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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
from openturns.usecases import coles
ot.TESTPREAMBLE()
ot.Log.Show(ot.Log.INFO)
size = 10000
factory = ot.GeneralizedParetoFactory()
for xi in [-0.75, 0.0, 0.75]:
distribution = ot.GeneralizedPareto(2.5, xi, 0.5)
sample = distribution.getSample(size)
estimatedDistribution = factory.build(sample)
print("Distribution =", distribution)
print("Estimated distribution=", estimatedDistribution)
ott.assert_almost_equal(
estimatedDistribution.getParameter(), distribution.getParameter(), 1e-1, 1e-1
)
estimatedGeneralizedPareto = factory.buildAsGeneralizedPareto(sample)
print("GeneralizedPareto =", distribution)
print("Estimated generalizedPareto=", estimatedGeneralizedPareto)
assert (
estimatedGeneralizedPareto.__class__.__name__ == "GeneralizedPareto"
), "wrong name"
# method of moments
if xi <= 0.0:
estimatedDistribution = factory.buildMethodOfMoments(sample)
print("GeneralizedPareto from moments=", estimatedDistribution)
ott.assert_almost_equal(
estimatedDistribution.getParameter(),
distribution.getParameter(),
1e-1,
1e-1,
)
# exponential regression
estimatedDistribution = factory.buildMethodOfExponentialRegression(sample)
print("GeneralizedPareto from exponential regression=", estimatedDistribution)
ott.assert_almost_equal(
estimatedDistribution.getParameter(), distribution.getParameter(), 1e-1, 1e-1
)
# pwm
if xi >= -0.5:
estimatedDistribution = factory.buildMethodOfProbabilityWeightedMoments(sample)
print("GeneralizedPareto from pwm=", estimatedDistribution)
ott.assert_almost_equal(
estimatedDistribution.getParameter(),
distribution.getParameter(),
1e-1,
1e-1,
)
estimatedDistribution = factory.build()
ott.assert_almost_equal(estimatedDistribution.getParameter(), [1.0, 0.0, 0.0])
print("Default distribution=", estimatedDistribution)
estimatedDistribution = factory.build(distribution.getParameter())
print("Distribution from parameters=", estimatedDistribution)
estimatedGeneralizedPareto = factory.buildAsGeneralizedPareto()
assert (
estimatedGeneralizedPareto.__class__.__name__ == "GeneralizedPareto"
), "wrong name"
print("Default generalizedPareto=", estimatedGeneralizedPareto)
estimatedGeneralizedPareto = factory.buildAsGeneralizedPareto(
distribution.getParameter()
)
assert (
estimatedGeneralizedPareto.__class__.__name__ == "GeneralizedPareto"
), "wrong name"
print("GeneralizedPareto from parameters=", estimatedGeneralizedPareto)
ott.assert_almost_equal(
estimatedGeneralizedPareto.getParameter(), distribution.getParameter()
)
if not ot.PlatformInfo.HasFeature("bison"):
exit(0)
# mean residual life
sample = coles.Coles().rain
graph = factory.drawMeanResidualLife(sample)
# MLE
u = 30.0
estimator_mle = factory.buildMethodOfLikelihoodMaximizationEstimator(sample, u)
print("MLE estimator=", estimator_mle)
inf_dist = estimator_mle.getDistribution()
print("GPD from MLE=", inf_dist)
pref_mle = [7.44573, 0.184112, 30.0]
ott.assert_almost_equal(inf_dist.getParameter(), pref_mle, 1e-2, 1e-2)
print("parameter dist=", estimator_mle.getParameterDistribution())
print(estimator_mle.getParameterDistribution().getCovariance())
cov_ref = [[0.920412, -0.0655531, 0], [-0.0655531, 0.0102358, 0], [0, 0, 0]]
ott.assert_almost_equal(
ot.Matrix(estimator_mle.getParameterDistribution().getCovariance()),
ot.Matrix(cov_ref),
2e-3,
1e-5,
)
ott.assert_almost_equal(estimator_mle.getLogLikelihood(), -485.094)
