# naginterfaces.library.stat.prob_​kolmogorov1¶

naginterfaces.library.stat.prob_kolmogorov1(n, d)[source]

prob_kolmogorov1 returns the upper tail probability associated with the one sample Kolmogorov–Smirnov distribution.

For full information please refer to the NAG Library document for g01ey

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/g01/g01eyf.html

Parameters
nint

, the number of observations in the sample.

dfloat

Contains the test statistic, or .

Returns
pfloat

The upper tail probability associated with the one sample Kolmogorov–Smirnov distribution.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, or : .

Notes

Let be the sample cumulative distribution function and the hypothesised theoretical distribution function.

prob_kolmogorov1 returns the upper tail probability, , associated with the one-sided Kolmogorov–Smirnov test statistic or , where these one-sided statistics are defined as follows;

If an exact method is used; for the details see Conover (1980). Otherwise a large sample approximation derived by Smirnov is used; see Feller (1948), Kendall and Stuart (1973) and Smirnov (1948).

References

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

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