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Illustration of the Kolmogorov–Smirnov statistic. The red line is a model CDF, the blue line is an empirical CDF, and the black arrow is the KS statistic.. In statistics, the Kolmogorov–Smirnov test (also K–S test or KS test) is a nonparametric test of the equality of continuous (or discontinuous, see Section 2.2), one-dimensional probability distributions.
Lilliefors test is a normality test based on the Kolmogorov–Smirnov test.It is used to test the null hypothesis that data come from a normally distributed population, when the null hypothesis does not specify which normal distribution; i.e., it does not specify the expected value and variance of the distribution. [1]
Confidence bands can be constructed around estimates of the empirical distribution function.Simple theory allows the construction of point-wise confidence intervals, but it is also possible to construct a simultaneous confidence band for the cumulative distribution function as a whole by inverting the Kolmogorov-Smirnov test, or by using non-parametric likelihood methods.
Together with Andrey Kolmogorov, Smirnov developed the Kolmogorov–Smirnov test and participated in the creation of the Cramér–von Mises–Smirnov criterion.. Smirnov made great efforts to popularize and widely disseminate methods of mathematical statistics in the natural sciences and engineering.
Most theoretical studies of minimum-distance estimation, and most applications, make use of "distance" measures which underlie already-established goodness of fit tests: the test statistic used in one of these tests is used as the distance measure to be minimised. Below are some examples of statistical tests that have been used for minimum ...
Kolmogorov's theorem is any of several different results by Andrey Kolmogorov: In statistics. Kolmogorov–Smirnov test; In probability theory. Hahn–Kolmogorov theorem; Kolmogorov extension theorem; Kolmogorov continuity theorem; Kolmogorov's three-series theorem; Kolmogorov's zero–one law; Chapman–Kolmogorov equations; Kolmogorov ...
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