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.
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. The vast majority of studies can be addressed by 30 of the 100 or so statistical tests in use. [3] [4] [5]
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]
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 ...
3.1 Pearson's chi-square test. 3.1 ... (see Kolmogorov–Smirnov test ... G-tests have been recommended at least since the 1981 edition of the popular statistics ...
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 ...
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.
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.