Note
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Select fitted distributionsΒΆ
In this example help to make a choice between several distributions fitted to a sample.
Several methods can be used:
the ranking by the Kolmogorov p-values (for continuous distributions),
the ranking by the ChiSquared p-values (for discrete distributions),
the ranking by BIC values.
import openturns as ot
import openturns.viewer as otv
ot.Log.Show(ot.Log.NONE)
Create a sample from a continuous distribution
distribution = ot.Beta(2.0, 2.0, 0.0, 1.0)
sample = distribution.getSample(1000)
graph = ot.UserDefined(sample).drawCDF()
view = otv.View(graph)
1. Specify the model only
Create the list of distribution estimators
factories = [ot.BetaFactory(), ot.TriangularFactory()]
Rank the continuous models by the Lilliefors p-values:
estimated_distribution, test_result = ot.FittingTest.BestModelLilliefors(
sample, factories
)
test_result
Rank the continuous models wrt the BIC criteria (no test result):
ot.FittingTest.BestModelBIC(sample, factories)
[class=Beta name=Beta dimension=1 alpha=1.74081 beta=1.71095 a=0.0330728 b=0.978656, -0.22004783945347892]
Rank the continuous models wrt the AIC criteria (no test result)
ot.FittingTest.BestModelAIC(sample, factories)
[class=Beta name=Beta dimension=1 alpha=1.74081 beta=1.71095 a=0.0330728 b=0.978656, -0.2396788605694075]
Rank the continuous models wrt the AICc criteria (no test result):
ot.FittingTest.BestModelAICC(sample, factories)
[class=Beta name=Beta dimension=1 alpha=1.74081 beta=1.71095 a=0.0330728 b=0.978656, -0.23963865956438235]
2. Specify the model and its parameters
Create a collection of the distributions to be tested
distributions = [ot.Beta(2.0, 2.0, 0.0, 1.0), ot.Triangular(0.0, 0.5, 1.0)]
Rank the continuous models by the Kolmogorov p-values:
estimated_distribution, test_result = ot.FittingTest.BestModelKolmogorov(
sample, distributions
)
test_result
Rank the continuous models wrt the BIC criteria:
ot.FittingTest.BestModelBIC(sample, distributions)
[class=Beta name=Beta dimension=1 alpha=2 beta=2 a=0 b=1, -0.2523568823599743]
Rank the continuous models wrt the AIC criteria:
ot.FittingTest.BestModelAIC(sample, distributions)
[class=Beta name=Beta dimension=1 alpha=2 beta=2 a=0 b=1, -0.2523568823599743]
Rank the continuous models wrt the AICc criteria:
ot.FittingTest.BestModelAICC(sample, distributions)
[class=Beta name=Beta dimension=1 alpha=2 beta=2 a=0 b=1, -0.2523568823599743]
Discrete distributions
Create a sample from a discrete distribution
distribution = ot.Poisson(2.0)
sample = distribution.getSample(1000)
graph = ot.UserDefined(sample).drawCDF()
view = otv.View(graph)
Create the list of distribution estimators
distributions = [ot.Poisson(2.0), ot.Geometric(0.1)]
Rank the discrete models with respect to the ChiSquared p-values:
ot.ResourceMap.SetAsBool("FittingTest-ChiSquaredCheckSample", False)
estimated_distribution, test_result = ot.FittingTest.BestModelChiSquared(
sample, distributions
)
test_result
Rank the discrete models with respect to the BIC criteria:
ot.FittingTest.BestModelBIC(sample, distributions)
otv.View.ShowAll()
Reset default settings
ot.ResourceMap.Reload()