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.

**Source**
(TeX , DVI )