1972•Journal of the American Statistical AssociationRequires access

A Kolmogorov Goodness-of-Fit Test for Discontinuous Distributions

W. J. Conover

Abstract

The Kolmogorov goodness-of-fit test is known to be conservative when the hypothesized distribution function is not continuous. A method for finding the exact critical level (approximate in the two-sided case) and the power in such cases is derived. Thus the Kolmogorov test may be used as an exact goodness-of-fit test for all completely specified distribution functions, whether continuous or not continuous. Several examples of the application of this extension of the Kolmogorov test are also included.

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Key concepts: Kolmogorov–Smirnov test, Goodness of fit, Mathematics, Anderson–Darling test, Kolmogorov equations (Markov jump process), Kolmogorov structure function, Test (biology), Extension (predicate logic)