ABSTRACT
Goodness-of-fit tests are designed to test a null hypothesis that some given data are a random sample from a specified probability distribution. The Kolmogorov-Smirnov tests are based on the maximum absolute difference Dn between the c.d.f. (cumulative distribution function) F0(x) of the hypothesised distribution and the c.d.f. of the sample (sometimes called the empirical c.d.f.) Fn(x). This sample c.d.f. is the step-function which starts at 0 and rises by 1/n at each observed value, where n is the sample size; i.e. Fn(x) is equal to the proportion of the sample values which are less than or equal to x.
