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3RNN/Lib/site-packages/scipy/stats/tests/test_continuous_basic.py

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1.0
2024-05-26 19:49:15 +02:00
import sys
import numpy as np
import numpy.testing as npt
import pytest
from pytest import raises as assert_raises
from scipy.integrate import IntegrationWarning
import itertools
from scipy import stats
from .common_tests import (check_normalization, check_moment,
check_mean_expect,
check_var_expect, check_skew_expect,
check_kurt_expect, check_entropy,
check_private_entropy, check_entropy_vect_scale,
check_edge_support, check_named_args,
check_random_state_property,
check_meth_dtype, check_ppf_dtype,
check_cmplx_deriv,
check_pickling, check_rvs_broadcast,
check_freezing, check_munp_expect,)
from scipy.stats._distr_params import distcont
from scipy.stats._distn_infrastructure import rv_continuous_frozen
"""
Test all continuous distributions.
Parameters were chosen for those distributions that pass the
Kolmogorov-Smirnov test. This provides safe parameters for each
distributions so that we can perform further testing of class methods.
These tests currently check only/mostly for serious errors and exceptions,
not for numerically exact results.
"""
# Note that you need to add new distributions you want tested
# to _distr_params
DECIMAL = 5 # specify the precision of the tests # increased from 0 to 5
_IS_32BIT = (sys.maxsize < 2**32)
# For skipping test_cont_basic
distslow = ['recipinvgauss', 'vonmises', 'kappa4', 'vonmises_line',
'gausshyper', 'norminvgauss', 'geninvgauss', 'genhyperbolic',
'truncnorm', 'truncweibull_min']
# distxslow are sorted by speed (very slow to slow)
distxslow = ['studentized_range', 'kstwo', 'ksone', 'wrapcauchy', 'genexpon']
# For skipping test_moments, which is already marked slow
distxslow_test_moments = ['studentized_range', 'vonmises', 'vonmises_line',
'ksone', 'kstwo', 'recipinvgauss', 'genexpon']
# skip check_fit_args (test is slow)
skip_fit_test_mle = ['exponpow', 'exponweib', 'gausshyper', 'genexpon',
'halfgennorm', 'gompertz', 'johnsonsb', 'johnsonsu',
'kappa4', 'ksone', 'kstwo', 'kstwobign', 'mielke', 'ncf',
'nct', 'powerlognorm', 'powernorm', 'recipinvgauss',
'trapezoid', 'vonmises', 'vonmises_line', 'levy_stable',
'rv_histogram_instance', 'studentized_range']
# these were really slow in `test_fit`.py.
# note that this list is used to skip both fit_test and fit_fix tests
slow_fit_test_mm = ['argus', 'exponpow', 'exponweib', 'gausshyper', 'genexpon',
'genhalflogistic', 'halfgennorm', 'gompertz', 'johnsonsb',
'kappa4', 'kstwobign', 'recipinvgauss',
'trapezoid', 'truncexpon', 'vonmises', 'vonmises_line',
'studentized_range']
# pearson3 fails due to something weird
# the first list fails due to non-finite distribution moments encountered
# most of the rest fail due to integration warnings
# pearson3 is overridden as not implemented due to gh-11746
fail_fit_test_mm = (['alpha', 'betaprime', 'bradford', 'burr', 'burr12',
'cauchy', 'crystalball', 'f', 'fisk', 'foldcauchy',
'genextreme', 'genpareto', 'halfcauchy', 'invgamma',
'jf_skew_t', 'kappa3', 'levy', 'levy_l', 'loglaplace',
'lomax', 'mielke', 'nakagami', 'ncf', 'skewcauchy', 't',
'tukeylambda', 'invweibull', 'rel_breitwigner']
+ ['genhyperbolic', 'johnsonsu', 'ksone', 'kstwo',
'nct', 'pareto', 'powernorm', 'powerlognorm']
+ ['pearson3'])
skip_fit_test = {"MLE": skip_fit_test_mle,
"MM": slow_fit_test_mm + fail_fit_test_mm}
# skip check_fit_args_fix (test is slow)
skip_fit_fix_test_mle = ['burr', 'exponpow', 'exponweib', 'gausshyper',
'genexpon', 'halfgennorm', 'gompertz', 'johnsonsb',
'johnsonsu', 'kappa4', 'ksone', 'kstwo', 'kstwobign',
'levy_stable', 'mielke', 'ncf', 'ncx2',
'powerlognorm', 'powernorm', 'rdist', 'recipinvgauss',
'trapezoid', 'truncpareto', 'vonmises', 'vonmises_line',
'studentized_range']
# the first list fails due to non-finite distribution moments encountered
# most of the rest fail due to integration warnings
# pearson3 is overridden as not implemented due to gh-11746
fail_fit_fix_test_mm = (['alpha', 'betaprime', 'burr', 'burr12', 'cauchy',
'crystalball', 'f', 'fisk', 'foldcauchy',
'genextreme', 'genpareto', 'halfcauchy', 'invgamma',
'jf_skew_t', 'kappa3', 'levy', 'levy_l', 'loglaplace',
'lomax', 'mielke', 'nakagami', 'ncf', 'nct',
'skewcauchy', 't', 'truncpareto', 'invweibull']
+ ['genhyperbolic', 'johnsonsu', 'ksone', 'kstwo',
'pareto', 'powernorm', 'powerlognorm']
+ ['pearson3'])
