文章基本信息

标题：Rational Arithmetic Mathematica Functions to Evaluate the Two-Sided One Sample K-S Cumulative Sampling Distribution
本地全文：下载
作者：J. Randall Brown ; Milton E. Harvey
期刊名称：Journal of Statistical Software
印刷版ISSN：1548-7660
电子版ISSN：1548-7660
出版年度：2008
卷号：26
期号：1
页码：1-40
语种：English
出版社：University of California, Los Angeles
摘要：One of the most widely used goodness-of-fit tests is the two-sided one sample Kolmogorov-Smirnov (K-S) test which has been implemented by many computer statistical software packages. To calculate a two-sided p value (evaluate the cumulative sampling distribution), these packages use various methods including recursion formulae, limiting distributions, and approximations of unknown accuracy developed over thirty years ago. Based on an extensive literature search for the two-sided one sample K-S test, this paper identifies an exact formula for sample sizes up to 31, six recursion formulae, and one matrix formula that can be used to calculate a p value. To ensure accurate calculation by avoiding catastrophic cancelation and eliminating rounding error, each of these formulae is implemented in rational arithmetic. For the six recursion formulae and the matrix formula, computational experience for sample sizes up to 500 shows that computational times are increasing functions of both the sample size and the number of digits in the numerator and denominator integers of the rational number test statistic. The computational times of the seven formulae vary immensely but the Durbin recursion formula is almost always the fastest. Linear search is used to calculate the inverse of the cumulative sampling distribution (find the confidence interval half-width) and tables of calculated half-widths are presented for sample sizes up to 500. Using calculated half-widths as input, computational times for the fastest formula, the Durbin recursion formula, are given for sample sizes up to two thousand.