#! /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