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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
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())
# Is this copula independent ?
print("Independent copula= ", copula.hasIndependentCopula())
# Test for realization of distribution
oneRealization = copula.getRealization()
print("oneRealization=", repr(oneRealization))
# Test for sampling
size = 10
oneSample = copula.getSample(size)
print("oneSample=", repr(oneSample))
# Test for sampling
size = 1000
anotherSample = copula.getSample(size)
print("anotherSample mean=", repr(anotherSample.computeMean()))
print("anotherSample covariance=", repr(anotherSample.computeCovariance()))
# Define a point
point = ot.Point(dim, 0.2)
# Show PDF and CDF of point
pointPDF = copula.computePDF(point)
pointCDF = copula.computeCDF(point)
pointPDFRef = copulaRef.computePDF(point)
pointCDFRef = copulaRef.computeCDF(point)
print(
"Point = ", repr(point), " pdf =%.6f" % pointPDF, " cdf =%.6f" % pointCDF
)
print(
"Point = ",
repr(point),
" pdf (ref)=%.6f" % pointPDFRef,
" cdf (ref)=%.6f" % pointCDFRef,
)
# Get 50% quantile
quantile = copula.computeQuantile(0.5)
quantileRef = copulaRef.computeQuantile(0.5)
print("Quantile =", repr(quantile))
print("Quantile (ref)=", repr(quantileRef))
print("CDF(quantile)=%.6f" % copula.computeCDF(quantile))
# Get 95% survival function
inverseSurvival = ot.Point(copula.computeInverseSurvivalFunction(0.95))
print("InverseSurvival=", repr(inverseSurvival))
print(
"Survival(inverseSurvival)=%.6f" % copula.computeSurvivalFunction(inverseSurvival)
)
# Takes too much time
# print("entropy=%.6f" % copula.computeEntropy())
# Confidence regions
if copula.getDimension() <= 2:
threshold = ot.Point()
print(
"Minimum volume interval=", copula.computeMinimumVolumeInterval(0.95, threshold)
)
print("threshold=", threshold)
beta = ot.Point()
levelSet = copula.computeMinimumVolumeLevelSet(0.95, beta)
print("Minimum volume level set=", levelSet)
print("beta=", beta)
print(
"Bilateral confidence interval=",
copula.computeBilateralConfidenceInterval(0.95, beta),
)
print("beta=", beta)
print(
"Unilateral confidence interval (lower tail)=",
copula.computeUnilateralConfidenceInterval(0.95, False, beta),
)
print("beta=", beta)
print(
"Unilateral confidence interval (upper tail)=",
copula.computeUnilateralConfidenceInterval(0.95, True, beta),
)
print("beta=", beta)
# Extract the marginals
for i in range(dim):
margin = copula.getMarginal(i)
marginRef = copulaRef.getMarginal(i)
print("margin=", repr(margin))
print("margin PDF =%.6f" % margin.computePDF(ot.Point(1, 0.25)))
print("margin PDF (ref)=%.6f" % marginRef.computePDF(ot.Point(1, 0.25)))
print("margin CDF =%.6f" % margin.computeCDF(ot.Point(1, 0.25)))
print("margin CDF (ref)=%.6f" % marginRef.computeCDF(ot.Point(1, 0.25)))
print("margin quantile =", repr(margin.computeQuantile(0.95)))
print("margin quantile (ref)=", repr(marginRef.computeQuantile(0.95)))
print("margin realization=", repr(margin.getRealization()))
# Extract a 2-D marginal
indices = ot.Indices([1, 0])
print("indices=", repr(indices))
margin = copula.getMarginal(indices)
marginRef = copulaRef.getMarginal(indices)
print("margin=", repr(margin))
print("margin PDF =%.6f" % margin.computePDF(ot.Point(2, 0.25)))
print("margin PDF (ref)=%.6f" % marginRef.computePDF(ot.Point(2, 0.25)))
print("margin CDF =%.6f" % margin.computeCDF(ot.Point(2, 0.25)))
print("margin CDF (ref)=%.6f" % marginRef.computeCDF(ot.Point(2, 0.25)))
print("margin quantile =", repr(margin.computeQuantile(0.95)))
print("margin quantile (ref)=", repr(marginRef.computeQuantile(0.95)))
print("margin realization=", repr(margin.getRealization()))
ot.Log.Show(ot.Log.TRACE)
validation = ott.DistributionValidation(copula)
validation.run()
# tbb nested parallelism issue
student = ot.Student(3.0, [1.0] * 2, [3.0] * 2, ot.CorrelationMatrix(2))
copula = ot.SklarCopula(student)
pdf_graph = copula.drawPDF()
cdf_graph = copula.drawCDF()
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