Use the Kolmogorov/Lilliefors test

In this example we are going to perform a Kolmogorov or a Lilliefors goodness-of-fit test for a 1-d continuous distribution.

from __future__ import print_function
import openturns as ot
ot.Log.Show(ot.Log.NONE)

Create the data.

distribution = ot.Normal()
sample = distribution.getSample(50)

Case 1 : the distribution parameters are known.

In the case where the parameters of the distribution are known, we must use the Kolmogorov static method and the distribution to be tested.

result = ot.FittingTest.Kolmogorov(sample, distribution, 0.01)
print('Conclusion=', result.getBinaryQualityMeasure(),
      'P-value=', result.getPValue())

Out:

Conclusion= True P-value= 0.9861140480396968

Test succeeded ?

result.getBinaryQualityMeasure()

Out:

True

P-Value associated to the risk

result.getPValue()

Out:

0.9861140480396968

Threshold associated to the test.

result.getThreshold()

Out:

0.01

Observed value of the statistic.

result.getStatistic()

Out:

0.06127263683768702

Case 2 : the distribution parameters are estimated from the sample.

In the case where the parameters of the distribution are estimated from the sample, we must use the Lilliefors static method and the distribution factory to be tested.

ot.ResourceMap.SetAsUnsignedInteger(
    "FittingTest-LillieforsMaximumSamplingSize", 1000)

distributionFactory = ot.NormalFactory()

dist, result = ot.FittingTest.Lilliefors(sample, distributionFactory, 0.01)
print('Conclusion=', result.getBinaryQualityMeasure(),
      'P-value=', result.getPValue())

Out:

Conclusion= True P-value= 0.983

dist

Normal(mu = -0.0222592, sigma = 0.956433)

Test succeeded ?

result.getBinaryQualityMeasure()

Out:

True

P-Value associated to the risk

result.getPValue()

Out:

0.983

Threshold associated to the test.

result.getThreshold()

Out:

0.01

Observed value of the statistic.

result.getStatistic()

Out:

0.05110645729712043