AIM-PIbd-32-Kurbanova-A-A/aimenv/Lib/site-packages/scipy/stats/tests/test_fit.py
2024-10-02 22:15:59 +04:00

1039 lines
45 KiB
Python

import os
import numpy as np
import numpy.testing as npt
from numpy.testing import assert_allclose, assert_equal
import pytest
from scipy import stats
from scipy.optimize import differential_evolution
from .test_continuous_basic import distcont
from scipy.stats._distn_infrastructure import FitError
from scipy.stats._distr_params import distdiscrete
from scipy.stats import goodness_of_fit
# this is not a proper statistical test for convergence, but only
# verifies that the estimate and true values don't differ by too much
fit_sizes = [1000, 5000, 10000] # sample sizes to try
thresh_percent = 0.25 # percent of true parameters for fail cut-off
thresh_min = 0.75 # minimum difference estimate - true to fail test
mle_failing_fits = [
'gausshyper',
'genexpon',
'gengamma',
'irwinhall',
'kappa4',
'ksone',
'kstwo',
'ncf',
'ncx2',
'truncexpon',
'tukeylambda',
'vonmises',
'levy_stable',
'trapezoid',
'truncweibull_min',
'studentized_range',
]
# these pass but are XSLOW (>1s)
mle_Xslow_fits = ['betaprime', 'crystalball', 'exponweib', 'f', 'geninvgauss',
'jf_skew_t', 'recipinvgauss', 'rel_breitwigner', 'vonmises_line']
# The MLE fit method of these distributions doesn't perform well when all
# parameters are fit, so test them with the location fixed at 0.
mle_use_floc0 = [
'burr',
'chi',
'chi2',
'mielke',
'pearson3',
'genhalflogistic',
'rdist',
'pareto',
'powerlaw', # distfn.nnlf(est2, rvs) > distfn.nnlf(est1, rvs) otherwise
'powerlognorm',
'wrapcauchy',
'rel_breitwigner',
]
mm_failing_fits = ['alpha', 'betaprime', 'burr', 'burr12', 'cauchy', 'chi',
'chi2', 'crystalball', 'dgamma', 'dweibull', 'f',
'fatiguelife', 'fisk', 'foldcauchy', 'genextreme',
'gengamma', 'genhyperbolic', 'gennorm', 'genpareto',
'halfcauchy', 'invgamma', 'invweibull', 'irwinhall', 'jf_skew_t',
'johnsonsu', 'kappa3', 'ksone', 'kstwo', 'levy', 'levy_l',
'levy_stable', 'loglaplace', 'lomax', 'mielke', 'nakagami',
'ncf', 'nct', 'ncx2', 'pareto', 'powerlognorm', 'powernorm',
'rel_breitwigner', 'skewcauchy', 't', 'trapezoid', 'triang',
'truncpareto', 'truncweibull_min', 'tukeylambda',
'studentized_range']
# not sure if these fail, but they caused my patience to fail
mm_XXslow_fits = ['argus', 'exponpow', 'exponweib', 'gausshyper', 'genexpon',
'genhalflogistic', 'halfgennorm', 'gompertz', 'johnsonsb',
'kappa4', 'kstwobign', 'recipinvgauss',
'truncexpon', 'vonmises', 'vonmises_line']
# these pass but are XSLOW (>1s)
mm_Xslow_fits = ['wrapcauchy']
failing_fits = {"MM": mm_failing_fits + mm_XXslow_fits, "MLE": mle_failing_fits}
xslow_fits = {"MM": mm_Xslow_fits, "MLE": mle_Xslow_fits}
fail_interval_censored = {"truncpareto"}
# Don't run the fit test on these:
skip_fit = [
'erlang', # Subclass of gamma, generates a warning.
'genhyperbolic', 'norminvgauss', # too slow
]
def cases_test_cont_fit():
# this tests the closeness of the estimated parameters to the true
# parameters with fit method of continuous distributions
# Note: is slow, some distributions don't converge with sample
# size <= 10000
for distname, arg in distcont:
if distname not in skip_fit:
yield distname, arg
@pytest.mark.slow
@pytest.mark.parametrize('distname,arg', cases_test_cont_fit())
@pytest.mark.parametrize('method', ["MLE", "MM"])
def test_cont_fit(distname, arg, method):
run_xfail = int(os.getenv('SCIPY_XFAIL', default=False))
run_xslow = int(os.getenv('SCIPY_XSLOW', default=False))
if distname in failing_fits[method] and not run_xfail:
# The generic `fit` method can't be expected to work perfectly for all
# distributions, data, and guesses. Some failures are expected.
msg = "Failure expected; set environment variable SCIPY_XFAIL=1 to run."
pytest.xfail(msg)
if distname in xslow_fits[method] and not run_xslow:
msg = "Very slow; set environment variable SCIPY_XSLOW=1 to run."
pytest.skip(msg)
distfn = getattr(stats, distname)
truearg = np.hstack([arg, [0.0, 1.0]])
diffthreshold = np.max(np.vstack([truearg*thresh_percent,
np.full(distfn.numargs+2, thresh_min)]),
0)
for fit_size in fit_sizes:
# Note that if a fit succeeds, the other fit_sizes are skipped
np.random.seed(1234)
with np.errstate(all='ignore'):
rvs = distfn.rvs(size=fit_size, *arg)
if method == 'MLE' and distfn.name in mle_use_floc0:
kwds = {'floc': 0}
else:
kwds = {}
# start with default values
est = distfn.fit(rvs, method=method, **kwds)
if method == 'MLE':
