Evaluating Kolmogorov's distribution

By George Marsaglia, Wai Wan Tsang, Jingbo Wang. 2003

879 citations recorded by the source corpus.

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

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/fd8325fd834e55dd6303380cc7138d79e99e3051

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In Computational Theory and Mathematics

Citations in the corpus

The Modifled Tempered Stable Distribution, GARCH Models and Option Pricing (2008, neutral): “[14].”
Weighted-permutation entropy: a complexity measure for time series incorporating amplitude information. (2013, neutral): “The null hypothesis is rejected at the α-level if √ (n1n2)/(n1 + n2)Sγ1,γ2 > Kα, where n1 and n2 denote the number of samples from each observation vector and K refers to the Kolmogorov distribution [18].”
A Kolmogorov-Smirnov Based Test for Comparing the Predictive Accuracy of Two Sets of Forecasts (2015, neutral): “See for example, [27–29].”
Tempered stable and tempered infinitely divisible GARCH models (2010, methodology): “The p-values of the KS statistic are calculated using the calculator designed by Marsaglia et al. (2003). Based on the results reported in the table, we conclude that”
Evaluating the Anderson-Darling Distribution (2004, methodology): “But there is some support for Lewis’s confidence: the approach is more rapid than that for the limiting form of Kolmogorov’s distribution, which has worst error of about .278/ √ n, also around the 33rd percentile [6].”
Description and validation of a two-step analogue/regression downscaling method (2013, methodology): “In this respect, two nonparametric tests were performed: the Kolmogorov–Smirnov test with a bootstrap treatment (KS; Marsaglia et al. 2003; Sekhon 2010) and the Anderson–Darling test (Scholz and”
Rational Arithmetic Mathematica Functions to Evaluate the One-sided One-sample K-S Cumulative Sample Distribution (2007, methodology): “Using the formula above, Marsaglia, Tsang, and Wang (2003) developed a double precision C program that for sample size n = 16, 000 and test statistic t = 171.9008 (d = t/n = 0.0107438) computes P (D16,000 ≤ 0.0107438) = 0.95060023909487545.”
Normalization of the Kolmogorov–Smirnov and Shapiro–Wilk tests of normality (2015, methodology): “…3 and the Kolmogorov–Smirnov test in Case 1 is not very interesting, because there exist other procedures giving p-values (Royston, 1992 for the Shapiro–Wilk and Marsaglia et al., 2003 for the Kolmogorov–Smirnov test), we give only an illustration of the Kolmogorov–Smirnov test for Cases 2 and 3.”
Tales from tails: On the empirical distributions of forecasting errors and their implication to risk (2019, methodology): “In this study, a two-sample Kolmogorov-Smirnov test (Marsaglia et al., 2003) is used to compare the distance between the Empirical Cumulative Distribution Function (ECDF) of the transformed data and a normal one N ( u BC , σ 2 u BC ).”