skip_fit_fix_test = {"MLE": skip_fit_fix_test_mle,
"MM": slow_fit_test_mm + fail_fit_fix_test_mm}
# These distributions fail the complex derivative test below.
# Here 'fail' mean produce wrong results and/or raise exceptions, depending
# on the implementation details of corresponding special functions.
# cf https://github.com/scipy/scipy/pull/4979 for a discussion.
fails_cmplx = {'argus', 'beta', 'betaprime', 'chi', 'chi2', 'cosine',
'dgamma', 'dweibull', 'erlang', 'f', 'foldcauchy', 'gamma',
'gausshyper', 'gengamma', 'genhyperbolic',
'geninvgauss', 'gennorm', 'genpareto',
'halfcauchy', 'halfgennorm', 'invgamma', 'jf_skew_t',
'ksone', 'kstwo', 'kstwobign', 'levy_l', 'loggamma',
'logistic', 'loguniform', 'maxwell', 'nakagami',
'ncf', 'nct', 'ncx2', 'norminvgauss', 'pearson3',
'powerlaw', 'rdist', 'reciprocal', 'rice',
'skewnorm', 't', 'truncweibull_min',
'tukeylambda', 'vonmises', 'vonmises_line',
'rv_histogram_instance', 'truncnorm', 'studentized_range',
'johnsonsb', 'halflogistic', 'rel_breitwigner'}
# rv_histogram instances, with uniform and non-uniform bins;
# stored as (dist, arg) tuples for cases_test_cont_basic
# and cases_test_moments.
histogram_test_instances = []
case1 = {'a': [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6,
6, 6, 6, 7, 7, 7, 8, 8, 9], 'bins': 8} # equal width bins
case2 = {'a': [1, 1], 'bins': [0, 1, 10]} # unequal width bins
for case, density in itertools.product([case1, case2], [True, False]):
_hist = np.histogram(**case, density=density)
_rv_hist = stats.rv_histogram(_hist, density=density)
histogram_test_instances.append((_rv_hist, tuple()))
def cases_test_cont_basic():
for distname, arg in distcont[:] + histogram_test_instances:
if distname == 'levy_stable':
continue
elif distname in distslow:
yield pytest.param(distname, arg, marks=pytest.mark.slow)
elif distname in distxslow:
yield pytest.param(distname, arg, marks=pytest.mark.xslow)
else:
yield distname, arg
@pytest.mark.parametrize('distname,arg', cases_test_cont_basic())
@pytest.mark.parametrize('sn, n_fit_samples', [(500, 200)])
def test_cont_basic(distname, arg, sn, n_fit_samples):
# this test skips slow distributions
try:
distfn = getattr(stats, distname)
except TypeError:
distfn = distname
distname = 'rv_histogram_instance'
rng = np.random.RandomState(765456)
rvs = distfn.rvs(size=sn, *arg, random_state=rng)
m, v = distfn.stats(*arg)
if distname not in {'laplace_asymmetric'}:
check_sample_meanvar_(m, v, rvs)
check_cdf_ppf(distfn, arg, distname)
check_sf_isf(distfn, arg, distname)
check_cdf_sf(distfn, arg, distname)
check_ppf_isf(distfn, arg, distname)
check_pdf(distfn, arg, distname)
check_pdf_logpdf(distfn, arg, distname)
check_pdf_logpdf_at_endpoints(distfn, arg, distname)
check_cdf_logcdf(distfn, arg, distname)
check_sf_logsf(distfn, arg, distname)
check_ppf_broadcast(distfn, arg, distname)
alpha = 0.01
if distname == 'rv_histogram_instance':
check_distribution_rvs(distfn.cdf, arg, alpha, rvs)
elif distname != 'geninvgauss':
# skip kstest for geninvgauss since cdf is too slow; see test for
# rv generation in TestGenInvGauss in test_distributions.py
check_distribution_rvs(distname, arg, alpha, rvs)
locscale_defaults = (0, 1)
meths = [distfn.pdf, distfn.logpdf, distfn.cdf, distfn.logcdf,
distfn.logsf]
# make sure arguments are within support
spec_x = {'weibull_max': -0.5, 'levy_l': -0.5,
'pareto': 1.5, 'truncpareto': 3.2, 'tukeylambda': 0.3,
'rv_histogram_instance': 5.0}
x = spec_x.get(distname, 0.5)
if distname == 'invweibull':
arg = (1,)
elif distname == 'ksone':
arg = (3,)