# Trivial test of the use of CensoredData. The fit() method
# will check that data contains no actual censored data, and
# do a regular uncensored fit.
data1 = stats.CensoredData(rvs)
est1 = distfn.fit(data1, **kwds)
msg = ('Different results fitting uncensored data wrapped as'
f' CensoredData: {distfn.name}: est={est} est1={est1}')
assert_allclose(est1, est, rtol=1e-10, err_msg=msg)
if method == 'MLE' and distname not in fail_interval_censored:
# Convert the first `nic` values in rvs to interval-censored
# values. The interval is small, so est2 should be close to
# est.
nic = 15
interval = np.column_stack((rvs, rvs))
interval[:nic, 0] *= 0.99
interval[:nic, 1] *= 1.01
interval.sort(axis=1)
data2 = stats.CensoredData(interval=interval)
est2 = distfn.fit(data2, **kwds)
msg = ('Different results fitting interval-censored'
f' data: {distfn.name}: est={est} est2={est2}')
assert_allclose(est2, est, rtol=0.05, err_msg=msg)
diff = est - truearg
# threshold for location
diffthreshold[-2] = np.max([np.abs(rvs.mean())*thresh_percent,
thresh_min])
if np.any(np.isnan(est)):
raise AssertionError('nan returned in fit')
else:
if np.all(np.abs(diff) <= diffthreshold):
break
else:
txt = 'parameter: %s\n' % str(truearg)
txt += 'estimated: %s\n' % str(est)
txt += 'diff : %s\n' % str(diff)
raise AssertionError('fit not very good in %s\n' % distfn.name + txt)
def _check_loc_scale_mle_fit(name, data, desired, atol=None):
d = getattr(stats, name)
actual = d.fit(data)[-2:]
assert_allclose(actual, desired, atol=atol,
err_msg='poor mle fit of (loc, scale) in %s' % name)
def test_non_default_loc_scale_mle_fit():
data = np.array([1.01, 1.78, 1.78, 1.78, 1.88, 1.88, 1.88, 2.00])
_check_loc_scale_mle_fit('uniform', data, [1.01, 0.99], 1e-3)
_check_loc_scale_mle_fit('expon', data, [1.01, 0.73875], 1e-3)
def test_expon_fit():
"""gh-6167"""
data = [0, 0, 0, 0, 2, 2, 2, 2]
phat = stats.expon.fit(data, floc=0)
assert_allclose(phat, [0, 1.0], atol=1e-3)
def test_fit_error():
data = np.concatenate([np.zeros(29), np.ones(21)])
message = "Optimization converged to parameters that are..."
with pytest.raises(FitError, match=message), \
pytest.warns(RuntimeWarning):
stats.beta.fit(data)
@pytest.mark.parametrize("dist, params",
[(stats.norm, (0.5, 2.5)), # type: ignore[attr-defined]
(stats.binom, (10, 0.3, 2))]) # type: ignore[attr-defined]
def test_nnlf_and_related_methods(dist, params):
rng = np.random.default_rng(983459824)
if hasattr(dist, 'pdf'):
logpxf = dist.logpdf
else:
logpxf = dist.logpmf
x = dist.rvs(*params, size=100, random_state=rng)
ref = -logpxf(x, *params).sum()
res1 = dist.nnlf(params, x)
res2 = dist._penalized_nnlf(params, x)
assert_allclose(res1, ref)
assert_allclose(res2, ref)
def cases_test_fit_mle():
# These fail default test or hang
skip_basic_fit = {'argus', 'irwinhall', 'foldnorm', 'truncpareto',
'truncweibull_min', 'ksone', 'levy_stable',
'studentized_range', 'kstwo', 'arcsine'}
# Please keep this list in alphabetical order...
slow_basic_fit = {'alpha', 'betaprime', 'binom', 'bradford', 'burr12',
'chi', 'crystalball', 'dweibull', 'erlang', 'exponnorm',
'exponpow', 'f', 'fatiguelife', 'fisk', 'foldcauchy', 'gamma',
'genexpon', 'genextreme', 'gennorm', 'genpareto',
'gompertz', 'halfgennorm', 'invgamma', 'invgauss', 'invweibull',
'jf_skew_t', 'johnsonsb', 'johnsonsu', 'kappa3',
'kstwobign', 'loglaplace', 'lognorm', 'lomax', 'mielke',
'nakagami', 'nbinom', 'norminvgauss',
'pareto', 'pearson3', 'powerlaw', 'powernorm',
'randint', 'rdist', 'recipinvgauss', 'rice', 'skewnorm',
't', 'uniform', 'weibull_max', 'weibull_min', 'wrapcauchy'}
# Please keep this list in alphabetical order...
xslow_basic_fit = {'beta', 'betabinom', 'betanbinom', 'burr', 'exponweib',
'gausshyper', 'gengamma', 'genhalflogistic',
'genhyperbolic', 'geninvgauss',
'hypergeom', 'kappa4', 'loguniform',
'ncf', 'nchypergeom_fisher', 'nchypergeom_wallenius',
'nct', 'ncx2', 'nhypergeom',
'powerlognorm', 'reciprocal', 'rel_breitwigner',
'skellam', 'trapezoid', 'triang', 'truncnorm',
'tukeylambda', 'vonmises', 'zipfian'}
for dist in dict(distdiscrete + distcont):
if dist in skip_basic_fit or not isinstance(dist, str):
reason = "tested separately"
yield pytest.param(dist, marks=pytest.mark.skip(reason=reason))
elif dist in slow_basic_fit:
reason = "too slow (>= 0.25s)"
yield pytest.param(dist, marks=pytest.mark.slow(reason=reason))
elif dist in xslow_basic_fit:
reason = "too slow (>= 1.0s)"
yield pytest.param(dist, marks=pytest.mark.xslow(reason=reason))
else:
yield dist
def cases_test_fit_mse():
