#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
ot.PlatformInfo.SetNumericalPrecision(3)
distribution = ot.Pareto(3.3, 7.5, 0.0)
print('distribution=', distribution)
sample = distribution.getSample(1000)
factory = ot.LeastSquaresDistributionFactory(ot.Pareto())
factory.setKnownParameter([0.0], [2])
inf_distribution = factory.build(sample)
print('estimated distribution=', inf_distribution)
#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
ot.TESTPREAMBLE()
distribution = ot.Pareto(2.0, 3.5, -1.0)
size = 100000
sample = distribution.getSample(size)
factory = ot.ParetoFactory()
print("distribution=", repr(distribution))
print("Estimated distribution (Moments)=",
factory.buildMethodOfMoments(sample))
print("Estimated distribution (MLE)=",
factory.buildMethodOfLikelihoodMaximization(sample))
print("Estimated distribution (LSQ)=",
factory.buildMethodOfLeastSquares(sample))
estimatedDistribution = factory.build()
print("Default distribution=", estimatedDistribution)
estimatedDistribution = factory.build(
distribution.getParameter())
print("Distribution from parameters=", estimatedDistribution)
estimatedPareto = factory.buildAsPareto(sample)
print("Estimated pareto=", estimatedPareto)
estimatedPareto = factory.buildAsPareto()
print("Default pareto=", estimatedPareto)
estimatedPareto = factory.buildAsPareto(
distribution.getParameter())
print("Pareto from parameters=", estimatedPareto)
#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
ot.TESTPREAMBLE()
# Instanciate one distribution object
distribution = ot.Pareto(7.5, 5.0, -7.0)
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()))
print(distribution.getParameter())
# %%
# Draw fitted distribution
graph = distribution.drawPDF()
graph.setTitle("Fitted Student distribution")
view = viewer.View(graph)
# %%
# The Pareto distribution
# -----------------------
#
# By default the parameters of the Pareto distribution are estimated by least squares.
#
# %%
# We use a sample from a Pareto distribution with a scale parameter :math:`\beta=1.0`, a shape parameter :math:`\alpha > 1.0` and a location parameter :math:`\gamma = 0.0`.
sample = ot.Pareto(1.0, 1.0, 0.0).getSample(1000)
# %%
# Draw fitted distribution
distribution = ot.ParetoFactory().build(sample)
print(distribution.getParameter())
graph = distribution.drawPDF()
graph.setTitle("Fitted Pareto distribution")
view = viewer.View(graph)
plt.show()
# %% # We observe on the two previous figures that the distribution is normal and centered around # the estimated value of the parameter. # %% # The Pareto distribution # ----------------------- # # We consider a Pareto distribution with a scale parameter :math:`\beta=1.0`, a shape parameter :math:`\alpha=1.0` and a location parameter :math:`\gamma = 0.0`. # We generate a sample from this distribution and use a `ParetoFactory` to fit the sample. # In that case the asymptotic parameters distribution is estimated by bootstrap on the initial # data and kernel fitting (see KernelSmoothing). # # %% distribution = ot.Pareto(1.0, 1.0, 0.0) sample = distribution.getSample(50) estimated = ot.ParetoFactory().build(sample) # %% # We take a look at the estimated parameters : print(estimated.getParameter()) # %% # The `buildEstimator` method gives the asymptotic parameters distribution. # fittedRes = ot.ParetoFactory().buildEstimator(sample) paramDist = fittedRes.getParameterDistribution() # %% # We draw scale parameter :math:`\beta` distribution
