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SampleKolmogorovSmirnovTest 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
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public TestResult KolmogorovSmirnovTest(
	ContinuousDistribution distribution
)

Parameters

distribution
Type: Meta.Numerics.Statistics.DistributionsContinuousDistribution
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 .
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