Meta.Numerics Library

## SampleKolmogorovSmirnovTest Method (ContinuousDistribution) |

Tests whether the sample is compatible with the given distribution.

Syntax

- distribution
- Type: Meta.Numerics.Statistics.DistributionsContinuousDistribution

The test distribution.

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

Exception | Condition |
---|---|

ArgumentNullException | distribution is . |

InsufficientDataException | There 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