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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
ot.PlatformInfo.SetNumericalPrecision(5)
# Instantiate one distribution object
dim = 2
copula = ot.EmpiricalBernsteinCopula(ot.Normal(2).getSample(12), 3)
print("Copula ", repr(copula))
print("Copula ", copula)
print("Mean ", repr(copula.getMean()))
print("Covariance ", repr(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 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 = 10000
anotherSample = copula.getSample(size)
print("anotherSample mean=", repr(anotherSample.computeMean()))
print("anotherSample covariance=", repr(anotherSample.computeCovariance()))
# Define a point
point = [0.2] * dim
# Show PDF and CDF of point
pointPDF = copula.computePDF(point)
pointCDF = copula.computeCDF(point)
print("Point = ", repr(point), " pdf=%.6f" % pointPDF, " cdf=%.6f" % pointCDF)
# Get 50% quantile
quantile = copula.computeQuantile(0.5)
print("Quantile=", repr(quantile))
print("CDF(quantile)=%.6f" % copula.computeCDF(quantile))
# Get 5% quantile
quantile = copula.computeQuantile(0.95, True)
print("Quantile=", repr(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))
print("parameters=", copula.getParameter())
copula.setParameter(copula.getParameter())
# Extract the marginals
for i in range(dim):
margin = copula.getMarginal(i)
print("margin=", repr(margin))
print("margin PDF=%.6f" % margin.computePDF([0.25]))
print("margin CDF=%.6f" % margin.computeCDF([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([0.25] * 2))
print("margins CDF=%.6f" % margins.computeCDF([0.25] * 2))
quantile = ot.Point(margins.computeQuantile(0.95))
print("margins quantile=", repr(quantile))
print("margins CDF(qantile)=%.6f" % margins.computeCDF(quantile))
print("margins realization=", repr(margins.getRealization()))
copula6D = ot.EmpiricalBernsteinCopula(ot.Normal(6).getSample(8), 4)
print("Entropy in higher dimension=%.6f" % copula6D.computeEntropy())
dim = 6
x = 0.6
y = [0.2] * (dim - 1)
print("conditional PDF=%.6f" % copula6D.computeConditionalPDF(x, y))
print(
"conditional PDF ref=%.6f"
% (copula6D.computePDF(y + [x]) / copula6D.getMarginal(range(5)).computePDF(y))
)
print("conditional CDF=%.6f" % copula6D.computeConditionalCDF(x, y))
print("conditional quantile=%.6f" % copula6D.computeConditionalQuantile(x, y))
pt = [0.05 * (1 + i) for i in range(dim)]
print("sequential conditional PDF=", copula6D.computeSequentialConditionalPDF(pt))
resCDF = copula6D.computeSequentialConditionalCDF(pt)
print("sequential conditional CDF(", pt, ")=", resCDF)
print(
"sequential conditional quantile(",
resCDF,
")=",
copula6D.computeSequentialConditionalQuantile(resCDF),
)
ot.Log.Show(ot.Log.TRACE)
validation = ott.DistributionValidation(copula)
validation.run()
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