In statistics, the Kolmogorov-Smirnov test is used to determine whether two empirical distributions are different or whether an empirical distribution differs from a theoretical distribution.
The empirical cumulative distribution for n observations yi is defined as E(x) = Σ i (yi < x). The two one-sided Kolmogorov-Smirnov test statistics statistics are given by
Note that when the underlying independent variable is cyclic, as with day of the year or day of the week, then Kuiper's test is more appropriate. Numerical Recipes is a good source of information on this. Note furthermore, that the Kolmogorov-Smirnov test is more sensitive at points near the median of the distribution than on its tails. The Anderson-Darling test is a test that provides equal sensitivity at the tails.
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