The Kolmogorov distribution is the distribution of the random variable
where B(t) is the Brownian bridge. The cumulative distribution function of K is given by
Both the form of the Kolmogorov–Smirnov test statistic and its asymptotic distribution under the null hypothesis were published by Andrey Kolmogorov, while a table of the distribution was published by Nikolai Vasilyevich Smirnov. Recurrence relations for the distribution of the test statistic in finite samples are available.
Read more about this topic: Kolmogorov–Smirnov Test
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