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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
parameters = ot.GammaMuSigma(0.1, 0.489898, -0.5)
distribution = ot.ParametrizedDistribution(parameters)
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)
# Define a point
point = ot.Point(distribution.getDimension(), 1.0)
print("Point= ", point)
# Show PDF and CDF of point
DDF = distribution.computeDDF(point)
print("ddf =", DDF)
LPDF = distribution.computeLogPDF(point)
print("log pdf= %.6g" % LPDF)
PDF = distribution.computePDF(point)
print("pdf =%.6g" % PDF)
CDF = distribution.computeCDF(point)
print("cdf= %.6g" % CDF)
CCDF = distribution.computeComplementaryCDF(point)
print("ccdf= %.6g" % CCDF)
Survival = distribution.computeSurvivalFunction(point)
print("survival= %.6g" % Survival)
CF = distribution.computeCharacteristicFunction(point[0])
print("characteristic function=(%.6g, %.6g)" % (CF.real, CF.imag))
LCF = distribution.computeLogCharacteristicFunction(point[0])
print("log characteristic function=(%.6g, %.6g)" % (LCF.real, LCF.imag))
PDFgr = distribution.computePDFGradient(point)
quantile = distribution.computeQuantile(0.95)
print("quantile=", quantile)
print("cdf(quantile)=", 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
interval, threshold = distribution.computeMinimumVolumeIntervalWithMarginalProbability(
0.95
)
ott.assert_almost_equal(interval.getLowerBound(), [-0.49937], 1e-4, 0.0)
ott.assert_almost_equal(interval.getUpperBound(), [1.06337], 1e-4, 0.0)
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)
covariance = distribution.getCovariance()
print("covariance=", covariance)
correlation = distribution.getCorrelation()
print("correlation=", correlation)
spearman = distribution.getSpearmanCorrelation()
print("spearman=", spearman)
kendall = distribution.getKendallTau()
print("kendall=", kendall)
parameters = distribution.getParametersCollection()
print("parameters=", parameters)
print("Standard representative=", distribution.getStandardRepresentative())
cpdf = distribution.computeConditionalPDF(0.0, [])
print(f"conditional PDF={cpdf:.6f}")
scpdf = distribution.computeSequentialConditionalPDF([0.0])
print(f"sequential conditional PDF={scpdf}")
ccdf = distribution.computeConditionalCDF(0.0, [])
print(f"conditional CDF={ccdf:.6f}")
sccdf = distribution.computeSequentialConditionalCDF([0.0])
print(f"sequential conditional CDF={sccdf}")
ot.RandomGenerator.SetSeed(2)
ot.Log.Show(ot.Log.TRACE)
validation = ott.DistributionValidation(distribution)
validation.run()
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