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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
# Instantiate one distribution object
allDistributions = [ot.Student(6.5, -0.5, 2.0)]
dim = 2
R = ot.CorrelationMatrix(dim)
mu = list()
sigma = list()
for i in range(dim):
mu.append(i)
sigma.append((1.0 + i) / dim)
for j in range(i):
R[i, j] = 1.0 / (1.0 + dim + i + j)
allDistributions.append(ot.Student(7.5, mu, sigma, R))
for distribution in allDistributions:
dim = distribution.getDimension()
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=", 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(distribution.getDimension(), 1.0)
print("Point= ", repr(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)
CDF = distribution.computeCDF(point)
print("cdf=%.6f" % CDF)
CCDF = distribution.computeComplementaryCDF(point)
print("ccdf=%.6f" % CCDF)
# quantile
quantile = distribution.computeQuantile(0.95)
print("quantile=", repr(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=", repr(mean))
standardDeviation = distribution.getStandardDeviation()
print("standard deviation=", repr(standardDeviation))
skewness = distribution.getSkewness()
print("skewness=", repr(skewness))
kurtosis = distribution.getKurtosis()
print("kurtosis=", repr(kurtosis))
covariance = distribution.getCovariance()
print("covariance=", repr(covariance))
parameters = distribution.getParametersCollection()
print("parameters=", repr(parameters))
print("Standard representative=", distribution.getStandardRepresentative())
# Specific to this distribution
beta = point.normSquare()
densityGenerator = distribution.computeDensityGenerator(beta)
print("density generator=%.6f" % densityGenerator)
print(
"pdf via density generator=%.6f"
% ot.EllipticalDistribution.computePDF(distribution, point)
)
densityGeneratorDerivative = distribution.computeDensityGeneratorDerivative(beta)
print("density generator derivative =%.6f" % densityGeneratorDerivative)
eps = 1e-5
print(
"density generator derivative (FD)=%.6f"
% (
(
distribution.computeDensityGenerator(beta + eps)
- distribution.computeDensityGenerator(beta - eps)
)
/ (2.0 * eps)
)
)
densityGeneratorSecondDerivative = distribution.computeDensityGeneratorSecondDerivative(
beta
)
print(
"density generator second derivative =%.6f" % densityGeneratorSecondDerivative
)
print(
"density generator second derivative (FD)=%.6f"
% (
(
distribution.computeDensityGeneratorDerivative(beta + eps)
- distribution.computeDensityGeneratorDerivative(beta - eps)
)
/ (2.0 * eps)
)
)
x = 0.6
y = [0.2] * (dim - 1)
print("conditional PDF=%.6f" % distribution.computeConditionalPDF(x, y))
print("conditional CDF=%.6f" % distribution.computeConditionalCDF(x, y))
print("conditional quantile=%.6f" % distribution.computeConditionalQuantile(x, y))
pt = ot.Point([i + 1.5 for i in range(dim)])
print(
"sequential conditional PDF=", distribution.computeSequentialConditionalPDF(point)
)
resCDF = distribution.computeSequentialConditionalCDF(pt)
print("sequential conditional CDF(", pt, ")=", resCDF)
print(
"sequential conditional quantile(",
resCDF,
")=",
distribution.computeSequentialConditionalQuantile(resCDF),
)
ot.Log.Show(ot.Log.TRACE)
validation = ott.DistributionValidation(distribution)
validation.skipCorrelation() # slow
validation.run()
# non-spd cov
dist = ot.Student(
4.2,
[0] * 3,
ot.CovarianceMatrix([[1.0, 1.0, 0.0], [1.0, 1.0, 0.0], [0.0, 0.0, 1.0]]),
)
sample = dist.getSample(10)
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