# the first four are so slow that I'm not sure whether they would pass
skip_basic_fit = {'levy_stable', 'studentized_range', 'ksone', 'skewnorm',
'irwinhall', # hangs
'norminvgauss', # super slow (~1 hr) but passes
'kstwo', # very slow (~25 min) but passes
'geninvgauss', # quite slow (~4 minutes) but passes
'gausshyper', 'genhyperbolic', # integration warnings
'tukeylambda', # close, but doesn't meet tolerance
'vonmises', # can have negative CDF; doesn't play nice
'argus'} # doesn't meet tolerance; tested separately
# Please keep this list in alphabetical order...
slow_basic_fit = {'alpha', 'anglit', 'arcsine', 'betabinom', 'bradford',
'chi', 'chi2', 'crystalball', 'dweibull',
'erlang', 'exponnorm', 'exponpow', 'exponweib',
'fatiguelife', 'fisk', 'foldcauchy', 'foldnorm',
'gamma', 'genexpon', 'genextreme', 'genhalflogistic',
'genlogistic', 'genpareto', 'gompertz',
'hypergeom', 'invweibull',
'johnsonsu', 'kappa3', 'kstwobign',
'laplace_asymmetric', 'loggamma', 'loglaplace',
'lognorm', 'lomax',
'maxwell', 'nhypergeom',
'pareto', 'powernorm', 'randint', 'recipinvgauss',
'semicircular',
't', 'triang', 'truncexpon', 'truncpareto',
'uniform',
'wald', 'weibull_max', 'weibull_min', 'wrapcauchy'}
# Please keep this list in alphabetical order...
xslow_basic_fit = {'argus', 'beta', 'betaprime', 'burr', 'burr12',
'dgamma', 'f', 'gengamma', 'gennorm',
'halfgennorm', 'invgamma', 'invgauss', 'jf_skew_t',
'johnsonsb', 'kappa4', 'loguniform', 'mielke',
'nakagami', 'ncf', 'nchypergeom_fisher',
'nchypergeom_wallenius', 'nct', 'ncx2',
'pearson3', 'powerlaw', 'powerlognorm',
'rdist', 'reciprocal', 'rel_breitwigner', 'rice',
'trapezoid', 'truncnorm', 'truncweibull_min',
'vonmises_line', 'zipfian'}
warns_basic_fit = {'skellam'} # can remove mark after gh-14901 is resolved
for dist in dict(distdiscrete + distcont):
if dist in skip_basic_fit or not isinstance(dist, str):
reason = "Fails. Oh well."
yield pytest.param(dist, marks=pytest.mark.skip(reason=reason))
elif dist in slow_basic_fit:
reason = "too slow (>= 0.25s)"
yield pytest.param(dist, marks=pytest.mark.slow(reason=reason))
elif dist in xslow_basic_fit:
reason = "too slow (>= 1.0s)"
yield pytest.param(dist, marks=pytest.mark.xslow(reason=reason))
elif dist in warns_basic_fit:
mark = pytest.mark.filterwarnings('ignore::RuntimeWarning')
yield pytest.param(dist, marks=mark)
else:
yield dist
def cases_test_fitstart():
for distname, shapes in dict(distcont).items():
if (not isinstance(distname, str) or
distname in {'studentized_range', 'recipinvgauss'}): # slow
continue
yield distname, shapes
@pytest.mark.parametrize('distname, shapes', cases_test_fitstart())
def test_fitstart(distname, shapes):
dist = getattr(stats, distname)
rng = np.random.default_rng(216342614)
data = rng.random(10)
with np.errstate(invalid='ignore', divide='ignore'): # irrelevant to test
guess = dist._fitstart(data)
assert dist._argcheck(*guess[:-2])
def assert_nlff_less_or_close(dist, data, params1, params0, rtol=1e-7, atol=0,
nlff_name='nnlf'):
nlff = getattr(dist, nlff_name)
nlff1 = nlff(params1, data)
nlff0 = nlff(params0, data)
if not (nlff1 < nlff0):
np.testing.assert_allclose(nlff1, nlff0, rtol=rtol, atol=atol)
class TestFit:
dist = stats.binom # type: ignore[attr-defined]
seed = 654634816187
rng = np.random.default_rng(seed)
data = stats.binom.rvs(5, 0.5, size=100, random_state=rng) # type: ignore[attr-defined] # noqa: E501
shape_bounds_a = [(1, 10), (0, 1)]
shape_bounds_d = {'n': (1, 10), 'p': (0, 1)}
atol = 5e-2
rtol = 1e-2
tols = {'atol': atol, 'rtol': rtol}
def opt(self, *args, **kwds):
return differential_evolution(*args, seed=0, **kwds)
def test_dist_iv(self):
message = "`dist` must be an instance of..."
with pytest.raises(ValueError, match=message):
stats.fit(10, self.data, self.shape_bounds_a)
def test_data_iv(self):
message = "`data` must be exactly one-dimensional."
with pytest.raises(ValueError, match=message):
stats.fit(self.dist, [[1, 2, 3]], self.shape_bounds_a)
message = "All elements of `data` must be finite numbers."
with pytest.raises(ValueError, match=message):
stats.fit(self.dist, [1, 2, 3, np.nan], self.shape_bounds_a)
with pytest.raises(ValueError, match=message):
stats.fit(self.dist, [1, 2, 3, np.inf], self.shape_bounds_a)
with pytest.raises(ValueError, match=message):
stats.fit(self.dist, ['1', '2', '3'], self.shape_bounds_a)
def test_bounds_iv(self):
message = "Bounds provided for the following unrecognized..."
