def generateDataForSpecificInstance(size): R = ot.CorrelationMatrix(3) R[0, 1] = 0.5 R[0, 2] = 0.45 collection = [ot.FrankCopula(3.0), ot.NormalCopula(R), ot.ClaytonCopula(2.0)] copula = ot.ComposedCopula(collection) return copula.getSample(size)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if ot.FrankCopula().__class__.__name__ == 'EmpiricalBernsteinCopula':
sample = ot.Dirichlet([1.0, 2.0, 3.0]).getSample(100)
copula = ot.EmpiricalBernsteinCopula(sample, 4)
elif ot.FrankCopula().__class__.__name__ == 'ExtremeValueCopula':
copula = ot.ExtremeValueCopula(ot.SymbolicFunction("t", "t^3/2-t/2+1"))
elif ot.FrankCopula(
).__class__.__name__ == 'MaximumEntropyOrderStatisticsCopula':
marginals = [ot.Beta(1.5, 3.2, 0.0, 1.0), ot.Beta(2.0, 4.3, 0.5, 1.2)]
copula = ot.MaximumEntropyOrderStatisticsCopula(marginals)
elif ot.FrankCopula().__class__.__name__ == 'NormalCopula':
R = ot.CorrelationMatrix(2)
R[1, 0] = 0.8
copula = ot.NormalCopula(R)
elif ot.FrankCopula().__class__.__name__ == 'SklarCopula':
student = ot.Student(3.0, [1.0] * 2, [3.0] * 2, ot.CorrelationMatrix(2))
copula = ot.SklarCopula(student)
else:
copula = ot.FrankCopula()
if copula.getDimension() == 1:
copula = ot.FrankCopula(2)
copula.setDescription(['$u_1$', '$u_2$'])
pdf_graph = copula.drawPDF()
cdf_graph = copula.drawCDF()
fig = plt.figure(figsize=(10, 4))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph,
figure=fig,
""" Assemble copulas ================ """ # %% # In this example we are going to merge a collection of independent copulas into one. # # %% from __future__ import print_function import openturns as ot import openturns.viewer as viewer from matplotlib import pylab as plt ot.Log.Show(ot.Log.NONE) # %% # create a collection of copulas R = ot.CorrelationMatrix(3) R[0, 1] = 0.5 R[0, 2] = 0.25 collection = [ot.FrankCopula(3.0), ot.NormalCopula(R), ot.ClaytonCopula(2.0)] # %% # merge the copulas copula = ot.ComposedCopula(collection) print(copula)
def check_bernstein_copula(est_copula):
"""
Check if an estimated distribution of kind EmpiricalBernstein
is of type copula and all marginals are also.
"""
print("Is estimation a copula ? --> ", est_copula.isCopula())
print("Maginal checking")
dimension = est_copula.getDimension()
for d in range(dimension):
print("Is marginal %d a copula ? --> %s" % (d, est_copula.isCopula()))
try:
coll = [ot.GumbelCopula(3.0), ot.ClaytonCopula(3.0), ot.FrankCopula(3.0)]
size = 100
for i, ref_copula in enumerate(coll):
ref_copula = coll[i]
print("Reference copula", str(ref_copula))
sample = ref_copula.getSample(size)
# Default method: log-likelihood
m = ot.BernsteinCopulaFactory.ComputeLogLikelihoodBinNumber(sample)
print("Log-likelihood m=", m)
est_copula = ot.BernsteinCopulaFactory().build(sample, m)
max_error = compute_max_error(ref_copula, est_copula)
print("Max. error=%.5f" % max_error)
check_bernstein_copula(est_copula)
# AMISE method
m = ot.BernsteinCopulaFactory.ComputeAMISEBinNumber(sample)
print("AMISE m=", m)
import openturns as ot from openturns.viewer import View ot.RandomGenerator.SetSeed(0) copula = ot.FrankCopula(1.5) sample = copula.getSample(100) graph = ot.VisualTest.DrawKendallPlot(sample, copula) View(graph)
# #Lakach
# muLog = 7.43459;sigmaLog = 0.555439;gamma = 4977.04
# marginal1 =ot.LogNormal(muLog, sigmaLog, gamma)
# mu = 0.165352;beta = 0.0193547;
# marginal2 =ot.Logistic(mu, beta)
# theta = -4.2364
# copula = ot.FrankCopula(theta)
#BF3
