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Sample.KolmogorovSmirnovTest Method (ContinuousDistribution)

Tests whether the sample is compatible with the given distribution.

Namespace:  Meta.Numerics.Statistics
Assembly:  Meta.Numerics (in Meta.Numerics.dll) Version: 4.1.4
Syntax
public TestResult KolmogorovSmirnovTest(
	ContinuousDistribution distribution
)

Parameters

distribution
Type: Meta.Numerics.Statistics.Distributions.ContinuousDistribution
The test distribution.

Return Value

Type: TestResult
The test result. The test statistic is the D statistic and the probability is the chance of obtaining such a large value of D under the assumption that the sample is drawn from the given distribution.
Exceptions
ExceptionCondition
ArgumentNullExceptiondistribution is null.
InsufficientDataExceptionThere is no data in the sample.
Remarks

The null hypothesis of the Kolmogorov-Smirnov (KS) test is that the sample is drawn from the given continuous distribution. The test statistic D is the maximum deviation of the sample's empirical distribution function (EDF) from the distribution's cumulative distribution function (CDF). A high value of the test statistic, corresponding to a low right tail probability, indicates that the sample distribution disagrees with the given distribution to a degree unlikely to arise from statistical fluctuations.

For small sample sizes, we compute the null distribution of D exactly. For large sample sizes, we use an accurate asymptotic approximation. Therefore it is safe to use this method for all sample sizes.

A variant of this test, KolmogorovSmirnovTest(Sample, Sample), allows you to non-parametrically test whether two samples are drawn from the same underlying distribution, without having to specify that distribution.

See Also