check_named_args(distfn, x, arg, locscale_defaults, meths)
check_random_state_property(distfn, arg)
if distname in ['rel_breitwigner'] and _IS_32BIT:
# gh18414
pytest.skip("fails on Linux 32-bit")
else:
check_pickling(distfn, arg)
check_freezing(distfn, arg)
# Entropy
if distname not in ['kstwobign', 'kstwo', 'ncf']:
check_entropy(distfn, arg, distname)
if distfn.numargs == 0:
check_vecentropy(distfn, arg)
if (distfn.__class__._entropy != stats.rv_continuous._entropy
and distname != 'vonmises'):
check_private_entropy(distfn, arg, stats.rv_continuous)
with npt.suppress_warnings() as sup:
sup.filter(IntegrationWarning, "The occurrence of roundoff error")
sup.filter(IntegrationWarning, "Extremely bad integrand")
sup.filter(RuntimeWarning, "invalid value")
check_entropy_vect_scale(distfn, arg)
check_retrieving_support(distfn, arg)
check_edge_support(distfn, arg)
check_meth_dtype(distfn, arg, meths)
check_ppf_dtype(distfn, arg)
if distname not in fails_cmplx:
check_cmplx_deriv(distfn, arg)
if distname != 'truncnorm':
check_ppf_private(distfn, arg, distname)
for method in ["MLE", "MM"]:
if distname not in skip_fit_test[method]:
check_fit_args(distfn, arg, rvs[:n_fit_samples], method)
if distname not in skip_fit_fix_test[method]:
check_fit_args_fix(distfn, arg, rvs[:n_fit_samples], method)
@pytest.mark.parametrize('distname,arg', cases_test_cont_basic())
def test_rvs_scalar(distname, arg):
# rvs should return a scalar when given scalar arguments (gh-12428)
try:
distfn = getattr(stats, distname)
except TypeError:
distfn = distname
distname = 'rv_histogram_instance'
assert np.isscalar(distfn.rvs(*arg))
assert np.isscalar(distfn.rvs(*arg, size=()))
assert np.isscalar(distfn.rvs(*arg, size=None))
def test_levy_stable_random_state_property():
# levy_stable only implements rvs(), so it is skipped in the
# main loop in test_cont_basic(). Here we apply just the test
# check_random_state_property to levy_stable.
check_random_state_property(stats.levy_stable, (0.5, 0.1))
def cases_test_moments():
fail_normalization = set()
fail_higher = {'ncf'}
fail_moment = {'johnsonsu'} # generic `munp` is inaccurate for johnsonsu
for distname, arg in distcont[:] + histogram_test_instances:
if distname == 'levy_stable':
continue
if distname in distxslow_test_moments:
yield pytest.param(distname, arg, True, True, True, True,
marks=pytest.mark.xslow(reason="too slow"))
continue
cond1 = distname not in fail_normalization
cond2 = distname not in fail_higher
cond3 = distname not in fail_moment
marks = list()
# Currently unused, `marks` can be used to add a timeout to a test of
# a specific distribution. For example, this shows how a timeout could
# be added for the 'skewnorm' distribution:
#
# marks = list()
# if distname == 'skewnorm':
# marks.append(pytest.mark.timeout(300))
yield pytest.param(distname, arg, cond1, cond2, cond3,
False, marks=marks)
if not cond1 or not cond2 or not cond3:
# Run the distributions that have issues twice, once skipping the
# not_ok parts, once with the not_ok parts but marked as knownfail
yield pytest.param(distname, arg, True, True, True, True,
marks=[pytest.mark.xfail] + marks)
@pytest.mark.slow
@pytest.mark.parametrize('distname,arg,normalization_ok,higher_ok,moment_ok,'
'is_xfailing',
cases_test_moments())
def test_moments(distname, arg, normalization_ok, higher_ok, moment_ok,
is_xfailing):
try:
distfn = getattr(stats, distname)
except TypeError:
distfn = distname
distname = 'rv_histogram_instance'
with npt.suppress_warnings() as sup:
sup.filter(IntegrationWarning,
"The integral is probably divergent, or slowly convergent.")