shape_bounds = {'n': (1, 10), 'p': (0, 1), '1': (0, 10)}
with pytest.warns(RuntimeWarning, match=message):
stats.fit(self.dist, self.data, shape_bounds)
message = "Each element of a `bounds` sequence must be a tuple..."
shape_bounds = [(1, 10, 3), (0, 1)]
with pytest.raises(ValueError, match=message):
stats.fit(self.dist, self.data, shape_bounds)
message = "Each element of `bounds` must be a tuple specifying..."
shape_bounds = [(1, 10, 3), (0, 1, 0.5)]
with pytest.raises(ValueError, match=message):
stats.fit(self.dist, self.data, shape_bounds)
shape_bounds = [1, 0]
with pytest.raises(ValueError, match=message):
stats.fit(self.dist, self.data, shape_bounds)
message = "A `bounds` sequence must contain at least 2 elements..."
shape_bounds = [(1, 10)]
with pytest.raises(ValueError, match=message):
stats.fit(self.dist, self.data, shape_bounds)
message = "A `bounds` sequence may not contain more than 3 elements..."
bounds = [(1, 10), (1, 10), (1, 10), (1, 10)]
with pytest.raises(ValueError, match=message):
stats.fit(self.dist, self.data, bounds)
message = "There are no values for `p` on the interval..."
shape_bounds = {'n': (1, 10), 'p': (1, 0)}
with pytest.raises(ValueError, match=message):
stats.fit(self.dist, self.data, shape_bounds)
message = "There are no values for `n` on the interval..."
shape_bounds = [(10, 1), (0, 1)]
with pytest.raises(ValueError, match=message):
stats.fit(self.dist, self.data, shape_bounds)
message = "There are no integer values for `n` on the interval..."
shape_bounds = [(1.4, 1.6), (0, 1)]
with pytest.raises(ValueError, match=message):
stats.fit(self.dist, self.data, shape_bounds)
message = "The intersection of user-provided bounds for `n`"
with pytest.raises(ValueError, match=message):
stats.fit(self.dist, self.data)
shape_bounds = [(-np.inf, np.inf), (0, 1)]
with pytest.raises(ValueError, match=message):
stats.fit(self.dist, self.data, shape_bounds)
def test_guess_iv(self):
message = "Guesses provided for the following unrecognized..."
guess = {'n': 1, 'p': 0.5, '1': 255}
with pytest.warns(RuntimeWarning, match=message):
stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
message = "Each element of `guess` must be a scalar..."
guess = {'n': 1, 'p': 'hi'}
with pytest.raises(ValueError, match=message):
stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
guess = [1, 'f']
with pytest.raises(ValueError, match=message):
stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
guess = [[1, 2]]
with pytest.raises(ValueError, match=message):
stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
message = "A `guess` sequence must contain at least 2..."
guess = [1]
with pytest.raises(ValueError, match=message):
stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
message = "A `guess` sequence may not contain more than 3..."
guess = [1, 2, 3, 4]
with pytest.raises(ValueError, match=message):
stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
message = "Guess for parameter `n` rounded.*|Guess for parameter `p` clipped.*"
guess = {'n': 4.5, 'p': -0.5}
with pytest.warns(RuntimeWarning, match=message):
stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
message = "Guess for parameter `loc` rounded..."
guess = [5, 0.5, 0.5]
with pytest.warns(RuntimeWarning, match=message):
stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
message = "Guess for parameter `p` clipped..."
guess = {'n': 5, 'p': -0.5}
with pytest.warns(RuntimeWarning, match=message):
stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
message = "Guess for parameter `loc` clipped..."
guess = [5, 0.5, 1]
with pytest.warns(RuntimeWarning, match=message):
stats.fit(self.dist, self.data, self.shape_bounds_d, guess=guess)
def basic_fit_test(self, dist_name, method):
N = 5000
dist_data = dict(distcont + distdiscrete)
rng = np.random.default_rng(self.seed)
dist = getattr(stats, dist_name)
shapes = np.array(dist_data[dist_name])
bounds = np.empty((len(shapes) + 2, 2), dtype=np.float64)
bounds[:-2, 0] = shapes/10.**np.sign(shapes)
bounds[:-2, 1] = shapes*10.**np.sign(shapes)
bounds[-2] = (0, 10)
bounds[-1] = (1e-16, 10)
loc = rng.uniform(*bounds[-2])
scale = rng.uniform(*bounds[-1])
ref = list(dist_data[dist_name]) + [loc, scale]
if getattr(dist, 'pmf', False):
ref = ref[:-1]
ref[-1] = np.floor(loc)
data = dist.rvs(*ref, size=N, random_state=rng)
bounds = bounds[:-1]
if getattr(dist, 'pdf', False):
data = dist.rvs(*ref, size=N, random_state=rng)
with npt.suppress_warnings() as sup:
sup.filter(RuntimeWarning, "overflow encountered")
res = stats.fit(dist, data, bounds, method=method,
optimizer=self.opt)
nlff_names = {'mle': 'nnlf', 'mse': '_penalized_nlpsf'}
nlff_name = nlff_names[method]
assert_nlff_less_or_close(dist, data, res.params, ref, **self.tols,
nlff_name=nlff_name)
@pytest.mark.parametrize("dist_name", cases_test_fit_mle())
def test_basic_fit_mle(self, dist_name):
self.basic_fit_test(dist_name, "mle")
@pytest.mark.parametrize("dist_name", cases_test_fit_mse())
def test_basic_fit_mse(self, dist_name):
self.basic_fit_test(dist_name, "mse")
def test_arcsine(self):
# Can't guarantee that all distributions will fit all data with
# arbitrary bounds. This distribution just happens to fail above.
# Try something slightly different.
N = 1000
rng = np.random.default_rng(self.seed)
dist = stats.arcsine
shapes = (1., 2.)
