#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
ot.TESTPREAMBLE()
ot.RandomGenerator.SetSeed(0)
# Instanciate one distribution object
distribution = ot.Frechet(6.0, 1.5, -1.0)
print("Distribution ", distribution)
# Is this distribution elliptical ?
print("Elliptical = ", distribution.isElliptical())
# Is this distribution continuous ?
print("Continuous = ", distribution.isContinuous())
# Test for realization of distribution
oneRealization = distribution.getRealization()
print("oneRealization=", oneRealization)
# Test for sampling
size = 10000
oneSample = distribution.getSample(size)
print("oneSample first=", oneSample[0], " last=", oneSample[size - 1])
print("mean=", oneSample.computeMean())
print("covariance=", oneSample.computeCovariance())
size = 100
for i in range(2):
print(
# %% # The :class:`~openturns.GeneralizedExtremeValue` distribution is a family of continuous probability distributions that combine the :class:`~openturns.Gumbel`, :class:`~openturns.Frechet` and :class:`~openturns.WeibullMax` distribution, all extreme value distribution. # # In this example we use the associated :class:`~openturns.GeneralizedExtremeValueFactory` to fit sample with extreme values. This factory returns the best model among the Frechet, Gumbel and Weibull estimates according to the BIC criterion. # # %% # We draw a sample from a Gumbel of parameters :math:`\beta = 1.0` and :math:`\gamma = 3.0` and another one from a Frechet with parameters :math:`\beta=1.0`, :math:`\alpha = 1.0` and :math:`\gamma = 0.0`. # We consider both samples as a single sample from an unknown extreme distribution to be fitted. # # %% # The distributions used: myGumbel = ot.Gumbel(1.0, 3.0) myFrechet = ot.Frechet(1.0, 1.0, 0.0) # %% # We build our experiment sample of size 2000. sample = ot.Sample() sampleFrechet = myFrechet.getSample(1000) sampleGumbel = myGumbel.getSample(1000) sample.add(sampleFrechet) sample.add(sampleGumbel) # %% # We fit the sample thanks to the `GeneralizedExtremeValueFactory`: myDistribution = ot.GeneralizedExtremeValueFactory( ).buildAsGeneralizedExtremeValue(sample) # %%
#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
ot.Log.Show(ot.Log.ALL)
distribution = ot.Frechet(2.5, 2.0, -1.5)
size = 10000
sample = distribution.getSample(size)
factory = ot.FrechetFactory()
print('Distribution =', repr(distribution))
result = factory.buildEstimator(sample)
estimatedDistribution = result.getDistribution()
print('Estimated distribution =', repr(estimatedDistribution))
parameterDistribution = result.getParameterDistribution()
print('Parameter distribution =', parameterDistribution)
defaultDistribution = factory.build()
print('Default distribution =', defaultDistribution)
fromParameterDistribution = factory.build(distribution.getParameter())
print('Distribution from parameters =', fromParameterDistribution)
typedEstimatedDistribution = factory.buildAsFrechet(sample)
print('Typed estimated distribution =', typedEstimatedDistribution)
defaultTypedDistribution = factory.buildAsFrechet()
print('Default typed distribution =', defaultTypedDistribution)
typedFromParameterDistribution = factory.buildAsFrechet(
distribution.getParameter())
print('Typed distribution from parameters=', typedFromParameterDistribution)
# More involved test: the sample distribution does not fit the factory
# The distributions used :
myFrechet = ot.Frechet(1.0, 1.0, 0.0)
def Frechet(alpha=1.0, beta=1.0, gamma=0.0):
"""
Frechet compatibility shim.
