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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
copula = ot.IndependentCopula(dim)
print("Copula =", repr(copula))
print("Copula =", copula)
# Is this copula an elliptical distribution?
print("Elliptical distribution = ", copula.isElliptical())
# Is this copula continuous ?
print("Continuous copula = ", copula.isContinuous())
# Is this copula elliptical ?
print("Elliptical copula = ", copula.hasEllipticalCopula())
# Is this copula independent ?
print("hasIndependentCopula = ", copula.hasIndependentCopula())
# Test for realization of copula
oneRealization = copula.getRealization()
print("oneRealization=", repr(oneRealization))
# Define a point
point = ot.Point(copula.getDimension(), 0.6)
print("Point= ", repr(point))
# derivative of PDF with regards its arguments
DDF = copula.computeDDF(point)
print("ddf =", repr(DDF))
# PDF value
PDF = copula.computePDF(point)
print("pdf =%.6f" % PDF)
# CDF value
CDF = copula.computeCDF(point)
print("cdf=%.6f" % CDF)
# derivative of the PDF with regards the parameters of the distribution
PDFgr = copula.computePDFGradient(point)
print("pdf gradient =", repr(PDFgr))
# derivative of the CDF with regards the parameters of the distribution
CDFgr = copula.computeCDFGradient(point)
print("cdf gradient =", repr(CDFgr))
# quantile
quantile = copula.computeQuantile(0.95)
print("quantile=", repr(quantile))
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)
)
print("entropy=%.6f" % copula.computeEntropy())
# Confidence regions
interval, threshold = copula.computeMinimumVolumeIntervalWithMarginalProbability(0.95)
print("Minimum volume interval=", interval)
print("threshold=", ot.Point(1, threshold))
levelSet, beta = copula.computeMinimumVolumeLevelSetWithThreshold(0.95)
print("Minimum volume level set=", levelSet)
print("beta=", ot.Point(1, beta))
interval, beta = copula.computeBilateralConfidenceIntervalWithMarginalProbability(0.95)
print("Bilateral confidence interval=", interval)
print("beta=", ot.Point(1, beta))
interval, beta = copula.computeUnilateralConfidenceIntervalWithMarginalProbability(
0.95, False
)
print("Unilateral confidence interval (lower tail)=", interval)
print("beta=", ot.Point(1, beta))
interval, beta = copula.computeUnilateralConfidenceIntervalWithMarginalProbability(
0.95, True
)
print("Unilateral confidence interval (upper tail)=", interval)
print("beta=", ot.Point(1, beta))
# mean
mean = copula.getMean()
print("mean=", repr(mean))
# covariance
covariance = copula.getCovariance()
print("covariance=", repr(covariance))
# parameters of the distribution
parameters = copula.getParametersCollection()
print("parameters=", repr(parameters))
# Specific to this copula
# Extract the marginals
for i in range(dim):
margin = copula.getMarginal(i)
print("margin=", repr(margin))
print("margin PDF=%.6f" % margin.computePDF(ot.Point(1, 0.25)))
print("margin CDF=%.6f" % margin.computeCDF(ot.Point(1, 0.25)))
print("margin quantile=", repr(margin.computeQuantile(0.95)))
print("margin realization=", repr(margin.getRealization()))
# Extract a 2-D marginal
indices = [1, 0]
print("indices=", repr(indices))
margins = copula.getMarginal(indices)
print("margins=", repr(margins))
print("margins PDF=%.6f" % margins.computePDF(ot.Point(2, 0.25)))
print("margins CDF=%.6f" % margins.computeCDF(ot.Point(2, 0.25)))
quantile = margins.computeQuantile(0.95)
print("margins quantile=", repr(quantile))
print("margins CDF(quantile)=%.6f" % margins.computeCDF(quantile))
print("margins realization=", repr(margins.getRealization()))
ot.Log.Show(ot.Log.TRACE)
validation = ott.DistributionValidation(copula)
validation.run()
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