Search results
Results from the WOW.Com Content Network
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.
Kolmogorov's theorem is any of several different results by Andrey Kolmogorov: In statistics. Kolmogorov–Smirnov test; In probability theory.
Statistical tests are used to test the fit between a hypothesis and the data. [1] [2] Choosing the right statistical test is not a trivial task. [1]The choice of the test depends on many properties of the research question.
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.
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]
The standard probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. [1] These axioms remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases. [2] There are several other (equivalent) approaches to formalising ...
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.
In probability theory, Kolmogorov's Three-Series Theorem, named after Andrey Kolmogorov, gives a criterion for the almost sure convergence of an infinite series of random variables in terms of the convergence of three different series involving properties of their probability distributions.