# specific check for covariates
covariates = ot.Sample([[i + 1] for i in range(sample.getSize())])
sigmaIndices = [0] # linear
xiIndices = [] # stationary
sigmaLink = ot.SymbolicFunction(["x"], ["exp(x)"])
estimator_covariate = factory.buildCovariates(
sample, u, covariates, sigmaIndices, xiIndices, sigmaLink
)
beta = estimator_covariate.getOptimalParameter()
print("beta*=", beta)
ott.assert_almost_equal(beta, [1.9582e-05, 1.80441, 0.197766], 1e-2, 1e-2)
beta_dist = estimator_covariate.getParameterDistribution()
print("beta dist=", beta_dist)
graph_sigma1d = estimator_covariate.drawParameterFunction1D(0)
graph_sigma2d = estimator_covariate.drawParameterFunction2D(0)
graph_q_sigma1d = estimator_covariate.drawQuantileFunction1D(0.9)
graph_q_sigma2d = estimator_covariate.drawQuantileFunction2D(0.9)
# functional
timeStamps = ot.Sample([[i + 1] for i in range(sample.getSize())])
constant = ot.SymbolicFunction(["t"], ["1.0"])
basis = ot.Basis([ot.SymbolicFunction(["t"], ["t"]), constant])
sigmaIndices = [0, 1] # linear
xiIndices = [1] # stationary
sigmaLink = ot.SymbolicFunction(["x"], ["exp(x)"])
estimator_timevar = factory.buildTimeVarying(
sample, u, timeStamps, basis, sigmaIndices, xiIndices, sigmaLink
)
beta = estimator_timevar.getOptimalParameter()
print("beta*=", beta)
ott.assert_almost_equal(beta, [0.343272, 1.80443, 0.197766], 1e-2, 1e-2)
beta_dist = estimator_timevar.getParameterDistribution()
print("beta dist=", beta_dist)
t0 = timeStamps[0, 0]
dist0 = estimator_timevar.getDistribution(t0)
print(dist0)
assert dist0.getImplementation().__class__.__name__ == "GeneralizedPareto"
graph_param = estimator_timevar.drawParameterFunction(0)
graph_quantile = estimator_timevar.drawQuantileFunction(0.99)
# specific check for return level, see coles2001 p86
xm = factory.buildReturnLevelEstimator(estimator_mle, sample, 100.0 * 365.0)
print("xm=", xm)
ott.assert_almost_equal(xm.getMean(), [106.284], 1e-2, 1e-2)
ott.assert_almost_equal(xm.getCovariance()[0, 0], 433.145, 1e-2, 1e-2)
# specific check for return level via profile likelihood
estimator_prof_rl = factory.buildReturnLevelProfileLikelihoodEstimator(
sample, u, 100.0 * 365.0
)
print(estimator_prof_rl)
zm = estimator_prof_rl.getParameter()
try:
ci = estimator_prof_rl.getParameterConfidenceInterval()
print("profile return level estimator zm=", zm, ci)
assert [zm] in ci, "zm should be inside confidence interval"
except Exception as exception:
print(exception)
ott.assert_almost_equal(ci.getLowerBound(), [80.8575], 1e-2, 1e-2)
ott.assert_almost_equal(ci.getUpperBound(), [184.988], 1e-2, 1e-2)
graph = estimator_prof_rl.drawProfileLikelihoodFunction()
# profile MLE (xi)
estimator_prof_mle = factory.buildMethodOfXiProfileLikelihoodEstimator(sample, u)
inf_dist = estimator_prof_mle.getDistribution()
print("Estimated GPD (profile MLE)=", inf_dist)
ott.assert_almost_equal(inf_dist.getParameter(), pref_mle, 1e-2, 1e-2)
# specific check for profile likelihood
xi = estimator_prof_mle.getParameter()
ci = estimator_prof_mle.getParameterConfidenceInterval()
print("profile MLE estimator xi=", xi, ci)
assert [xi] in ci, "xi should be inside confidence interval"
graph = estimator_prof_mle.drawProfileLikelihoodFunction()
# parameter stability
u_range = ot.Interval(0.5, 50.0)
graph = factory.drawParameterThresholdStability(sample, u_range)
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