data = dist.rvs(*shapes, size=N, random_state=rng)
shape_bounds = {'loc': (0.1, 10), 'scale': (0.1, 10)}
res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
assert_nlff_less_or_close(dist, data, res.params, shapes, **self.tols)
@pytest.mark.parametrize("method", ('mle', 'mse'))
def test_argus(self, method):
# Can't guarantee that all distributions will fit all data with
# arbitrary bounds. This distribution just happens to fail above.
# Try something slightly different.
N = 1000
rng = np.random.default_rng(self.seed)
dist = stats.argus
shapes = (1., 2., 3.)
data = dist.rvs(*shapes, size=N, random_state=rng)
shape_bounds = {'chi': (0.1, 10), 'loc': (0.1, 10), 'scale': (0.1, 10)}
res = stats.fit(dist, data, shape_bounds, optimizer=self.opt, method=method)
assert_nlff_less_or_close(dist, data, res.params, shapes, **self.tols)
def test_foldnorm(self):
# Can't guarantee that all distributions will fit all data with
# arbitrary bounds. This distribution just happens to fail above.
# Try something slightly different.
N = 1000
rng = np.random.default_rng(self.seed)
dist = stats.foldnorm
shapes = (1.952125337355587, 2., 3.)
data = dist.rvs(*shapes, size=N, random_state=rng)
shape_bounds = {'c': (0.1, 10), 'loc': (0.1, 10), 'scale': (0.1, 10)}
res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
assert_nlff_less_or_close(dist, data, res.params, shapes, **self.tols)
def test_truncpareto(self):
# Can't guarantee that all distributions will fit all data with
# arbitrary bounds. This distribution just happens to fail above.
# Try something slightly different.
N = 1000
rng = np.random.default_rng(self.seed)
dist = stats.truncpareto
shapes = (1.8, 5.3, 2.3, 4.1)
data = dist.rvs(*shapes, size=N, random_state=rng)
shape_bounds = [(0.1, 10)]*4
res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
assert_nlff_less_or_close(dist, data, res.params, shapes, **self.tols)
def test_truncweibull_min(self):
# Can't guarantee that all distributions will fit all data with
# arbitrary bounds. This distribution just happens to fail above.
# Try something slightly different.
N = 1000
rng = np.random.default_rng(self.seed)
dist = stats.truncweibull_min
shapes = (2.5, 0.25, 1.75, 2., 3.)
data = dist.rvs(*shapes, size=N, random_state=rng)
shape_bounds = [(0.1, 10)]*5
res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
assert_nlff_less_or_close(dist, data, res.params, shapes, **self.tols)
def test_missing_shape_bounds(self):
# some distributions have a small domain w.r.t. a parameter, e.g.
# $p \in [0, 1]$ for binomial distribution
# User does not need to provide these because the intersection of the
# user's bounds (none) and the distribution's domain is finite
N = 1000
rng = np.random.default_rng(self.seed)
dist = stats.binom
n, p, loc = 10, 0.65, 0
data = dist.rvs(n, p, loc=loc, size=N, random_state=rng)
shape_bounds = {'n': np.array([0, 20])} # check arrays are OK, too
res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
assert_allclose(res.params, (n, p, loc), **self.tols)
dist = stats.bernoulli
p, loc = 0.314159, 0
data = dist.rvs(p, loc=loc, size=N, random_state=rng)
res = stats.fit(dist, data, optimizer=self.opt)
assert_allclose(res.params, (p, loc), **self.tols)
def test_fit_only_loc_scale(self):
# fit only loc
N = 5000
rng = np.random.default_rng(self.seed)
dist = stats.norm
loc, scale = 1.5, 1
data = dist.rvs(loc=loc, size=N, random_state=rng)
loc_bounds = (0, 5)
bounds = {'loc': loc_bounds}
res = stats.fit(dist, data, bounds, optimizer=self.opt)
assert_allclose(res.params, (loc, scale), **self.tols)
# fit only scale
loc, scale = 0, 2.5
data = dist.rvs(scale=scale, size=N, random_state=rng)
scale_bounds = (0.01, 5)
bounds = {'scale': scale_bounds}
res = stats.fit(dist, data, bounds, optimizer=self.opt)
assert_allclose(res.params, (loc, scale), **self.tols)
# fit only loc and scale
dist = stats.norm
loc, scale = 1.5, 2.5
data = dist.rvs(loc=loc, scale=scale, size=N, random_state=rng)
bounds = {'loc': loc_bounds, 'scale': scale_bounds}
res = stats.fit(dist, data, bounds, optimizer=self.opt)
