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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
# need a proper LS solver
if not ot.PlatformInfo.HasFeature("cminpack") or not ot.PlatformInfo.HasFeature(
"ceres"
):
exit(0)
size = 10000
# gumbel
distribution = ot.Gumbel(1.5, -0.5)
print("distribution=", distribution)
sample = distribution.getSample(size)
factory = ot.QuantileMatchingFactory(ot.Gumbel(), [0.01, 0.99])
inf_dist = factory.build(sample)
print("estimated distribution=", inf_dist)
ott.assert_almost_equal(
distribution.getParameter(), inf_dist.getParameter(), 1e-2, 1e-2
)
# set (a,b) out of (r, t, a, b)
distribution = ot.Beta(2.3, 2.2, -1.0, 1.0)
p_ref = distribution.getParameter()
print("distribution=", distribution)
sample = distribution.getSample(size)
factory = ot.QuantileMatchingFactory(ot.Beta(), [0.01, 0.99])
factory.setKnownParameter([2, 3], [-1.0, 1.0])
inf_dist = factory.build(sample)
print("estimated distribution=", inf_dist)
ott.assert_almost_equal(inf_dist.getParameter(), p_ref, 1e-2, 1e-2)
# full probas
probabilities = [0.01, 1 / 3, 2 / 3, 0.99]
factory = ot.QuantileMatchingFactory(ot.Beta(), probabilities)
quantiles = [distribution.computeQuantile(pi)[0] for pi in probabilities]
inf_dist = factory.buildFromQuantiles(quantiles)
print("estimated distribution (quantiles)=", inf_dist)
ott.assert_almost_equal(inf_dist.getParameter(), p_ref, 1e-2, 1e-2)
# from quantiles, known parameters
factory = ot.QuantileMatchingFactory(ot.Beta(), [0.01, 0.99])
factory.setKnownParameter([2, 3], [-1.0, 1.0])
quantiles = [-0.847, 0.867]
inf_dist = factory.buildFromQuantiles(quantiles)
print("estimated distribution (quantiles)=", inf_dist)
probabilities = factory.getProbabilities()
ott.assert_almost_equal(inf_dist.getParameter(), p_ref, 1e-2, 1e-2)
# ill defined case
probabilities = [0.05, 0.25, 0.75, 0.95]
factory = ot.QuantileMatchingFactory(ot.Beta(), probabilities)
quantiles = [-4.0, 1.0, 2.0, 10.0]
ok = False
try:
match_dist = factory.buildFromQuantiles(quantiles)
except Exception:
ok = True
assert ok, "should raise"
# Normal, optimal far away
distribution = ot.Normal(17.0, 1.0)
print("distribution=", distribution)
sample = distribution.getSample(size)
factory = ot.QuantileMatchingFactory(ot.Normal(), [0.01, 0.99])
inf_dist = factory.build(sample)
ott.assert_almost_equal(
inf_dist.getParameter(), distribution.getParameter(), 1e-2, 1e-2
)
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