sup.filter(IntegrationWarning,
"The maximum number of subdivisions.")
sup.filter(IntegrationWarning,
"The algorithm does not converge.")
if is_xfailing:
sup.filter(IntegrationWarning)
m, v, s, k = distfn.stats(*arg, moments='mvsk')
with np.errstate(all="ignore"):
if normalization_ok:
check_normalization(distfn, arg, distname)
if higher_ok:
check_mean_expect(distfn, arg, m, distname)
check_skew_expect(distfn, arg, m, v, s, distname)
check_var_expect(distfn, arg, m, v, distname)
check_kurt_expect(distfn, arg, m, v, k, distname)
check_munp_expect(distfn, arg, distname)
check_loc_scale(distfn, arg, m, v, distname)
if moment_ok:
check_moment(distfn, arg, m, v, distname)
@pytest.mark.parametrize('dist,shape_args', distcont)
def test_rvs_broadcast(dist, shape_args):
if dist in ['gausshyper', 'studentized_range']:
pytest.skip("too slow")
if dist in ['rel_breitwigner'] and _IS_32BIT:
# gh18414
pytest.skip("fails on Linux 32-bit")
# If shape_only is True, it means the _rvs method of the
# distribution uses more than one random number to generate a random
# variate. That means the result of using rvs with broadcasting or
# with a nontrivial size will not necessarily be the same as using the
# numpy.vectorize'd version of rvs(), so we can only compare the shapes
# of the results, not the values.
# Whether or not a distribution is in the following list is an
# implementation detail of the distribution, not a requirement. If
# the implementation the rvs() method of a distribution changes, this
# test might also have to be changed.
shape_only = dist in ['argus', 'betaprime', 'dgamma', 'dweibull',
'exponnorm', 'genhyperbolic', 'geninvgauss',
'levy_stable', 'nct', 'norminvgauss', 'rice',
'skewnorm', 'semicircular', 'gennorm', 'loggamma']
distfunc = getattr(stats, dist)
loc = np.zeros(2)
scale = np.ones((3, 1))
nargs = distfunc.numargs
allargs = []
bshape = [3, 2]
# Generate shape parameter arguments...
for k in range(nargs):
shp = (k + 4,) + (1,)*(k + 2)
allargs.append(shape_args[k]*np.ones(shp))
bshape.insert(0, k + 4)
allargs.extend([loc, scale])
# bshape holds the expected shape when loc, scale, and the shape
# parameters are all broadcast together.
check_rvs_broadcast(distfunc, dist, allargs, bshape, shape_only, 'd')
# Expected values of the SF, CDF, PDF were computed using
# mpmath with mpmath.mp.dps = 50 and output at 20:
#
# def ks(x, n):
# x = mpmath.mpf(x)
# logp = -mpmath.power(6.0*n*x+1.0, 2)/18.0/n
# sf, cdf = mpmath.exp(logp), -mpmath.expm1(logp)
# pdf = (6.0*n*x+1.0) * 2 * sf/3
# print(mpmath.nstr(sf, 20), mpmath.nstr(cdf, 20), mpmath.nstr(pdf, 20))
#
# Tests use 1/n < x < 1-1/n and n > 1e6 to use the asymptotic computation.
# Larger x has a smaller sf.
@pytest.mark.parametrize('x,n,sf,cdf,pdf,rtol',
[(2.0e-5, 1000000000,
0.44932297307934442379, 0.55067702692065557621,
35946.137394996276407, 5e-15),
(2.0e-9, 1000000000,
0.99999999061111115519, 9.3888888448132728224e-9,
8.6666665852962971765, 5e-14),
(5.0e-4, 1000000000,
7.1222019433090374624e-218, 1.0,
1.4244408634752704094e-211, 5e-14)])
def test_gh17775_regression(x, n, sf, cdf, pdf, rtol):