"""
return ot.Frechet(beta, alpha, gamma)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.Frechet().__class__.__name__ == 'ComposedDistribution':
correlation = ot.CorrelationMatrix(2)
correlation[1, 0] = 0.25
aCopula = ot.NormalCopula(correlation)
marginals = [ot.Normal(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, aCopula)
elif ot.Frechet().__class__.__name__ == 'CumulativeDistributionNetwork':
distribution = ot.CumulativeDistributionNetwork(
[ot.Normal(2), ot.Dirichlet([0.5, 1.0, 1.5])],
ot.BipartiteGraph([[0, 1], [0, 1]]))
elif ot.Frechet().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
else:
distribution = ot.Frechet()
dimension = distribution.getDimension()
if dimension == 1:
distribution.setDescription(['$x$'])
pdf_graph = distribution.drawPDF()
cdf_graph = distribution.drawCDF()
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(distribution))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph, figure=fig, axes=[pdf_axis], add_legend=False)
View(cdf_graph, figure=fig, axes=[cdf_axis], add_legend=False)
elif dimension == 2:
distribution.setDescription(['$x_1$', '$x_2$'])
pdf_graph = distribution.drawPDF()
#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
ot.Log.Show(ot.Log.ALL)
distribution = ot.Frechet(2.0, 2.5, -1.5)
size = 10000
sample = distribution.getSample(size)
factory = ot.FrechetFactory()
print('Distribution =', repr(distribution))
result = factory.buildEstimator(sample)
estimatedDistribution = result.getDistribution()
print('Estimated distribution =', repr(estimatedDistribution))
parameterDistribution = result.getParameterDistribution()
print('Parameter distribution =', parameterDistribution)
defaultDistribution = factory.build()
print('Default distribution =', defaultDistribution)
fromParameterDistribution = factory.build(distribution.getParameter())
print('Distribution from parameters =', fromParameterDistribution)
typedEstimatedDistribution = factory.buildAsFrechet(sample)
print('Typed estimated distribution =', typedEstimatedDistribution)
defaultTypedDistribution = factory.buildAsFrechet()
print('Default typed distribution =', defaultTypedDistribution)
typedFromParameterDistribution = factory.buildAsFrechet(
distribution.getParameter())
print('Typed distribution from parameters=', typedFromParameterDistribution)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.Frechet().__class__.__name__ == 'Bernoulli':
distribution = ot.Bernoulli(0.7)
elif ot.Frechet().__class__.__name__ == 'Binomial':
distribution = ot.Binomial(5, 0.2)
elif ot.Frechet().__class__.__name__ == 'ComposedDistribution':
copula = ot.IndependentCopula(2)
marginals = [ot.Uniform(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, copula)
elif ot.Frechet().__class__.__name__ == 'CumulativeDistributionNetwork':
coll = [ot.Normal(2),ot.Dirichlet([0.5, 1.0, 1.5])]
distribution = ot.CumulativeDistributionNetwork(coll, ot.BipartiteGraph([[0,1], [0,1]]))
elif ot.Frechet().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
elif ot.Frechet().__class__.__name__ == 'KernelMixture':
kernel = ot.Uniform()
sample = ot.Normal().getSample(5)
bandwith = [1.0]
distribution = ot.KernelMixture(kernel, bandwith, sample)
elif ot.Frechet().__class__.__name__ == 'MaximumDistribution':
coll = [ot.Uniform(2.5, 3.5), ot.LogUniform(1.0, 1.2), ot.Triangular(2.0, 3.0, 4.0)]
distribution = ot.MaximumDistribution(coll)
elif ot.Frechet().__class__.__name__ == 'Multinomial':
distribution = ot.Multinomial(5, [0.2])
elif ot.Frechet().__class__.__name__ == 'RandomMixture':
coll = [ot.Triangular(0.0, 1.0, 5.0), ot.Uniform(-2.0, 2.0)]
weights = [0.8, 0.2]
cst = 3.0
distribution = ot.RandomMixture(coll, weights, cst)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if (ot.Frechet().__class__.__name__ == 'ComposedDistribution'):
correlation = ot.CorrelationMatrix(2)
correlation[1, 0] = 0.25
aCopula = ot.NormalCopula(correlation)
marginals = [ot.Normal(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, aCopula)
elif (ot.Frechet().__class__.__name__ == 'CumulativeDistributionNetwork'):
distribution = ot.CumulativeDistributionNetwork(
[ot.Normal(2), ot.Dirichlet([0.5, 1.0, 1.5])],
ot.BipartiteGraph([[0, 1], [0, 1]]))
else:
distribution = ot.Frechet()
dimension = distribution.getDimension()
if dimension <= 2:
if distribution.getDimension() == 1:
distribution.setDescription(['$x$'])
pdf_graph = distribution.drawPDF()
cdf_graph = distribution.drawCDF()
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(distribution))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph, figure=fig, axes=[pdf_axis], add_legend=False)
View(cdf_graph, figure=fig, axes=[cdf_axis], add_legend=False)
else:
distribution.setDescription(['$x_1$', '$x_2$'])
pdf_graph = distribution.drawPDF()
fig = plt.figure(figsize=(10, 5))