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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
# Instantiate one distribution object
dim = 2
copula = ot.FarlieGumbelMorgensternCopula(0.7)
copula.setName("a farlieGumbelMorgenstern copula")
print("Copula ", repr(copula))
print("Copula ", copula)
print("Mean ", copula.getMean())
print("Covariance ", copula.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 copula
oneRealization = copula.getRealization()
print("oneRealization=", oneRealization)
# Define a point
point = ot.Point(dim, 0.2)
# Show PDF and CDF of zero point
zeroPDF = copula.computePDF(point)
zeroCDF = copula.computeCDF(point)
print("point= ", point, " pdf=", zeroPDF, " cdf= %.12g" % zeroCDF)
# Get 50% quantile
quantile = copula.computeQuantile(0.5)
print("Quantile=", quantile)
print("CDF(quantile)= %.12g" % 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))
# Extract the marginals
for i in range(dim):
margin = copula.getMarginal(i)
print("margin=", margin)
print("margin PDF=", margin.computePDF(ot.Point(1, 0.25)))
print("margin CDF=", margin.computeCDF(ot.Point(1, 0.25)))
print("margin quantile=", margin.computeQuantile(0.95))
print("margin realization=", margin.getRealization())
# Extract a 2-D marginal
indices = [1, 0]
print("indices=", indices)
margins = copula.getMarginal(indices)
print("margins=", margins)
print("margins PDF=", margins.computePDF(ot.Point(2, 0.25)))
print("margins CDF= %.12g" % margins.computeCDF(ot.Point(2, 0.25)))
quantile = margins.computeQuantile(0.95)
print("margins quantile=", quantile)
print("margins CDF(quantile)= %.12g" % margins.computeCDF(quantile))
print("margins realization=", margins.getRealization())
ot.Log.Show(ot.Log.TRACE)
validation = ott.DistributionValidation(copula)
validation.run()
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