# Regression test for gh-17775. In scipy 1.9.3 and earlier,
# these test would fail.
#
# KS one asymptotic sf ~ e^(-(6nx+1)^2 / 18n)
# Given a large 32-bit integer n, 6n will overflow in the c implementation.
# Example of broken behaviour:
# ksone.sf(2.0e-5, 1000000000) == 0.9374359693473666
ks = stats.ksone
vals = np.array([ks.sf(x, n), ks.cdf(x, n), ks.pdf(x, n)])
expected = np.array([sf, cdf, pdf])
npt.assert_allclose(vals, expected, rtol=rtol)
# The sf+cdf must sum to 1.0.
npt.assert_equal(vals[0] + vals[1], 1.0)
# Check inverting the (potentially very small) sf (uses a lower tolerance)
npt.assert_allclose([ks.isf(sf, n)], [x], rtol=1e-8)
def test_rvs_gh2069_regression():
# Regression tests for gh-2069. In scipy 0.17 and earlier,
# these tests would fail.
#
# A typical example of the broken behavior:
# >>> norm.rvs(loc=np.zeros(5), scale=np.ones(5))
# array([-2.49613705, -2.49613705, -2.49613705, -2.49613705, -2.49613705])
rng = np.random.RandomState(123)
vals = stats.norm.rvs(loc=np.zeros(5), scale=1, random_state=rng)
d = np.diff(vals)
npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
vals = stats.norm.rvs(loc=0, scale=np.ones(5), random_state=rng)
d = np.diff(vals)
npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
vals = stats.norm.rvs(loc=np.zeros(5), scale=np.ones(5), random_state=rng)
d = np.diff(vals)
npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
vals = stats.norm.rvs(loc=np.array([[0], [0]]), scale=np.ones(5),
random_state=rng)
d = np.diff(vals.ravel())
npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
assert_raises(ValueError, stats.norm.rvs, [[0, 0], [0, 0]],
[[1, 1], [1, 1]], 1)
assert_raises(ValueError, stats.gamma.rvs, [2, 3, 4, 5], 0, 1, (2, 2))
assert_raises(ValueError, stats.gamma.rvs, [1, 1, 1, 1], [0, 0, 0, 0],
[[1], [2]], (4,))
def test_nomodify_gh9900_regression():
# Regression test for gh-9990
# Prior to gh-9990, calls to stats.truncnorm._cdf() use what ever was
# set inside the stats.truncnorm instance during stats.truncnorm.cdf().
# This could cause issues with multi-threaded code.
# Since then, the calls to cdf() are not permitted to modify the global
# stats.truncnorm instance.
tn = stats.truncnorm
# Use the right-half truncated normal
# Check that the cdf and _cdf return the same result.
npt.assert_almost_equal(tn.cdf(1, 0, np.inf),
0.6826894921370859)
npt.assert_almost_equal(tn._cdf([1], [0], [np.inf]),
0.6826894921370859)
# Now use the left-half truncated normal
npt.assert_almost_equal(tn.cdf(-1, -np.inf, 0),
0.31731050786291415)
npt.assert_almost_equal(tn._cdf([-1], [-np.inf], [0]),
0.31731050786291415)
# Check that the right-half truncated normal _cdf hasn't changed
npt.assert_almost_equal(tn._cdf([1], [0], [np.inf]),
0.6826894921370859) # Not 1.6826894921370859
npt.assert_almost_equal(tn.cdf(1, 0, np.inf),
0.6826894921370859)
# Check that the left-half truncated normal _cdf hasn't changed
npt.assert_almost_equal(tn._cdf([-1], [-np.inf], [0]),
0.31731050786291415) # Not -0.6826894921370859
npt.assert_almost_equal(tn.cdf(1, -np.inf, 0),
1) # Not 1.6826894921370859
npt.assert_almost_equal(tn.cdf(-1, -np.inf, 0),
0.31731050786291415) # Not -0.6826894921370859
def test_broadcast_gh9990_regression():
