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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
ot.ResourceMap.SetAsUnsignedInteger("MeixnerDistribution-CDFIntegrationNodesNumber", 8)
ot.ResourceMap.SetAsUnsignedInteger("MeixnerDistribution-CDFDiscretization", 100)
ot.ResourceMap.SetAsScalar("MeixnerDistribution-MaximumAbsoluteError", 1.0e-6)
ot.ResourceMap.SetAsScalar("MeixnerDistribution-MaximumRelativeError", 1.0e-6)
ot.ResourceMap.SetAsScalar("MeixnerDistribution-MaximumConstraintError", 1.0e-6)
ot.ResourceMap.SetAsScalar("MeixnerDistribution-MaximumObjectiveError", 1.0e-6)
# Instantiate one distribution object
distribution = ot.MeixnerDistribution(1.5, 0.5, 2.5, -0.5)
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)
# Define a point
point = ot.Point(distribution.getDimension(), 1.0)
print("Point= ", point)
# Show PDF and CDF of point
LPDF = distribution.computeLogPDF(point)
print("log pdf=%.6f" % LPDF)
PDF = distribution.computePDF(point)
print("pdf =%.6f" % PDF)
print("PDF gradient=", distribution.computePDFGradient(point))
CDF = distribution.computeCDF(point)
print("cdf=%.6f" % CDF)
print("CDF gradient=", distribution.computeCDFGradient(point))
CCDF = distribution.computeComplementaryCDF(point)
print("ccdf=%.6f" % CCDF)
CF = distribution.computeCharacteristicFunction(point[0])
print("characteristic function=(%.12g%+.12gj)" % (CF.real, CF.imag))
LCF = distribution.computeLogCharacteristicFunction(point[0])
print("log characteristic function=(%.12g%+.12gj)" % (LCF.real, LCF.imag))
quantile = distribution.computeQuantile(0.95)
print("quantile=", quantile)
print("cdf(quantile)=%.6f" % 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)
)
print("entropy=%.6f" % distribution.computeEntropy())
# Confidence regions
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)
covariance = distribution.getCovariance()
print("covariance=", covariance)
parameters = distribution.getParametersCollection()
print("parameters=", parameters)
print("Standard representative=", distribution.getStandardRepresentative())
# Specific to this distribution
alpha = distribution.getAlpha()
print("alpha=%.6f" % alpha)
beta = distribution.getBeta()
print("beta=%.6f" % beta)
delta = distribution.getDelta()
print("delta=%.6f" % delta)
gamma = distribution.getGamma()
print("gamma=%.6f" % gamma)
standardDeviation = distribution.getStandardDeviation()
print("standard deviation=", standardDeviation)
skewness = distribution.getSkewness()
print("skewness=", skewness)
kurtosis = distribution.getKurtosis()
print("kurtosis=", kurtosis)
ot.Log.Show(ot.Log.TRACE)
validation = ott.DistributionValidation(distribution)
validation.run()
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