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The algorithm calculates the exact cumulative distribution of the two-sided Kolmogorov-Smirnov statistic for samples with few observations. The general problem for which the formula is needed is to assess the probability that a particular sample comes from a proposed distribution. The problem arises specifically in data sampling and in discrete system simulation. Typically, some finite number of observations are available, and some underlying distribution is being considered as characterizing the source of the observations.
Richard P. Brent (Sun,) studied this question.
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