Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0
Syntax
C# |
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[SerializableAttribute] public class KolmogorovTwoSample |
Visual Basic (Declaration) |
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<SerializableAttribute> _ Public Class KolmogorovTwoSample |
Visual C++ |
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[SerializableAttribute] public ref class KolmogorovTwoSample |
Remarks
Class KolmogorovTwoSample computes Kolmogorov-Smirnov two-sample test statistics for testing that two continuous cumulative distribution functions (CDF's) are identical based upon two random samples. One- or two-sided alternatives are allowed. Exact p-values are computed for the two-sided test when , where n is the number of non-missing X observations and m the number of non-missing Y observation.
Let denote the empirical CDF in the X sample, let denote the empirical CDF in the Y sample and let the corresponding population distribution functions be denoted by and , respectively. Then, the hypotheses tested by KolmogorovTwoSample are as follows:
The test statistics are given as follows: Asymptotically, the distribution of the statistic converges to a distribution given by Smirnov (1939).Exact probabilities for the two-sided test are computed when , according to an algorithm given by Kim and Jennrich (1973). When , the very good approximations given by Kim and Jennrich are used to obtain the two-sided p-values. The one-sided probability is taken as one half the two-sided probability. This is a very good approximation when the p-value is small (say, less than 0.10) and not very good for large p-values.