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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.NormalCopula(R)
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))
# Define a point
point = ot.Point(dim, 0.2)
# 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 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
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)
# Covariance and correlation
covariance = copula.getCovariance()
print("covariance=", covariance)
correlation = copula.getCorrelation()
print("correlation=", correlation)
spearman = copula.getSpearmanCorrelation()
print("spearman=", spearman)
kendall = copula.getKendallTau()
print("kendall=", kendall)
x = 0.6
y = [0.2] * (dim - 1)
print("conditional PDF=%.6f" % copula.computeConditionalPDF(x, y))
print("conditional CDF=%.6f" % copula.computeConditionalCDF(x, y))
print("conditional quantile=%.6f" % copula.computeConditionalQuantile(x, y))
pt = ot.Point([0.1 * i + 0.05 for i in range(dim)])
print("sequential conditional PDF=", copula.computeSequentialConditionalPDF(point))
resCDF = copula.computeSequentialConditionalCDF(pt)
print("sequential conditional CDF(", pt, ")=", resCDF)
print(
"sequential conditional quantile(",
resCDF,
")=",
copula.computeSequentialConditionalQuantile(resCDF),
)
# 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 = 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()))
# Creation of the correlation matrix from a Spearman correlation matrix
spearman = ot.CorrelationMatrix(dim)
for i in range(1, dim):
spearman[i, i - 1] = 0.25
correlation = ot.NormalCopula.GetCorrelationFromSpearmanCorrelation(spearman)
print(
"Normal copula correlation=",
repr(correlation),
" from the Spearman correlation=",
repr(spearman),
)
ot.Log.Show(ot.Log.TRACE)
validation = ott.DistributionValidation(copula)
validation.run()
# computeProbability
spearman_corr = ot.CorrelationMatrix([[1.0, 0.74], [0.74, 1.0]])
copula = ot.NormalCopula(
ot.NormalCopula.GetCorrelationFromSpearmanCorrelation(spearman_corr)
)
interval = ot.Interval([0.958722, 0.902063], [1.0, 1.0])
prob = copula.computeProbability(interval)
print("prob=%.6f" % prob)
print(ot.NormalCopula(1).getParametersCollection())
# normal quantile inf propagation bug in iso transfo
R = ot.CorrelationMatrix(2)
R[0, 1] = 0.2
copula = ot.NormalCopula(R)
standard_list = [ot.Uniform(), ot.Beta()]
distribution = ot.JointDistribution(standard_list, copula)
standard = ot.JointDistribution(standard_list)
transformation = ot.DistributionTransformation(distribution, standard)
standard_sample = transformation(ot.Normal(distribution.getDimension()).getSample(10))
print(standard_sample)
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