Published by the Foundation for Open Access Statistics Editors-in-chief: Bettina Grün, Torsten Hothorn, Edzer Pebesma, Achim Zeileis    ISSN 1548-7660; CODEN JSSOBK
Authors: George Marsaglia, Wai Wan Tsang, Jingbo Wang
Title: Evaluating Kolmogorov's Distribution
Abstract: Kolmogorov's goodness-of-fit measure, Dn , for a sample CDF has consistently been set aside for methods such as the D+n or D-n of Smirnov, primarily, it seems, because of the difficulty of computing the distribution of Dn . As far as we know, no easy way to compute that distribution has ever been provided in the 70+ years since Kolmogorov's fundamental paper. We provide one here, a C procedure that provides Pr(Dn < d) with 13-15 digit accuracy for n ranging from 2 to at least 16000. We assess the (rather slow) approach to limiting form, and because computing time can become excessive for probabilities>.999 with n's of several thousand, we provide a quick approximation that gives accuracy to the 7th digit for such cases.

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Paper: Evaluating Kolmogorov's Distribution     Download PDF (Downloads: 45149)
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DOI: 10.18637/jss.v008.i18

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Code: GNU General Public License (at least one of version 2 or version 3) or a GPL-compatible license.