Test distribution fitting using Kolmogorov

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

[1]:

from __future__ import print_function
import openturns as ot

Create the data.

[2]:

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, the second parameter of the Kolmogorov static method is the distribution to be tested.

[3]:

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

Conclusion= True P-value= 0.6411393475140432

Test succeeded ?

[4]:

result.getBinaryQualityMeasure()

[4]:

True

P-Value associated to the risk

[5]:

result.getPValue()

[5]:

0.6411393475140432

Threshold associated to the test.

[6]:

result.getThreshold()

[6]:

0.01

Observed value of the statistic.

[7]:

result.getStatistic()

[7]:

0.10176815459988908

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

In the case where the parameters of the distribution are estimated from the sample, the second parameter of the Kolmogorov static method is the associated distribution factory to be tested.

[8]:

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

[9]:

distributionFactory = ot.NormalFactory()

[10]:

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

Conclusion= True P-value= 0.353

[11]:

dist

[11]:

Normal(mu = 0.0353171, sigma = 0.968336)

Test succeeded ?

[12]:

result.getBinaryQualityMeasure()

[12]:

True

P-Value associated to the risk

[13]:

result.getPValue()

[13]:

0.353

Threshold associated to the test.

[14]:

result.getThreshold()

[14]:

0.01

Observed value of the statistic.

[15]:

result.getStatistic()

[15]:

0.09091079601468799