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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
# Instantiate one distribution object
f = ot.SymbolicFunction("x", "x^2 + 2 * sin(x)")
distribution = ot.CompositeDistribution(f, ot.Normal())
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 = 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= %.12g" % LPDF)
PDF = distribution.computePDF(point)
print("pdf = %.10g" % PDF)
CDF = distribution.computeCDF(point)
print("cdf= %.12g" % CDF)
CCDF = distribution.computeComplementaryCDF(point)
print("ccdf= %.12g" % CCDF)
Survival = distribution.computeSurvivalFunction(point)
print("survival= %.12g" % Survival)
quantile = distribution.computeQuantile(0.95)
print("quantile=", quantile)
print("cdf(quantile)= %.12g" % distribution.computeCDF(quantile))
quantileTail = distribution.computeQuantile(0.95, True)
print("quantile (tail)=", quantileTail)
CDFTail = distribution.computeComplementaryCDF(quantileTail)
print("cdf (tail)= %.12g" % CDFTail)
# 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
)
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))
CF = distribution.computeCharacteristicFunction(point[0])
print("characteristic function=(%.6g+%.6gj)" % (CF.real, CF.imag))
LCF = distribution.computeLogCharacteristicFunction(point[0])
print("log characteristic function=(%.6g+%.6gj)" % (LCF.real, LCF.imag))
PDFgr = distribution.computePDFGradient(point)
print("pdf gradient =", PDFgr)
CDFgr = distribution.computeCDFGradient(point)
print("cdf gradient =", CDFgr)
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())
# Specific to this distribution
antecedent = distribution.getAntecedent()
print("antecedent=", antecedent)
function = distribution.getFunction()
print("function=", function)
newDistribution = ot.CompositeDistribution(function, antecedent)
print("newDistribution=", newDistribution)
ot.Log.Show(ot.Log.TRACE)
validation = ott.DistributionValidation(distribution)
validation.skipEntropy() # slow
validation.skipMinimumVolumeInterval() # wrong proba
validation.skipMinimumVolumeLevelSet() # slow
validation.run()
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