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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
# First constructor: distribution of the maximum of the components
# of a random vector given its joint distribution
# Second constructor: distribution of the maximum of independent
# random variables given their distributions
# Third constructor: distribution of the maximum of independent
# identically distributed random variables
R = ot.CorrelationMatrix(3)
R[0, 1] = 0.5
coll = [
ot.MaximumDistribution(ot.Normal(5)),
ot.MaximumDistribution([ot.Normal()] * 5),
ot.MaximumDistribution(ot.Normal(), 5),
ot.MaximumDistribution(ot.Normal([0.0] * 3, [1.0] * 3, R)),
]
for index, distribution in enumerate(coll):
print("Distribution ", distribution)
# Is this distribution elliptical ?
print("Elliptical = ", distribution.isElliptical())
# Is this distribution continuous ?
print("Continuous = ", distribution.isContinuous())
# Confidence regions
(
interval,
threshold,
) = distribution.computeMinimumVolumeIntervalWithMarginalProbability(0.95)
if index < 3:
ott.assert_almost_equal(interval.getLowerBound(), [-0.11278], 1e-4, 0.0)
ott.assert_almost_equal(interval.getUpperBound(), [2.50221], 1e-4, 0.0)
else:
ott.assert_almost_equal(interval.getLowerBound(), [-0.770165], 1e-4, 0.0)
ott.assert_almost_equal(interval.getUpperBound(), [2.33536], 1e-4, 0.0)
print("threshold=", threshold)
levelSet, beta = distribution.computeMinimumVolumeLevelSetWithThreshold(0.95)
print("Minimum volume level set=", levelSet)
print("beta=%.5g" % beta)
(
interval,
beta,
) = distribution.computeBilateralConfidenceIntervalWithMarginalProbability(0.95)
print("Bilateral confidence interval=", interval)
print("beta=%.5g" % beta)
(
interval,
beta,
) = distribution.computeUnilateralConfidenceIntervalWithMarginalProbability(
0.95, False
)
if index < 3:
ott.assert_almost_equal(interval.getLowerBound(), [-7.65063], 1e-4, 0.0)
ott.assert_almost_equal(interval.getUpperBound(), [2.31868], 1e-4, 0.0)
else:
ott.assert_almost_equal(interval.getLowerBound(), [-7.65063], 1e-4, 0.0)
ott.assert_almost_equal(interval.getUpperBound(), [2.10094], 1e-4, 0.0)
print("beta=%.5g" % beta)
(
interval,
beta,
) = distribution.computeUnilateralConfidenceIntervalWithMarginalProbability(
0.95, True
)
if index < 3:
ott.assert_almost_equal(interval.getLowerBound(), [0.123843], 1e-4, 0.0)
ott.assert_almost_equal(interval.getUpperBound(), [7.65063], 1e-4, 0.0)
else:
ott.assert_almost_equal(interval.getLowerBound(), [-0.502767], 1e-4, 0.0)
ott.assert_almost_equal(interval.getUpperBound(), [7.65063], 1e-4, 0.0)
print("beta=%.5g" % beta)
spearman = distribution.getSpearmanCorrelation()
print("spearman=", spearman)
kendall = distribution.getKendallTau()
print("kendall=", kendall)
print("Standard representative=", distribution.getStandardRepresentative())
ot.Log.Show(ot.Log.TRACE)
ot.RandomGenerator.SetSeed(1234)
validation = ott.DistributionValidation(distribution)
validation.skipEntropy() # slow
validation.skipMinimumVolumeLevelSet() # slow
validation.run()
# Issue #1643
coll = [ot.Uniform(), ot.Normal()]
distribution = ot.MaximumDistribution(coll)
print("%.5g" % distribution.computePDF([1.1]))
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