AISM 54, 577-584
© 2002 ISM

Beta approximation to the distribution of Kolmogorov-Smirnov statistic

Jin Zhang and Yuehua Wu

Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3

(Received July 21, 2000; revised April 9, 2001)

Abstract.    The distribution of Kolmogorov-Smirnov statistic can be globally approximated by a general beta distribution. The approximation is very simple and accurate. It can be easily implemented in any statistical software. Therefore, we can use a beta distribution to find the practical $p$-value of a goodness-of-fit test, which is much simpler than existing methods in the literature.

Key words and phrases:    Kolmogorov-Smirnov statistic, beta distribution, approximation, skewness, kurtosis, $p$-value.

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