beta1 = 2458.48
gamma1 = 28953.5
marginal1 = ot.Gumbel(beta1, gamma1)
beta2 = 0.0489963
gamma2 = 0.156505
marginal2 = ot.Gumbel(beta2, gamma2)
theta = -5.21511
copula = ot.FrankCopula(theta)
bivariate_distribution_data = ot.ComposedDistribution([marginal1, marginal2],
copula)
marginal_data = [bivariate_distribution_data.getMarginal(i) for i in [0, 1]]
copula_data = bivariate_distribution_data.getCopula()
#Weights#
w1 = [1, 1]
w = [w0[0] * w1[0], w0[1] * w1[1]]
##Objective function##
F = fo.funcobj_cond(w,
Data_Grid_nc,
Data_Conditioning,
svt,
lag_tolerance,
expression += "+"
expression += "cos(" + str(i + 1) + "*" + inputVar[i] + ")"
formula[0] = expression
model = ot.SymbolicFunction(inputVar, formula)
outputSample = model(inputSample)
cobwebValue = ot.VisualTest.DrawParallelCoordinates(
inputSample, outputSample, 2.5, 3.0, "red", False)
print("cobwebValue = ", cobwebValue)
cobwebQuantile = ot.VisualTest.DrawParallelCoordinates(
inputSample, outputSample, 0.7, 0.9, "red", False)
print("cobwebQuantile = ", cobwebQuantile)
# KendallPlot tests
size = 100
copula1 = ot.FrankCopula(1.5)
copula2 = ot.GumbelCopula(4.5)
sample1 = copula1.getSample(size)
sample1.setName("data 1")
sample2 = copula2.getSample(size)
sample2.setName("data 2")
kendallPlot1 = ot.VisualTest.DrawKendallPlot(sample1, copula2)
print("KendallPlot1 = ", kendallPlot1)
kendallPlot2 = ot.VisualTest.DrawKendallPlot(sample2, sample1)
print("KendallPlot2 = ", kendallPlot2)
# Clouds
sample = ot.Normal(4).getSample(200)
clouds = ot.VisualTest.DrawPairs(sample)
print("Clouds = ", clouds)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
if (ot.FrankCopula().__class__.__name__ == 'SklarCopula'):
myStudent = ot.Student(3.0, [1.0] * 2, [3.0] * 2, ot.CorrelationMatrix(2))
copula = ot.SklarCopula(myStudent)
else:
copula = ot.FrankCopula()
if copula.getDimension() == 1:
copula = ot.FrankCopula(2)
copula.setDescription(['$u_1$', '$u_2$'])
pdf_graph = copula.drawPDF()
cdf_graph = copula.drawCDF()
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(copula))
pdf_axis = fig.add_subplot(121)
cdf_axis = fig.add_subplot(122)
View(pdf_graph,
figure=fig,
axes=[pdf_axis],
add_legend=False,
square_axes=True)
View(cdf_graph,
figure=fig,
axes=[cdf_axis],
add_legend=False,
square_axes=True)
print("Inverse survival (ref)=", ref.computeInverseSurvivalFunction(0.95))
print("Survival(inverse survival)=%.5f" %
distribution.computeSurvivalFunction(InverseSurvival))
# Get 50% quantile
quantile = distribution.computeQuantile(0.5)
print("Quantile =", quantile)
print("Quantile (ref)=", ref.computeQuantile(0.5))
print("CDF(quantile) =%.5f" % distribution.computeCDF(quantile))
# Instantiate one distribution object
R = ot.CorrelationMatrix(3)
R[0, 1] = 0.5
R[0, 2] = 0.25
collection = [ot.ComposedDistribution([ot.Normal()]*2, ot.AliMikhailHaqCopula(0.5)),
ot.Normal([1.0]*3, [2.0]*3, R),
ot.ComposedDistribution([ot.Exponential()]*2, ot.FrankCopula(0.5))]
distribution = ot.BlockIndependentDistribution(collection)
print("Distribution ", distribution)
# Is this distribution elliptical ?
print("Elliptical distribution= ", distribution.isElliptical())
# Is this distribution continuous ?
print("Continuous = ", distribution.isContinuous())
# Has this distribution an elliptical copula ?
print("Elliptical = ", distribution.hasEllipticalCopula())
# Has this distribution an independent copula ?
print("Independent = ", distribution.hasIndependentCopula())
