# 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.
In [62]:

from __future__ import print_function
import openturns as ot

In [131]:

# Create a sample from a continuous distribution
distribution = ot.Beta(2.0, 4.0, 0.0, 1.)
sample = distribution.getSample(1000)
ot.VisualTest.DrawEmpiricalCDF(sample)

Out[131]:


1. Specify the model only

In [64]:

# Create the list of distribution estimators
factories = [ot.BetaFactory(), ot.TriangularFactory()]

In [65]:

# Rank the continuous models by the Kolmogorov p-values:
estimated_distribution, test_result = ot.FittingTest.BestModelKolmogorov(sample, factories)
test_result

Out[65]:


class=TestResult name=Unnamed type=KolmogorovDistribution binaryQualityMeasure=true p-value threshold=0.5 p-value=0.962664 description=[Beta(r = 1.78975, t = 3.63985, a = 0.0115899, b = 0.986749) vs sample Beta]

In [66]:

# Rank the continuous models wrt the BIC criteria (no test result):
ot.FittingTest.BestModelBIC(sample, factories)

Out[66]:


Beta(r = 1.78975, t = 3.63985, a = 0.0115899, b = 0.986749)

2. Specify the model and its parameters

In [67]:

# Create a collection of the distributions to be tested
distributions = [ot.Beta(2.0, 4.0, 0.0, 1.0), ot.Triangular(0.0, 0.5, 1.0)]

In [68]:

# Rank the continuous models by the Kolmogorov p-values:
estimated_distribution, test_result = ot.FittingTest.BestModelKolmogorov(sample, distributions)
test_result

Out[68]:


class=TestResult name=Unnamed type=KolmogorovDistribution binaryQualityMeasure=true p-value threshold=0.05 p-value=0.552764 description=[Beta(r = 2, t = 4, a = 0, b = 1) vs sample Beta]

In [69]:

# Rank the continuous models wrt the BIC criteria:
ot.FittingTest.BestModelBIC(sample, distributions)

Out[69]:


Beta(r = 2, t = 4, a = 0, b = 1)

Discrete distributions

In [130]:

# Create a sample from a discrete distribution
distribution = ot.Poisson(2.0)
sample = distribution.getSample(1000)
ot.VisualTest.DrawEmpiricalCDF(sample)

Out[130]:

In [123]:

# Create the list of distribution estimators
distributions = [ot.Poisson(2.0), ot.Geometric(0.1)]

In [124]:

# Rank the discrete models wrt the ChiSquared p-values:
estimated_distribution, test_result = ot.FittingTest.BestModelChiSquared(sample, distributions)
test_result

Out[124]:


class=TestResult name=Unnamed type=ChiSquaredPoisson binaryQualityMeasure=true p-value threshold=0.05 p-value=0.839723 description=[]

In [132]:

# Rank the discrete models wrt the BIC criteria:
ot.FittingTest.BestModelBIC(sample, distributions)

Out[132]:


Poisson(lambda = 2)