import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if (ot.ClaytonCopula().__class__.__name__ == 'SklarCopula'):
myStudent = ot.Student(3.0, [1.0] * 2, [3.0] * 2, ot.CorrelationMatrix(2))
copula = ot.SklarCopula(myStudent)
else:
copula = ot.ClaytonCopula()
if copula.getDimension() == 1:
copula = ot.ClaytonCopula(2)
copula.setDescription(['$u_1$', '$u_2$'])
pdf_graph = copula.drawPDF()
cdf_graph = copula.drawCDF()
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(copula))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph,
figure=fig,
axes=[pdf_axis],
add_legend=False,
square_axes=True)
View(cdf_graph,
figure=fig,
axes=[cdf_axis],
add_legend=False,
square_axes=True)
if ot.FrankCopula().__class__.__name__ == 'EmpiricalBernsteinCopula':
sample = ot.Dirichlet([1.0, 2.0, 3.0]).getSample(100)
copula = ot.EmpiricalBernsteinCopula(sample, 4)
elif ot.FrankCopula().__class__.__name__ == 'ExtremeValueCopula':
copula = ot.ExtremeValueCopula(ot.SymbolicFunction("t", "t^3/2-t/2+1"))
elif ot.FrankCopula(
).__class__.__name__ == 'MaximumEntropyOrderStatisticsCopula':
marginals = [ot.Beta(1.5, 3.2, 0.0, 1.0), ot.Beta(2.0, 4.3, 0.5, 1.2)]
copula = ot.MaximumEntropyOrderStatisticsCopula(marginals)
elif ot.FrankCopula().__class__.__name__ == 'NormalCopula':
R = ot.CorrelationMatrix(2)
R[1, 0] = 0.8
copula = ot.NormalCopula(R)
elif ot.FrankCopula().__class__.__name__ == 'SklarCopula':
student = ot.Student(3.0, [1.0] * 2, [3.0] * 2, ot.CorrelationMatrix(2))
copula = ot.SklarCopula(student)
else:
copula = ot.FrankCopula()
if copula.getDimension() == 1:
copula = ot.FrankCopula(2)
copula.setDescription(['$u_1$', '$u_2$'])
pdf_graph = copula.drawPDF()
cdf_graph = copula.drawCDF()
fig = plt.figure(figsize=(10, 4))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph,
figure=fig,
axes=[pdf_axis],
add_legend=False,
square_axes=True)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.SklarCopula().__class__.__name__ == 'EmpiricalBernsteinCopula':
sample = ot.Dirichlet([1.0, 2.0, 3.0]).getSample(100)
copula = ot.EmpiricalBernsteinCopula(sample, 4)
elif ot.SklarCopula().__class__.__name__ == 'ExtremeValueCopula':
copula = ot.ExtremeValueCopula(ot.SymbolicFunction("t", "t^3/2-t/2+1"))
elif ot.SklarCopula(
).__class__.__name__ == 'MaximumEntropyOrderStatisticsCopula':
marginals = [ot.Beta(1.5, 3.2, 0.0, 1.0), ot.Beta(2.0, 4.3, 0.5, 1.2)]
copula = ot.MaximumEntropyOrderStatisticsCopula(marginals)
elif ot.SklarCopula().__class__.__name__ == 'NormalCopula':
R = ot.CorrelationMatrix(2)
R[1, 0] = 0.8
copula = ot.NormalCopula(R)
elif ot.SklarCopula().__class__.__name__ == 'SklarCopula':
student = ot.Student(3.0, [1.0] * 2, [3.0] * 2, ot.CorrelationMatrix(2))
copula = ot.SklarCopula(student)
else:
copula = ot.SklarCopula()
if copula.getDimension() == 1:
copula = ot.SklarCopula(2)
copula.setDescription(['$u_1$', '$u_2$'])
pdf_graph = copula.drawPDF()
cdf_graph = copula.drawCDF()
fig = plt.figure(figsize=(10, 4))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph,
figure=fig,
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if (ot.SklarCopula().__class__.__name__=='SklarCopula'):
myStudent = ot.Student(3.0, [1.0]*2, [3.0]*2, ot.CorrelationMatrix(2))
copula = ot.SklarCopula(myStudent)
else:
copula = ot.SklarCopula()
if copula.getDimension() == 1:
copula = ot.SklarCopula(2)
copula.setDescription(['$u_1$', '$u_2$'])
pdf_graph = copula.drawPDF()
cdf_graph = copula.drawCDF()
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(copula))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph, figure=fig, axes=[pdf_axis], add_legend=False, square_axes=True)
View(cdf_graph, figure=fig, axes=[cdf_axis], add_legend=False, square_axes=True)
indices = [1, 2, 3, 5, 6]
print("indices=", indices)
margins = distribution.getMarginal(indices)
print("margins=", margins)
print("margins PDF=%.5f" % margins.computePDF(point))
print("margins CDF=%.5f" % margins.computeCDF(point))
quantile = margins.computeQuantile(0.95)
print("margins quantile=", quantile)
print("margins CDF(quantile)=%.5f" % margins.computeCDF(quantile))
print("margins realization=", margins.getRealization())
# Tests o the isoprobabilistic transformation
# General case with normal standard distribution
print("isoprobabilistic transformation (general normal)=",
distribution.getIsoProbabilisticTransformation())
# General case with non-normal standard distribution
collection[0] = ot.SklarCopula(ot.Student(
3.0, [1.0]*2, [3.0]*2, ot.CorrelationMatrix(2)))
collection.append(ot.Triangular(2.0, 3.0, 4.0))
distribution = ot.BlockIndependentDistribution(collection)
print("isoprobabilistic transformation (general non-normal)=",
distribution.getIsoProbabilisticTransformation())
dim = distribution.getDimension()
x = 0.6
y = [0.2] * (dim - 1)
print("conditional PDF=%.5f" % distribution.computeConditionalPDF(x, y))
print("conditional CDF=%.5f" % distribution.computeConditionalCDF(x, y))
print("conditional quantile=%.5f" %
distribution.computeConditionalQuantile(x, y))
pt = ot.Point(dim)
for i in range(dim):
pt[i] = 0.1 * i + 0.05
print("sequential conditional PDF=",
#! /usr/bin/env python
import openturns as ot
ot.TESTPREAMBLE()
# Instantiate one distribution object
dim = 3
R = ot.CorrelationMatrix(dim)
for i in range(dim - 1):
R[i, i + 1] = 0.25
copula = ot.SklarCopula(
ot.Distribution(ot.Normal([1.0, 2.0, 3.0], [2.0, 3.0, 1.0], R)))
copulaRef = ot.NormalCopula(R)
print("Copula ", repr(copula))
print("Copula ", copula)
print("Mean =", repr(copula.getMean()))
print("Mean (ref)=", repr(copulaRef.getMean()))
ot.ResourceMap.SetAsUnsignedInteger("GaussKronrod-MaximumSubIntervals", 20)
ot.ResourceMap.SetAsScalar("GaussKronrod-MaximumError", 1.0e-4)
print("Covariance =", repr(copula.getCovariance()))
ot.ResourceMap.SetAsUnsignedInteger("GaussKronrod-MaximumSubIntervals", 100)
ot.ResourceMap.SetAsScalar("GaussKronrod-MaximumError", 1.0e-12)
print("Covariance (ref)=", repr(copulaRef.getCovariance()))
# Is this copula an elliptical distribution?
print("Elliptical distribution= ", copula.isElliptical())
# Is this copula elliptical ?
print("Elliptical copula= ", copula.hasEllipticalCopula())
