Kolmogorov

Kolmogorov(sample, distribution, level=0.05)

Perform a Kolmogorov goodness-of-fit test for 1-d continuous distributions.

Refer to Kolmogorov-Smirnov fitting test.

Parameters:

sample2-d sequence of float

Tested sample.

modelDistribution.

levelfloat, , optional (default level = 0.05).

This is the risk of committing a Type I error, that is an incorrect rejection of a true null hypothesis.

Returns:

test_resultTestResult

Test result.

Raises:

TypeError

If the distribution is not continuous or if the sample is multivariate.

Notes

The distribution is supposed to be fully specified, i.e. no parameter has been estimated from the given sample. This uses an external C implementation of the Kolmogorov cumulative distribution function by [simard2011].

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> distribution = ot.Normal()
>>> sample = distribution.getSample(30)
>>> test_result = ot.FittingTest.Kolmogorov(sample, distribution)
>>> test_result
class=TestResult name=Unnamed type=Kolmogorov Normal binaryQualityMeasure=true p-value threshold=0.05 p-value=0.970418 statistic=0.0845532 description=[Normal(mu = 0, sigma = 1) vs sample Normal]

We set the level of the Kolmogorov-Smirnov test to 0.01. This parameter value rejects a sample less often than the default value 0.05.

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> distribution = ot.Normal()
>>> sample = distribution.getSample(30)
>>> level = 0.01
>>> test_result = ot.FittingTest.Kolmogorov(sample, distribution, level)