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Evaluating Kolmogorov's Distribution
Open accessAbstract
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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Numerical Tabulation of the Distribution of Kolmogorov's Statistic for Finite Sample Size
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Computing the cumulative distribution function of the Kolmogorov–Smirnov statistic
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Metadata
- Authors
- Marsaglia, G., Tsang, W. W., & Wang, J.
- Venue
- Journal of Statistical Software
- Publisher
- Foundation for Open Access Statistic
- Published
- 2003
- Volume
- 8
- Issue
- 18
- ISSN
- 1548-7660 (ISSN-L)
- OpenAlex
- W1623768750
- Cited by
- 979
- References
- 5
- FWCI
- 2.61
- Type
- journal article
- Language
- en
- Open access
- diamond
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