assert_allclose(res.params, (loc, scale), **self.tols)
def test_everything_fixed(self):
N = 5000
rng = np.random.default_rng(self.seed)
dist = stats.norm
loc, scale = 1.5, 2.5
data = dist.rvs(loc=loc, scale=scale, size=N, random_state=rng)
# loc, scale fixed to 0, 1 by default
res = stats.fit(dist, data)
assert_allclose(res.params, (0, 1), **self.tols)
# loc, scale explicitly fixed
bounds = {'loc': (loc, loc), 'scale': (scale, scale)}
res = stats.fit(dist, data, bounds)
assert_allclose(res.params, (loc, scale), **self.tols)
# `n` gets fixed during polishing
dist = stats.binom
n, p, loc = 10, 0.65, 0
data = dist.rvs(n, p, loc=loc, size=N, random_state=rng)
shape_bounds = {'n': (0, 20), 'p': (0.65, 0.65)}
res = stats.fit(dist, data, shape_bounds, optimizer=self.opt)
assert_allclose(res.params, (n, p, loc), **self.tols)
def test_failure(self):
N = 5000
rng = np.random.default_rng(self.seed)
dist = stats.nbinom
shapes = (5, 0.5)
data = dist.rvs(*shapes, size=N, random_state=rng)
assert data.min() == 0
# With lower bounds on location at 0.5, likelihood is zero
bounds = [(0, 30), (0, 1), (0.5, 10)]
res = stats.fit(dist, data, bounds)
message = "Optimization converged to parameter values that are"
assert res.message.startswith(message)
assert res.success is False
@pytest.mark.xslow
def test_guess(self):
# Test that guess helps DE find the desired solution
N = 2000
# With some seeds, `fit` doesn't need a guess
rng = np.random.default_rng(196390444561)
dist = stats.nhypergeom
params = (20, 7, 12, 0)
bounds = [(2, 200), (0.7, 70), (1.2, 120), (0, 10)]
data = dist.rvs(*params, size=N, random_state=rng)
res = stats.fit(dist, data, bounds, optimizer=self.opt)
assert not np.allclose(res.params, params, **self.tols)
res = stats.fit(dist, data, bounds, guess=params, optimizer=self.opt)
assert_allclose(res.params, params, **self.tols)
def test_mse_accuracy_1(self):
# Test maximum spacing estimation against example from Wikipedia
# https://en.wikipedia.org/wiki/Maximum_spacing_estimation#Examples
data = [2, 4]
dist = stats.expon
bounds = {'loc': (0, 0), 'scale': (1e-8, 10)}
res_mle = stats.fit(dist, data, bounds=bounds, method='mle')
assert_allclose(res_mle.params.scale, 3, atol=1e-3)
res_mse = stats.fit(dist, data, bounds=bounds, method='mse')
assert_allclose(res_mse.params.scale, 3.915, atol=1e-3)
def test_mse_accuracy_2(self):
# Test maximum spacing estimation against example from Wikipedia
# https://en.wikipedia.org/wiki/Maximum_spacing_estimation#Examples
rng = np.random.default_rng(9843212616816518964)
dist = stats.uniform
n = 10
data = dist(3, 6).rvs(size=n, random_state=rng)
bounds = {'loc': (0, 10), 'scale': (1e-8, 10)}
res = stats.fit(dist, data, bounds=bounds, method='mse')
# (loc=3.608118420015416, scale=5.509323262055043)
x = np.sort(data)
a = (n*x[0] - x[-1])/(n - 1)
b = (n*x[-1] - x[0])/(n - 1)
ref = a, b-a # (3.6081133632151503, 5.509328130317254)
assert_allclose(res.params, ref, rtol=1e-4)
# Data from Matlab: https://www.mathworks.com/help/stats/lillietest.html
examgrades = [65, 61, 81, 88, 69, 89, 55, 84, 86, 84, 71, 81, 84, 81, 78, 67,
96, 66, 73, 75, 59, 71, 69, 63, 79, 76, 63, 85, 87, 88, 80, 71,
65, 84, 71, 75, 81, 79, 64, 65, 84, 77, 70, 75, 84, 75, 73, 92,
90, 79, 80, 71, 73, 71, 58, 79, 73, 64, 77, 82, 81, 59, 54, 82,
57, 79, 79, 73, 74, 82, 63, 64, 73, 69, 87, 68, 81, 73, 83, 73,
80, 73, 73, 71, 66, 78, 64, 74, 68, 67, 75, 75, 80, 85, 74, 76,
80, 77, 93, 70, 86, 80, 81, 83, 68, 60, 85, 64, 74, 82, 81, 77,
66, 85, 75, 81, 69, 60, 83, 72]
class TestGoodnessOfFit:
def test_gof_iv(self):
dist = stats.norm
x = [1, 2, 3]
message = r"`dist` must be a \(non-frozen\) instance of..."
with pytest.raises(TypeError, match=message):
goodness_of_fit(stats.norm(), x)
message = "`data` must be a one-dimensional array of numbers."
with pytest.raises(ValueError, match=message):
goodness_of_fit(dist, [[1, 2, 3]])
message = "`statistic` must be one of..."
with pytest.raises(ValueError, match=message):
goodness_of_fit(dist, x, statistic='mm')
message = "`n_mc_samples` must be an integer."
