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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
# Instantiate one distribution object
graph = ot.BipartiteGraph([[0, 1], [0, 1]])
distribution = ot.CumulativeDistributionNetwork([ot.Normal(2)] * 2, graph)
print("Distribution ", repr(distribution))
print("Distribution ", distribution)
# Is this distribution elliptical ?
print("Elliptical = ", distribution.isElliptical())
# Is this distribution continuous ?
print("Continuous = ", distribution.isContinuous())
# Test for realization of distribution
oneRealization = distribution.getRealization()
print("oneRealization=", oneRealization)
# Test for sampling
size = 10000
oneSample = distribution.getSample(size)
print("oneSample first=", oneSample[0], " last=", oneSample[size - 1])
print("mean=", oneSample.computeMean())
print("covariance=", oneSample.computeCovariance())
# Define a point
point = [1.0] * distribution.getDimension()
print("Point= ", point)
# Show PDF and CDF of point
LPDF = distribution.computeLogPDF(point)
print("log pdf =%.4e" % LPDF)
PDF = distribution.computePDF(point)
print("pdf =%.4e" % PDF)
CDF = distribution.computeCDF(point)
print("cdf =%.4e" % CDF)
CCDF = distribution.computeComplementaryCDF(point)
print("ccdf =%.4e" % CCDF)
Survival = distribution.computeSurvivalFunction(point)
print("survival=%.4e" % Survival)
quantile = distribution.computeQuantile(0.95)
print("quantile=", quantile)
print("cdf(quantile)= %.12g" % distribution.computeCDF(quantile))
# Get 95% survival function
inverseSurvival = ot.Point(distribution.computeInverseSurvivalFunction(0.95))
print("InverseSurvival=", repr(inverseSurvival))
print(
"Survival(inverseSurvival)=%.6f"
% distribution.computeSurvivalFunction(inverseSurvival)
)
# Confidence regions. Some computations take ages so they are commented
if distribution.getDimension() <= 2:
# interval, threshold = distribution.computeMinimumVolumeIntervalWithMarginalProbability(0.95)
# print("Minimum volume interval=", interval)
# print("threshold=", ot.Point(1, threshold))
# levelSet, beta = distribution.computeMinimumVolumeLevelSetWithThreshold(0.95)
# print("Minimum volume level set=", levelSet)
# print("beta=", ot.Point(1, beta))
# interval, beta = distribution.computeBilateralConfidenceIntervalWithMarginalProbability(0.95)
# print("Bilateral confidence interval=", interval)
# print("beta=", ot.Point(1, beta))
(
interval,
beta,
) = distribution.computeUnilateralConfidenceIntervalWithMarginalProbability(
0.95, False
)
print("Unilateral confidence interval (lower tail)=", interval)
print("beta=", ot.Point(1, beta))
(
interval,
beta,
) = distribution.computeUnilateralConfidenceIntervalWithMarginalProbability(
0.95, True
)
print("Unilateral confidence interval (upper tail)=", interval)
print("beta=", ot.Point(1, beta))
mean = distribution.getMean()
print("mean=", mean)
standardDeviation = distribution.getStandardDeviation()
print("standard deviation=", standardDeviation)
skewness = distribution.getSkewness()
print("skewness=", skewness)
kurtosis = distribution.getKurtosis()
print("kurtosis=", kurtosis)
covariance = distribution.getCovariance()
print("covariance=", covariance)
correlation = distribution.getCorrelation()
print("correlation=", correlation)
spearman = distribution.getSpearmanCorrelation()
print("spearman=", spearman)
kendall = distribution.getKendallTau()
print("kendall=", kendall)
# Build a distribution with no specific implementation of getMarginal()
atom = ot.JointDistribution([ot.Uniform(0.0, 1.0)] * 3)
graph = ot.BipartiteGraph([[0, 1, 2], [0, 1, 2]])
distribution = ot.CumulativeDistributionNetwork([atom] * 2, graph)
# Extract its marginal using the generic implementation
marginal = distribution.getMarginal([0, 1])
# Build by hands the exact marginal
atom_ref = ot.JointDistribution([ot.Uniform(0.0, 1.0)] * 2)
graph_ref = ot.BipartiteGraph([[0, 1], [0, 1]])
ref = ot.CumulativeDistributionNetwork([atom_ref] * 2, graph_ref)
# test getMarginal generic implementation
print(ref)
print(distribution.getMarginal([0, 1]))
X = atom_ref.getSample(10000)
error = (
ref.computeCDF(X) - distribution.getMarginal([0, 1]).computeCDF(X)
).computeStandardDeviation()
ott.assert_almost_equal(error[0], 0.0)
# test getMarginal with full indices
print(distribution)
print(distribution.getMarginal([0, 1, 2]))
ot.Log.Show(ot.Log.TRACE)
validation = ott.DistributionValidation(distribution)
validation.skipMoments() # slow
validation.skipCorrelation() # slow
validation.skipConditional() # FIXME
validation.skipTransformation() # FIXME
validation.run()
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