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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
all_cases = [
ot.GeneralizedExtremeValue(2.0, 1.5, -0.15),
ot.GeneralizedExtremeValue(2.0, 1.5, 0.0),
ot.GeneralizedExtremeValue(2.0, 1.5, 0.15),
]
for i in range(len(all_cases)):
distribution = all_cases[i]
print("#" * 50)
print("Distribution ", distribution)
for dist in ["WeibullMax", "Frechet", "Gumbel"]:
try:
eval("print('conversion as ', distribution.as" + dist + "())")
except Exception:
pass
# 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 = [1.0] * distribution.getDimension()
print("Point= ", point)
# Show PDF and CDF of point
DDF = distribution.computeDDF(point)
print("ddf =", DDF)
LPDF = distribution.computeLogPDF(point)
print("log pdf=", ot.Point(1, LPDF))
PDF = distribution.computePDF(point)
print("pdf =", ot.Point(1, PDF))
CDF = distribution.computeCDF(point)
print("cdf=", ot.Point(1, CDF))
CCDF = distribution.computeComplementaryCDF(point)
print("ccdf=", ot.Point(1, CCDF))
Survival = distribution.computeSurvivalFunction(point)
print("survival=", ot.Point(1, Survival))
InverseSurvival = distribution.computeInverseSurvivalFunction(0.95)
print("Inverse survival=", InverseSurvival)
print(
"Survival(inverse survival)=",
ot.Point(1, distribution.computeSurvivalFunction(InverseSurvival)),
)
PDFgr = distribution.computePDFGradient(point)
print("pdf gradient =", PDFgr)
CDFgr = distribution.computeCDFGradient(point)
print("cdf gradient =", CDFgr)
quantile = distribution.computeQuantile(0.95)
print("quantile=", quantile)
rl = distribution.computeReturnLevel(10.0)
print(f"return level={rl:.6f}")
print("cdf(quantile)=", distribution.computeCDF(quantile))
print("entropy=%.6f" % distribution.computeEntropy())
# Confidence regions
prob, threshold = distribution.computeMinimumVolumeIntervalWithMarginalProbability(
0.95
)
print("Minimum volume interval=", prob)
print("threshold=", 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)
parameters = distribution.getParametersCollection()
print("parameters=", parameters)
print("Standard representative=", distribution.getStandardRepresentative())
print("mu=", distribution.getMu())
print("sigma=", distribution.getSigma())
print("xi=", distribution.getXi())
print("Actual distribution=", distribution.getActualDistribution())
distribution.setActualDistribution(distribution.getActualDistribution())
print("Distribution from actual distribution=", distribution)
ot.Log.Show(ot.Log.TRACE)
validation = ott.DistributionValidation(distribution)
validation.skipMinimumVolumeLevelSet()
validation.run()
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