with pytest.raises(TypeError, match=message):
goodness_of_fit(dist, x, n_mc_samples=1000.5)
message = "'herring' cannot be used to seed a"
with pytest.raises(ValueError, match=message):
goodness_of_fit(dist, x, random_state='herring')
def test_against_ks(self):
rng = np.random.default_rng(8517426291317196949)
x = examgrades
known_params = {'loc': np.mean(x), 'scale': np.std(x, ddof=1)}
res = goodness_of_fit(stats.norm, x, known_params=known_params,
statistic='ks', random_state=rng)
ref = stats.kstest(x, stats.norm(**known_params).cdf, method='exact')
assert_allclose(res.statistic, ref.statistic) # ~0.0848
assert_allclose(res.pvalue, ref.pvalue, atol=5e-3) # ~0.335
def test_against_lilliefors(self):
rng = np.random.default_rng(2291803665717442724)
x = examgrades
res = goodness_of_fit(stats.norm, x, statistic='ks', random_state=rng)
known_params = {'loc': np.mean(x), 'scale': np.std(x, ddof=1)}
ref = stats.kstest(x, stats.norm(**known_params).cdf, method='exact')
assert_allclose(res.statistic, ref.statistic) # ~0.0848
assert_allclose(res.pvalue, 0.0348, atol=5e-3)
def test_against_cvm(self):
rng = np.random.default_rng(8674330857509546614)
x = examgrades
known_params = {'loc': np.mean(x), 'scale': np.std(x, ddof=1)}
res = goodness_of_fit(stats.norm, x, known_params=known_params,
statistic='cvm', random_state=rng)
ref = stats.cramervonmises(x, stats.norm(**known_params).cdf)
assert_allclose(res.statistic, ref.statistic) # ~0.090
assert_allclose(res.pvalue, ref.pvalue, atol=5e-3) # ~0.636
def test_against_anderson_case_0(self):
# "Case 0" is where loc and scale are known [1]
rng = np.random.default_rng(7384539336846690410)
x = np.arange(1, 101)
# loc that produced critical value of statistic found w/ root_scalar
known_params = {'loc': 45.01575354024957, 'scale': 30}
res = goodness_of_fit(stats.norm, x, known_params=known_params,
statistic='ad', random_state=rng)
assert_allclose(res.statistic, 2.492) # See [1] Table 1A 1.0
assert_allclose(res.pvalue, 0.05, atol=5e-3)
def test_against_anderson_case_1(self):
# "Case 1" is where scale is known and loc is fit [1]
rng = np.random.default_rng(5040212485680146248)
x = np.arange(1, 101)
# scale that produced critical value of statistic found w/ root_scalar
known_params = {'scale': 29.957112639101933}
res = goodness_of_fit(stats.norm, x, known_params=known_params,
statistic='ad', random_state=rng)
assert_allclose(res.statistic, 0.908) # See [1] Table 1B 1.1
assert_allclose(res.pvalue, 0.1, atol=5e-3)
def test_against_anderson_case_2(self):
# "Case 2" is where loc is known and scale is fit [1]
rng = np.random.default_rng(726693985720914083)
x = np.arange(1, 101)
# loc that produced critical value of statistic found w/ root_scalar
known_params = {'loc': 44.5680212261933}
res = goodness_of_fit(stats.norm, x, known_params=known_params,
statistic='ad', random_state=rng)
assert_allclose(res.statistic, 2.904) # See [1] Table 1B 1.2
assert_allclose(res.pvalue, 0.025, atol=5e-3)
def test_against_anderson_case_3(self):
# "Case 3" is where both loc and scale are fit [1]
rng = np.random.default_rng(6763691329830218206)
# c that produced critical value of statistic found w/ root_scalar
x = stats.skewnorm.rvs(1.4477847789132101, loc=1, scale=2, size=100,
random_state=rng)
res = goodness_of_fit(stats.norm, x, statistic='ad', random_state=rng)
assert_allclose(res.statistic, 0.559) # See [1] Table 1B 1.2
assert_allclose(res.pvalue, 0.15, atol=5e-3)
@pytest.mark.xslow
def test_against_anderson_gumbel_r(self):
rng = np.random.default_rng(7302761058217743)
# c that produced critical value of statistic found w/ root_scalar
x = stats.genextreme(0.051896837188595134, loc=0.5,
scale=1.5).rvs(size=1000, random_state=rng)
res = goodness_of_fit(stats.gumbel_r, x, statistic='ad',
random_state=rng)
ref = stats.anderson(x, dist='gumbel_r')
assert_allclose(res.statistic, ref.critical_values[0])
assert_allclose(res.pvalue, ref.significance_level[0]/100, atol=5e-3)
def test_against_filliben_norm(self):
# Test against `stats.fit` ref. [7] Section 8 "Example"
rng = np.random.default_rng(8024266430745011915)
y = [6, 1, -4, 8, -2, 5, 0]
known_params = {'loc': 0, 'scale': 1}
res = stats.goodness_of_fit(stats.norm, y, known_params=known_params,
statistic="filliben", random_state=rng)
# Slight discrepancy presumably due to roundoff in Filliben's
# calculation. Using exact order statistic medians instead of
# Filliben's approximation doesn't account for it.
assert_allclose(res.statistic, 0.98538, atol=1e-4)
assert 0.75 < res.pvalue < 0.9
# Using R's ppcc library:
# library(ppcc)
# options(digits=16)
# x < - c(6, 1, -4, 8, -2, 5, 0)
# set.seed(100)
# ppccTest(x, "qnorm", ppos="Filliben")
# Discrepancy with
assert_allclose(res.statistic, 0.98540957187084, rtol=2e-5)
assert_allclose(res.pvalue, 0.8875, rtol=2e-3)
def test_filliben_property(self):
# Filliben's statistic should be independent of data location and scale
rng = np.random.default_rng(8535677809395478813)
x = rng.normal(loc=10, scale=0.5, size=100)
res = stats.goodness_of_fit(stats.norm, x,
statistic="filliben", random_state=rng)
known_params = {'loc': 0, 'scale': 1}
ref = stats.goodness_of_fit(stats.norm, x, known_params=known_params,
statistic="filliben", random_state=rng)
assert_allclose(res.statistic, ref.statistic, rtol=1e-15)
@pytest.mark.parametrize('case', [(25, [.928, .937, .950, .958, .966]),
(50, [.959, .965, .972, .977, .981]),
(95, [.977, .979, .983, .986, .989])])
def test_against_filliben_norm_table(self, case):
# Test against `stats.fit` ref. [7] Table 1
rng = np.random.default_rng(504569995557928957)
n, ref = case
x = rng.random(n)
known_params = {'loc': 0, 'scale': 1}
res = stats.goodness_of_fit(stats.norm, x, known_params=known_params,
statistic="filliben", random_state=rng)
percentiles = np.array([0.005, 0.01, 0.025, 0.05, 0.1])
res = stats.scoreatpercentile(res.null_distribution, percentiles*100)
assert_allclose(res, ref, atol=2e-3)
@pytest.mark.xslow
@pytest.mark.parametrize('case', [(5, 0.95772790260469, 0.4755),
(6, 0.95398832257958, 0.3848),
(7, 0.9432692889277, 0.2328)])
def test_against_ppcc(self, case):
