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Biometrika 1971 58(3):653-656; doi:10.1093/biomet/58.3.653
© 1971 by Biometrika Trust
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On Kolmogorov-Smirnov type one-sample statistics

URS R. MAAG and GHISLAINE DICAIRE

Universitá de Montréal

Asymptotic expansions with a term in n–1/2 of the distributions of Pyke's modified one-sample Kolmogorov-Smirnov statistics, C+n, C–n and Cn are derived. From these expansions and the already known ones for D+n, D–n, Dn, Vn = D+n + D–n and Kn = C+n + C–n are deduced expansions for the percentage points. The approximate percentage points determined by these expansions are sufficiently accurate to be used in applications.

Key Words: Kolmogorov-Smirnov statistics • Goodness of fit • Asymptotic expansions • Percentage points.


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