Note
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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.
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())
Conclusion= True P-value= 0.9861140480396968
Test succeeded ?
result.getBinaryQualityMeasure()
True
P-Value associated to the risk
result.getPValue()
0.9861140480396968
Threshold associated to the test.
result.getThreshold()
0.01
Observed value of the statistic.
result.getStatistic()
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())
Conclusion= True P-value= 0.983
dist
Test succeeded ?
result.getBinaryQualityMeasure()
True
P-Value associated to the risk
result.getPValue()
0.983
Threshold associated to the test.
result.getThreshold()
0.01
Observed value of the statistic.
result.getStatistic()
0.05110645729712043
Reset default settings
ot.ResourceMap.Reload()