# add a 2-d test
dimension = 2
# This distribution takes too much time for the test
#size = 70
#ref = ot.Normal(dimension)
#sample = ref.getSample(size)
#ks = ot.KernelSmoothing().build(sample)
# Use a multivariate Normal distribution instead
ks = ot.Normal(2)
truncatedKS = ot.TruncatedDistribution(
ks, ot.Interval([-0.5] * dimension, [2.0] * dimension))
distribution.append(truncatedKS)
referenceDistribution.append(ks) # N/A
# Add a non-truncated example
weibull = ot.Weibull(2.0, 3.0)
distribution.append(ot.TruncatedDistribution(weibull))
referenceDistribution.append(weibull)
ot.RandomGenerator.SetSeed(0)
for testCase in range(len(distribution)):
print('Distribution ', distribution[testCase])
# Is this distribution elliptical ?
print('Elliptical = ', distribution[testCase].isElliptical())
# Is this distribution continuous ?
print('Continuous = ', distribution[testCase].isContinuous())
# Test for realization of distribution
oneRealization = distribution[testCase].getRealization()
graph = result.drawPDF()
result = ot.LogUniform() * ot.LogUniform()
print('logu*logu:', result)
graph = result.drawPDF()
result = ot.LogUniform() * ot.LogNormal()
print('logu*logn:', result)
graph = result.drawPDF()
result = ot.LogNormal() * ot.LogUniform()
print('logn*logu:', result)
graph = result.drawPDF()
# For ticket #917
result = ot.Weibull() + ot.Exponential()
print('Weibull+Exponential:', result)
print('result.CDF(1.0)=%.6f' % result.computeCDF(1.0))
result = -1.0 * ot.Weibull() + ot.Exponential()
print('-Weibull+Exponential:', result)
print('result.CDF(1.0)=%.6f' % result.computeCDF(1.0))
result = ot.Weibull() - ot.Exponential()
print('Weibull-Exponential:', result)
print('result.CDF(1.0)=%.6f' % result.computeCDF(1.0))
result = -1.0 * ot.Weibull() - ot.Exponential()
print('-Weibull-Exponential:', result)
print('result.CDF(-1.0)=%.6f' % result.computeCDF(-1.0))
# 2-d
print(ot.Normal(2) + ot.Normal(2))
print(ot.Normal(2) + 3.0)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.Weibull().__class__.__name__ == 'ComposedDistribution':
correlation = ot.CorrelationMatrix(2)
correlation[1, 0] = 0.25
aCopula = ot.NormalCopula(correlation)
marginals = [ot.Normal(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, aCopula)
elif ot.Weibull().__class__.__name__ == 'CumulativeDistributionNetwork':
distribution = ot.CumulativeDistributionNetwork(
[ot.Normal(2), ot.Dirichlet([0.5, 1.0, 1.5])],
ot.BipartiteGraph([[0, 1], [0, 1]]))
elif ot.Weibull().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
else:
distribution = ot.Weibull()
dimension = distribution.getDimension()
if dimension == 1:
distribution.setDescription(['$x$'])
pdf_graph = distribution.drawPDF()
cdf_graph = distribution.drawCDF()
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(distribution))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph, figure=fig, axes=[pdf_axis], add_legend=False)
View(cdf_graph, figure=fig, axes=[cdf_axis], add_legend=False)
elif dimension == 2:
distribution.setDescription(['$x_1$', '$x_2$'])
pdf_graph = distribution.drawPDF()
coefficients[i] = 0.0
return ot.UniVariatePolynomial(coefficients)
iMax = 5
distributionCollection = [
ot.Laplace(1.0, 0.0),
ot.Logistic(0.0, 1.0),
ot.Normal(0.0, 1.0),
ot.Normal(1.0, 1.0),
ot.Rayleigh(1.0),
ot.Student(22.0),
ot.Triangular(-1.0, 0.3, 1.0),
ot.Uniform(-1.0, 1.0),
ot.Uniform(-1.0, 3.0),
ot.Weibull(1.0, 3.0),
ot.Beta(1.0, 3.0, -1.0, 1.0),
ot.Beta(0.5, 1.0, -1.0, 1.0),
ot.Beta(0.5, 1.0, -2.0, 3.0),
ot.Gamma(1.0, 3.0),
ot.Arcsine()
]
for n in range(len(distributionCollection)):
distribution = distributionCollection[n]
name = distribution.getClassName()
polynomialFactory = ot.StandardDistributionPolynomialFactory(
