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|Title: ||The two-dimensional Kolmogorov-Smirnov test|
|Authors: ||Lopes, RHC|
|Publication Date: ||2007|
|Publisher: ||Proceedings of Science|
|Citation: ||XI International Workshop on Advanced Computing and Analysis Techniques in Physics Research, Nikhef, Amsterdam, the Netherlands, April 23-27, 2007|
|Abstract: ||Goodness-of-fit statistics measure the compatibility of random samples against some theoretical
probability distribution function. The classical one-dimensional Kolmogorov-Smirnov test is a
non-parametric statistic for comparing two empirical distributions which defines the largest absolute
difference between the two cumulative distribution functions as a measure of disagreement.
Adapting this test to more than one dimension is a challenge because there are 2d −1 independent
ways of defining a cumulative distribution function when d dimensions are involved. In this paper
three variations on the Kolmogorov-Smirnov test for multi-dimensional data sets are surveyed:
Peacock’s test  that computes in O(n3); Fasano and Franceschini’s test  that computes in
O(n2); Cooke’s test that computes in O(n2).
We prove that Cooke’s algorithm runs in O(n2), contrary to his claims that it runs in O(nlgn).
We also compare these algorithms with ROOT’s version of the Kolmogorov-Smirnov test.|
|Appears in Collections:||School of Engineering and Design Research papers|
Electronic and Computer Engineering
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