test, Kuiper test, p-value, asymptotic distribution, statistical power
Subjects:	H Social Sciences > HA Statistics
Departments:	Bayes Business School Bayes Business School > Faculty of Actuarial Science & Insurance
SWORD Depositor:	Symplectic Administrator

Export

Downloads