ot.AdaptiveStieltjesAlgorithm(distribution))
print("polynomialFactory(", name, "=", polynomialFactory, ")")
for i in range(iMax):
print(name, " polynomial(", i, ")=", clean(polynomialFactory.build(i)))
roots = polynomialFactory.getRoots(iMax - 1)
xMax = sample.getMax()[0]
delta = xMax - xMin
a = xMin - delta / (size + 2)
b = xMax + delta / (size + 2)
distribution = ot.TruncatedNormal()
factory = ot.MethodOfMomentsFactory(distribution)
factory.setKnownParameter([a, b], [2, 3])
solver = factory.getOptimizationAlgorithm()
sampleMean = sample.computeMean()[0]
sampleSigma = sample.computeStandardDeviationPerComponent()[0]
startingPoint = [sampleMean, sampleSigma]
solver.setStartingPoint(startingPoint)
factory.setOptimizationAlgorithm(solver)
lowerBound = [-1.0, 0]
upperBound = [-1.0, 1.5]
finiteLowerBound = [False, True]
finiteUpperBound = [False, True]
bounds = ot.Interval(lowerBound, upperBound, finiteLowerBound,
finiteUpperBound)
factory.setOptimizationBounds(bounds)
inf_distribution = factory.build(sample)
print('estimated distribution=', inf_distribution)
# setKnownParameter+buildEstimator
sample = ot.Normal(2.0, 1.0).getSample(10)
factory = ot.MethodOfMomentsFactory(ot.Weibull())
factory.setBootstrapSize(5)
factory.setKnownParameter([1.0], [1]) # set the sigma parameter to 1.0
result = factory.buildEstimator(sample)
print('ok')
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if (ot.Weibull().__class__.__name__=='ComposedDistribution'):
correlation = ot.CorrelationMatrix(2)
correlation[1, 0] = 0.25
aCopula = ot.NormalCopula(correlation)
marginals = [ot.Normal(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, aCopula)
elif (ot.Weibull().__class__.__name__=='CumulativeDistributionNetwork'):
distribution = ot.CumulativeDistributionNetwork([ot.Normal(2),ot.Dirichlet([0.5, 1.0, 1.5])], ot.BipartiteGraph([[0,1], [0,1]]))
else:
distribution = ot.Weibull()
dimension = distribution.getDimension()
if dimension <= 2:
if distribution.getDimension() == 1:
distribution.setDescription(['$x$'])
pdf_graph = distribution.drawPDF()
cdf_graph = distribution.drawCDF()
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(distribution))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph, figure=fig, axes=[pdf_axis], add_legend=False)
View(cdf_graph, figure=fig, axes=[cdf_axis], add_legend=False)
else:
distribution.setDescription(['$x_1$', '$x_2$'])
pdf_graph = distribution.drawPDF()
fig = plt.figure(figsize=(10, 5))
plt.suptitle(str(distribution))
pdf_axis = fig.add_subplot(111)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.Weibull().__class__.__name__ == 'Bernoulli':
distribution = ot.Bernoulli(0.7)
elif ot.Weibull().__class__.__name__ == 'Binomial':
distribution = ot.Binomial(5, 0.2)
elif ot.Weibull().__class__.__name__ == 'ComposedDistribution':
copula = ot.IndependentCopula(2)
marginals = [ot.Uniform(1.0, 2.0), ot.Normal(2.0, 3.0)]
distribution = ot.ComposedDistribution(marginals, copula)
elif ot.Weibull().__class__.__name__ == 'CumulativeDistributionNetwork':
coll = [ot.Normal(2), ot.Dirichlet([0.5, 1.0, 1.5])]
distribution = ot.CumulativeDistributionNetwork(
coll, ot.BipartiteGraph([[0, 1], [0, 1]]))
elif ot.Weibull().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
elif ot.Weibull().__class__.__name__ == 'KernelMixture':
kernel = ot.Uniform()
sample = ot.Normal().getSample(5)
bandwith = [1.0]
distribution = ot.KernelMixture(kernel, bandwith, sample)
elif ot.Weibull().__class__.__name__ == 'MaximumDistribution':
coll = [
ot.Uniform(2.5, 3.5),
ot.LogUniform(1.0, 1.2),
ot.Triangular(2.0, 3.0, 4.0)
]
distribution = ot.MaximumDistribution(coll)
elif ot.Weibull().__class__.__name__ == 'Multinomial':
distribution = ot.Multinomial(5, [0.2])