# Test against R ppcc, e.g.
# library(ppcc)
# options(digits=16)
# x < - c(0.52325412, 1.06907699, -0.36084066, 0.15305959, 0.99093194)
# set.seed(100)
# ppccTest(x, "qrayleigh", ppos="Filliben")
n, ref_statistic, ref_pvalue = case
rng = np.random.default_rng(7777775561439803116)
x = rng.normal(size=n)
res = stats.goodness_of_fit(stats.rayleigh, x, statistic="filliben",
random_state=rng)
assert_allclose(res.statistic, ref_statistic, rtol=1e-4)
assert_allclose(res.pvalue, ref_pvalue, atol=1.5e-2)
def test_params_effects(self):
# Ensure that `guessed_params`, `fit_params`, and `known_params` have
# the intended effects.
rng = np.random.default_rng(9121950977643805391)
x = stats.skewnorm.rvs(-5.044559778383153, loc=1, scale=2, size=50,
random_state=rng)
# Show that `guessed_params` don't fit to the guess,
# but `fit_params` and `known_params` respect the provided fit
guessed_params = {'c': 13.4}
fit_params = {'scale': 13.73}
known_params = {'loc': -13.85}
rng = np.random.default_rng(9121950977643805391)
res1 = goodness_of_fit(stats.weibull_min, x, n_mc_samples=2,
guessed_params=guessed_params,
fit_params=fit_params,
known_params=known_params, random_state=rng)
assert not np.allclose(res1.fit_result.params.c, 13.4)
assert_equal(res1.fit_result.params.scale, 13.73)
assert_equal(res1.fit_result.params.loc, -13.85)
# Show that changing the guess changes the parameter that gets fit,
# and it changes the null distribution
guessed_params = {'c': 2}
rng = np.random.default_rng(9121950977643805391)
res2 = goodness_of_fit(stats.weibull_min, x, n_mc_samples=2,
guessed_params=guessed_params,
fit_params=fit_params,
known_params=known_params, random_state=rng)
assert not np.allclose(res2.fit_result.params.c,
res1.fit_result.params.c, rtol=1e-8)
assert not np.allclose(res2.null_distribution,
res1.null_distribution, rtol=1e-8)
assert_equal(res2.fit_result.params.scale, 13.73)
assert_equal(res2.fit_result.params.loc, -13.85)
# If we set all parameters as fit_params and known_params,
# they're all fixed to those values, but the null distribution
# varies.
fit_params = {'c': 13.4, 'scale': 13.73}
rng = np.random.default_rng(9121950977643805391)
res3 = goodness_of_fit(stats.weibull_min, x, n_mc_samples=2,
guessed_params=guessed_params,
fit_params=fit_params,
known_params=known_params, random_state=rng)
assert_equal(res3.fit_result.params.c, 13.4)
assert_equal(res3.fit_result.params.scale, 13.73)
assert_equal(res3.fit_result.params.loc, -13.85)
assert not np.allclose(res3.null_distribution, res1.null_distribution)
def test_custom_statistic(self):
# Test support for custom statistic function.
# References:
# [1] Pyke, R. (1965). "Spacings". Journal of the Royal Statistical
# Society: Series B (Methodological), 27(3): 395-436.
# [2] Burrows, P. M. (1979). "Selected Percentage Points of
# Greenwood's Statistics". Journal of the Royal Statistical
# Society. Series A (General), 142(2): 256-258.
# Use the Greenwood statistic for illustration; see [1, p.402].
def greenwood(dist, data, *, axis):
x = np.sort(data, axis=axis)
y = dist.cdf(x)
d = np.diff(y, axis=axis, prepend=0, append=1)
return np.sum(d ** 2, axis=axis)
# Run the Monte Carlo test with sample size = 5 on a fully specified
# null distribution, and compare the simulated quantiles to the exact
# ones given in [2, Table 1, column (n = 5)].
rng = np.random.default_rng(9121950977643805391)
data = stats.expon.rvs(size=5, random_state=rng)
result = goodness_of_fit(stats.expon, data,
known_params={'loc': 0, 'scale': 1},
statistic=greenwood, random_state=rng)
p = [.01, .05, .1, .2, .3, .4, .5, .6, .7, .8, .9, .95, .99]
exact_quantiles = [
.183863, .199403, .210088, .226040, .239947, .253677, .268422,
.285293, .306002, .334447, .382972, .432049, .547468]
simulated_quantiles = np.quantile(result.null_distribution, p)
assert_allclose(simulated_quantiles, exact_quantiles, atol=0.005)
class TestFitResult:
def test_plot_iv(self):
rng = np.random.default_rng(1769658657308472721)
data = stats.norm.rvs(0, 1, size=100, random_state=rng)
def optimizer(*args, **kwargs):
return differential_evolution(*args, **kwargs, seed=rng)
bounds = [(0, 30), (0, 1)]
res = stats.fit(stats.norm, data, bounds, optimizer=optimizer)
try:
import matplotlib # noqa: F401
message = r"`plot_type` must be one of \{'..."
with pytest.raises(ValueError, match=message):
res.plot(plot_type='llama')
except (ModuleNotFoundError, ImportError):
# Avoid trying to call MPL with numpy 2.0-dev, because that fails
# too often due to ABI mismatches and is hard to avoid. This test
# will work fine again once MPL has done a 2.0-compatible release.
if not np.__version__.startswith('2.0.0.dev0'):
message = r"matplotlib must be installed to use method `plot`."
with pytest.raises(ModuleNotFoundError, match=message):
res.plot(plot_type='llama')