KolmogorovSmirnovin

KolmogorovSmirnovin is not a standard term in statistics. In most sources, the concept is referred to as the Kolmogorov–Smirnov test (KS test), named after Andrey Kolmogorov and Nikolai Smirnov. When encountered as a single word, KolmogorovSmirnovin is usually a nonstandard or stylistic rendering that points to the same idea, rather than a distinct, widely recognized method.

The Kolmogorov–Smirnov test is a nonparametric method used for goodness-of-fit testing or for comparing two samples. There are two main variants: the one-sample KS test compares an empirical distribution function of a sample with a specified cumulative distribution function, while the two-sample KS test compares the empirical distributions of two samples. The test statistic is D, the maximum absolute difference between the respective cumulative distribution functions. Under the null hypothesis, the distribution of D is known (the Kolmogorov distribution for the one-sample case), allowing computation of p-values; exact procedures exist for small samples, and asymptotic approximations are common for larger samples.

When parameters of the reference distribution are estimated from the data, the null distribution of D changes, and adjustments or resampling methods (such as Monte Carlo simulations) are used. Practical use often involves software implementations in R, Python, and other statistical environments.

Limitations include varying sensitivity across parts of the distribution and reduced power for certain alternative hypotheses, especially with small samples or when distributions have similar shapes but different tails. The KS test is most informative about differences in distribution shape rather than specific parameters.

See also Kolmogorov distribution, Smirnov statistic, and goodness-of-fit tests.