Kolmogorov Distribution
The Kolmogorov distribution, often denoted as D, represents the cumulative distribution function (CDF) of the maximum difference between the empirical distribution function of the sample and the cumulative distribution function of the reference distribution.
The probability distribution function (PDF) of the Kolmogorov distribution itself is not expressed in a simple analytical form. Instead, tables or statistical software are commonly used to obtain critical values for the test. The distribution is influenced by sample size, and the critical values depend on the significance level chosen for the test.
where
- n is the sample size.
- x is the normalized Kolmogorov-Smirnov statistic.
- k is the index of summation in the series
Kolmogorov-Smirnov Test (KS Test)
The Kolmogorov-Smirnov (KS) test is a non-parametric method for comparing distributions, essential for various applications in diverse fields.
In this article, we will look at the non-parametric test which can be used to determine whether the shape of the two distributions is the same or not.