- naginterfaces.library.stat.prob_kolmogorov2(n1, n2, d)[source]¶
prob_kolmogorov2returns the probability associated with the upper tail of the Kolmogorov–Smirnov two sample distribution.
For full information please refer to the NAG Library document for g01ez
The number of observations in the first sample, .
The number of observations in the second sample, .
The test statistic , for the two sample Kolmogorov–Smirnov goodness-of-fit test, that is the maximum difference between the empirical cumulative distribution functions (CDFs) of the two samples.
The probability associated with the upper tail of the Kolmogorov–Smirnov two sample distribution.
- (errno )
On entry, and .
Constraint: and .
- (errno )
On entry, or : .
- (errno )
The Smirnov approximation used for large samples did not converge in iterations. The probability is set to .
Let and denote the empirical cumulative distribution functions for the two samples, where and are the sizes of the first and second samples respectively.
prob_kolmogorov2computes the upper tail probability for the Kolmogorov–Smirnov two sample two-sided test statistic , where
The probability is computed exactly if and using a method given by Kim and Jenrich (1973). For the case where of the and the Smirnov approximation is used. For all other cases the Kolmogorov approximation is used. These two approximations are discussed in Kim and Jenrich (1973).
Conover, W J, 1980, Practical Nonparametric Statistics, Wiley
Feller, W, 1948, On the Kolmogorov–Smirnov limit theorems for empirical distributions, Ann. Math. Statist. (19), 179–181
Kendall, M G and Stuart, A, 1973, The Advanced Theory of Statistics (Volume 2), (3rd Edition), Griffin
Kim, P J and Jenrich, R I, 1973, Tables of exact sampling distribution of the two sample Kolmogorov–Smirnov criterion , Selected Tables in Mathematical Statistics (1), 80–129, American Mathematical Society
Siegel, S, 1956, Non-parametric Statistics for the Behavioral Sciences, McGraw–Hill
Smirnov, N, 1948, Table for estimating the goodness of fit of empirical distributions, Ann. Math. Statist. (19), 279–281