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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
# Force the use of the approximation to avoid timeout
ot.ResourceMap.SetAsBool(
"MaximumEntropyOrderStatisticsDistribution-UseApproximation", True
)
# Instantiate one distribution object
distribution = ot.MaximumEntropyOrderStatisticsDistribution(
[
ot.Trapezoidal(-2.0, -1.1, -1.0, 1.0),
ot.LogUniform(1.0, 1.2),
ot.Triangular(3.0, 4.5, 5.0),
ot.Beta(2.5, 3.5, 4.7, 5.2),
]
)
dim = distribution.getDimension()
print("Distribution ", distribution)
# Is this distribution elliptical ?
print("Elliptical = ", distribution.isElliptical())
# Test for realization of distribution
oneRealization = distribution.getRealization()
print("oneRealization=", repr(oneRealization))
# Test for sampling
size = 10000
oneSample = distribution.getSample(size)
print("oneSample first=", repr(oneSample[0]), " last=", repr(oneSample[size - 1]))
print("mean=", repr(oneSample.computeMean()))
print("covariance=", repr(oneSample.computeCovariance()))
# Define a point
point = ot.Point([0.0, 3.2, 4.2, 5.0])
print("Point= ", point)
# derivative of PDF with regards its arguments
DDF = distribution.computeDDF(point)
print("ddf =", repr(DDF))
# PDF value
LPDF = distribution.computeLogPDF(point)
print("log pdf=%.6f" % LPDF)
PDF = distribution.computePDF(point)
print("pdf =%.6f" % PDF)
condPDF = distribution.computeConditionalPDF(4.0, [0.0, 2.0])
print("condPDF =%.6f" % condPDF)
# derivative of the PDF with regards the parameters of the distribution
CDF = distribution.computeCDF(point)
print("cdf=%.6f" % CDF)
CCDF = distribution.computeComplementaryCDF(point)
print("ccdf=%.6f" % CCDF)
condCDF = distribution.computeConditionalCDF(4.0, [0.0, 2.0])
print("condCDF =%.6f" % condCDF)
# PDFgr = distribution.computePDFGradient(point)
# print "pdf gradient =", repr(PDFgr)
# quantile
quantile = distribution.computeQuantile(0.95)
print("quantile=", repr(quantile))
print("cdf(quantile)=%.6f" % distribution.computeCDF(quantile))
condQuantile = distribution.computeConditionalQuantile(0.4, [0.0, 2.0])
print("condQuantile =%.6f" % condQuantile)
mean = distribution.getMean()
print("mean=", repr(mean))
standardDeviation = distribution.getStandardDeviation()
print("standard deviation=", repr(standardDeviation))
skewness = distribution.getSkewness()
print("skewness=", repr(skewness))
kurtosis = distribution.getKurtosis()
print("kurtosis=", repr(kurtosis))
ot.ResourceMap.SetAsUnsignedInteger("GaussKronrod-MaximumSubIntervals", 20)
ot.ResourceMap.SetAsScalar("GaussKronrod-MaximumError", 1.0e-4)
covariance = distribution.getCovariance()
print("covariance=", repr(covariance))
correlation = distribution.getCorrelation()
print("correlation=", repr(correlation))
spearman = distribution.getSpearmanCorrelation()
print("spearman=", repr(spearman))
ot.ResourceMap.SetAsUnsignedInteger("GaussKronrod-MaximumSubIntervals", 100)
ot.ResourceMap.SetAsScalar("GaussKronrod-MaximumError", 1.0e-12)
parameters = distribution.getParametersCollection()
print("parameters=", repr(parameters))
# Extract the marginals
for i in range(dim):
margin = distribution.getMarginal(i)
print("margin=", repr(margin))
print("margin PDF=%.6f" % margin.computePDF(point[i]))
print("margin CDF=%.6f" % margin.computeCDF(point[i]))
print("margin quantile=", repr(margin.computeQuantile(0.5)))
print("margin realization=", repr(margin.getRealization()))
print("margin range=", repr(margin.getRange()))
# Extract a 2-D marginal
indices = [0, 1]
print("indices=", repr(indices))
margins = distribution.getMarginal(indices)
print("margins=", repr(margins))
print("margins PDF=%.6f" % margins.computePDF([point[i] for i in indices]))
print("margins CDF=%.6f" % margins.computeCDF([point[i] for i in indices]))
quantile = ot.Point(margins.computeQuantile(0.8))
print("margins quantile=", repr(quantile))
print("margins CDF(qantile)=%.6f" % margins.computeCDF(quantile))
print("margins realization=", repr(margins.getRealization()))
ot.Log.Show(ot.Log.TRACE)
validation = ott.DistributionValidation(distribution)
validation.skipMoments() # slow
validation.skipCorrelation() # slow
validation.skipParameters() # slow
validation.skipConditional() # FIXME
validation.skipTransformation() # FIXME
validation.run()
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