algo9.setUpperBound(1.0)
ks9 = algo9.build(sample)
print(
"with user defined boundaries correction, pdf(left)=%.6g" %
ks9.computePDF(left), ", pdf(right)=%.6g" % ks9.computePDF(right))
# full degenerate case
sample = ot.ComposedDistribution(
[ot.Dirac(-7.0), ot.Dirac(0.0),
ot.Dirac(8.0)]).getSample(50)
smoothed = ot.KernelSmoothing().build(sample)
print(smoothed.getSample(3))
# n-d degenerate case
sample = ot.ComposedDistribution(
[ot.Dirac(-7.0), ot.Arcsine(2.0, 3.0),
ot.Dirac(8.0)]).getSample(50)
sample.setDescription(['d7', 'a23', 'd8'])
smoothed = ot.KernelSmoothing().build(sample)
print(smoothed.getSample(3))
# Test with reduced Cutoff - generates non positive phiGammaH
distribution = ot.Normal()
kernel = ot.Normal()
factory = ot.KernelSmoothing(kernel)
ot.ResourceMap.SetAsScalar("KernelSmoothing-CutOffPlugin", 3.0)
ot.RandomGenerator.SetSeed(8457)
sample = distribution.getSample(30)
h = factory.computePluginBandwidth(sample)[0]
print("with reduced cutoff. h=%.6g" % (h))
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.Arcsine().__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.Arcsine().__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.Arcsine().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
else:
distribution = ot.Arcsine()
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()
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if (ot.Arcsine().__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.Arcsine().__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.Arcsine()
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))
#
# %%
from __future__ import print_function
import openturns as ot
import math as m
ot.Log.Show(ot.Log.NONE)
# %%
# generate some multivariate data to estimate, with correlation
cop1 = ot.AliMikhailHaqCopula(0.6)
cop2 = ot.ClaytonCopula(2.5)
copula = ot.ComposedCopula([cop1, cop2])
marginals = [
ot.Uniform(5.0, 6.0),
ot.Arcsine(),
ot.Normal(-40.0, 3.0),
ot.Triangular(100.0, 150.0, 300.0)
]
distribution = ot.ComposedDistribution(marginals, copula)
sample = distribution.getSample(10000).getMarginal([0, 2, 3, 1])
# %%
# estimate marginals
dimension = sample.getDimension()
marginalFactories = []
for factory in ot.DistributionFactory.GetContinuousUniVariateFactories():
if str(factory).startswith('Histogram'):
# ~ non-parametric
continue
marginalFactories.append(factory)
algo9 = ot.KernelSmoothing(ot.Normal(), False)
algo9.setBoundingOption(ot.KernelSmoothing.BOTH)
algo9.setLowerBound(-1.0)
algo9.setUpperBound(1.0)
ks9 = algo9.build(sample)
print("with user defined boundaries correction, pdf(left)=%.6g" %
ks9.computePDF(left), ", pdf(right)=%.6g" % ks9.computePDF(right))
# full degenerate case
sample = ot.ComposedDistribution(
[ot.Dirac(-7.0), ot.Dirac(0.0), ot.Dirac(8.0)]).getSample(50)
smoothed = ot.KernelSmoothing().build(sample)
print(smoothed.getSample(3))
# n-d degenerate case
sample = ot.ComposedDistribution(
[ot.Dirac(-7.0), ot.Arcsine(2.0, 3.0), ot.Dirac(8.0)]).getSample(50)
sample.setDescription(['d7', 'a23', 'd8'])
smoothed = ot.KernelSmoothing().build(sample)
print(smoothed.getSample(3))
# Test with reduced Cutoff - generates non positive phiGammaH
distribution = ot.Normal()
kernel = ot.Normal()
factory = ot.KernelSmoothing(kernel)
ot.ResourceMap_SetAsScalar("KernelSmoothing-CutOffPlugin", 3.0)
ot.RandomGenerator.SetSeed(8457)
sample = distribution.getSample(30)
h = factory.computePluginBandwidth(sample)[0]
print("with reduced cutoff. h=%.6g" % (h))
from __future__ import print_function
import openturns as ot
from math import pi
ot.TESTPREAMBLE()
ot.Log.Show(0)
ot.PlatformInfo.SetNumericalPrecision(3)
dim = 2
R = ot.CorrelationMatrix(2)
R[0, 1] = 0.5
src = [
ot.ComposedDistribution([ot.Uniform(-pi, pi)] * dim),
ot.ComposedDistribution([ot.Normal(4.0, 2.0)] * dim),
ot.ComposedDistribution([ot.Gamma()] * dim),
ot.ComposedDistribution([ot.Gamma(1.5, 2.5, -0.5)] * dim),
ot.ComposedDistribution([ot.Arcsine(5.2, 11.6)] * dim),
ot.Normal([3.0] * dim, [2.0] * dim, R)
]
for sd in src:
sample = sd.getSample(2000)
d = ot.MetaModelAlgorithm.BuildDistribution(sample)
print(d)
sample = ot.Sample([[0], [142.857], [285.714], [428.571], [571.429], [714.286],
[857.143], [1000.0]])
d = ot.MetaModelAlgorithm.BuildDistribution(sample)
print(d)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.Arcsine().__class__.__name__ == 'Bernoulli':
distribution = ot.Bernoulli(0.7)
elif ot.Arcsine().__class__.__name__ == 'Binomial':
distribution = ot.Binomial(5, 0.2)
elif ot.Arcsine().__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.Arcsine().__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.Arcsine().__class__.__name__ == 'Histogram':
distribution = ot.Histogram([-1.0, 0.5, 1.0, 2.0], [0.45, 0.4, 0.15])
elif ot.Arcsine().__class__.__name__ == 'KernelMixture':
kernel = ot.Uniform()
sample = ot.Normal().getSample(5)
bandwith = [1.0]
distribution = ot.KernelMixture(kernel, bandwith, sample)
elif ot.Arcsine().__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.Arcsine().__class__.__name__ == 'Multinomial':
distribution = ot.Multinomial(5, [0.2])
elif ot.Arcsine().__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)
