meanPoint = [0.5, -0.5]
sigma = [2.0, 3.0]
R = ot.CorrelationMatrix(dim)
for i in range(1, dim):
R[i, i - 1] = 0.5
distribution = ot.Normal(meanPoint, sigma, R)
discretization = 100
kernel = ot.KernelSmoothing()
sample = distribution.getSample(discretization)
kernels = ot.DistributionCollection(0)
kernels.add(ot.Normal())
kernels.add(ot.Epanechnikov())
kernels.add(ot.Uniform())
kernels.add(ot.Triangular())
kernels.add(ot.Logistic())
kernels.add(ot.Beta(2.0, 2.0, -1.0, 1.0))
kernels.add(ot.Beta(3.0, 3.0, -1.0, 1.0))
meanExact = distribution.getMean()
covarianceExact = distribution.getCovariance()
for i in range(kernels.getSize()):
kernel = kernels[i]
print("kernel=", kernel.getName())
smoother = ot.KernelSmoothing(kernel)
smoothed = smoother.build(sample)
bw = smoother.getBandwidth()
print("kernel bandwidth=[ %.6g" % bw[0], ", %.6g" % bw[1], "]")
meanSmoothed = smoothed.getMean()
print("mean(smoothed)=[ %.6g" % meanSmoothed[0],
", %.6g" % meanSmoothed[1], "] mean(exact)=[", meanExact[0], ", ",
meanExact[1], "]")
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.Logistic().__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.Logistic().__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.Logistic().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
else:
distribution = ot.Logistic()
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()
distributionCollection.add(beta) continuousDistributionCollection.add(beta) gamma = ot.Gamma(1.0, 2.0, 3.0) distributionCollection.add(gamma) continuousDistributionCollection.add(gamma) gumbel = ot.Gumbel(1.0, 2.0) distributionCollection.add(gumbel) continuousDistributionCollection.add(gumbel) lognormal = ot.LogNormal(1.0, 1.0, 2.0) distributionCollection.add(lognormal) continuousDistributionCollection.add(lognormal) logistic = ot.Logistic(1.0, 1.0) distributionCollection.add(logistic) continuousDistributionCollection.add(logistic) normal = ot.Normal(1.0, 2.0) distributionCollection.add(normal) continuousDistributionCollection.add(normal) truncatednormal = ot.TruncatedNormal(1.0, 1.0, 0.0, 3.0) distributionCollection.add(truncatednormal) continuousDistributionCollection.add(truncatednormal) student = ot.Student(10.0, 10.0) distributionCollection.add(student) continuousDistributionCollection.add(student)
ot.TESTPREAMBLE()
ot.RandomGenerator.SetSeed(0)
def clean(polynomial):
coefficients = polynomial.getCoefficients()
for i in range(coefficients.getDimension()):
if abs(coefficients[i]) < 1.0e-12:
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)):
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if (ot.Logistic().__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.Logistic().__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.Logistic()
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))
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.Logistic().__class__.__name__ == 'Bernoulli':
distribution = ot.Bernoulli(0.7)
elif ot.Logistic().__class__.__name__ == 'Binomial':
distribution = ot.Binomial(5, 0.2)
elif ot.Logistic().__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.Logistic().__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.Logistic().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
elif ot.Logistic().__class__.__name__ == 'KernelMixture':
kernel = ot.Uniform()
sample = ot.Normal().getSample(5)
bandwith = [1.0]
distribution = ot.KernelMixture(kernel, bandwith, sample)
elif ot.Logistic().__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.Logistic().__class__.__name__ == 'Multinomial':
distribution = ot.Multinomial(5, [0.2])
elif ot.Logistic().__class__.__name__ == 'RandomMixture':
coll = [ot.Triangular(0.0, 1.0, 5.0), ot.Uniform(-2.0, 2.0)]
weights = [0.8, 0.2]
cst = 3.0
distribution = ot.RandomMixture(coll, weights, cst)