# Regression test for gh-9990
# The x-value 7 only lies within the support of 4 of the supplied
# distributions. Prior to 9990, one array passed to
# stats.reciprocal._cdf would have 4 elements, but an array
# previously stored by stats.reciprocal_argcheck() would have 6, leading
# to a broadcast error.
a = np.array([1, 2, 3, 4, 5, 6])
b = np.array([8, 16, 1, 32, 1, 48])
ans = [stats.reciprocal.cdf(7, _a, _b) for _a, _b in zip(a,b)]
npt.assert_array_almost_equal(stats.reciprocal.cdf(7, a, b), ans)
ans = [stats.reciprocal.cdf(1, _a, _b) for _a, _b in zip(a,b)]
npt.assert_array_almost_equal(stats.reciprocal.cdf(1, a, b), ans)
ans = [stats.reciprocal.cdf(_a, _a, _b) for _a, _b in zip(a,b)]
npt.assert_array_almost_equal(stats.reciprocal.cdf(a, a, b), ans)
ans = [stats.reciprocal.cdf(_b, _a, _b) for _a, _b in zip(a,b)]
npt.assert_array_almost_equal(stats.reciprocal.cdf(b, a, b), ans)
def test_broadcast_gh7933_regression():
# Check broadcast works
stats.truncnorm.logpdf(
np.array([3.0, 2.0, 1.0]),
a=(1.5 - np.array([6.0, 5.0, 4.0])) / 3.0,
b=np.inf,
loc=np.array([6.0, 5.0, 4.0]),
scale=3.0
)
def test_gh2002_regression():
# Add a check that broadcast works in situations where only some
# x-values are compatible with some of the shape arguments.
x = np.r_[-2:2:101j]
a = np.r_[-np.ones(50), np.ones(51)]
expected = [stats.truncnorm.pdf(_x, _a, np.inf) for _x, _a in zip(x, a)]
ans = stats.truncnorm.pdf(x, a, np.inf)
npt.assert_array_almost_equal(ans, expected)
def test_gh1320_regression():
# Check that the first example from gh-1320 now works.
c = 2.62
stats.genextreme.ppf(0.5, np.array([[c], [c + 0.5]]))
# The other examples in gh-1320 appear to have stopped working
# some time ago.
# ans = stats.genextreme.moment(2, np.array([c, c + 0.5]))
# expected = np.array([25.50105963, 115.11191437])
# stats.genextreme.moment(5, np.array([[c], [c + 0.5]]))
# stats.genextreme.moment(5, np.array([c, c + 0.5]))
def test_method_of_moments():
# example from https://en.wikipedia.org/wiki/Method_of_moments_(statistics)
np.random.seed(1234)
x = [0, 0, 0, 0, 1]
a = 1/5 - 2*np.sqrt(3)/5
b = 1/5 + 2*np.sqrt(3)/5
# force use of method of moments (uniform.fit is overridden)
loc, scale = super(type(stats.uniform), stats.uniform).fit(x, method="MM")
npt.assert_almost_equal(loc, a, decimal=4)
npt.assert_almost_equal(loc+scale, b, decimal=4)
def check_sample_meanvar_(popmean, popvar, sample):
if np.isfinite(popmean):
check_sample_mean(sample, popmean)
if np.isfinite(popvar):
check_sample_var(sample, popvar)
def check_sample_mean(sample, popmean):
# Checks for unlikely difference between sample mean and population mean
prob = stats.ttest_1samp(sample, popmean).pvalue
assert prob > 0.01
def check_sample_var(sample, popvar):
# check that population mean lies within the CI bootstrapped from the
# sample. This used to be a chi-squared test for variance, but there were
# too many false positives
res = stats.bootstrap(
(sample,),
lambda x, axis: x.var(ddof=1, axis=axis),
confidence_level=0.995,
)
conf = res.confidence_interval
low, high = conf.low, conf.high
assert low <= popvar <= high
def check_cdf_ppf(distfn, arg, msg):
values = [0.001, 0.5, 0.999]
npt.assert_almost_equal(distfn.cdf(distfn.ppf(values, *arg), *arg),
values, decimal=DECIMAL, err_msg=msg +
' - cdf-ppf roundtrip')
def check_sf_isf(distfn, arg, msg):
npt.assert_almost_equal(distfn.sf(distfn.isf([0.1, 0.5, 0.9], *arg), *arg),
[0.1, 0.5, 0.9], decimal=DECIMAL, err_msg=msg +
' - sf-isf roundtrip')
def check_cdf_sf(distfn, arg, msg):
npt.assert_almost_equal(distfn.cdf([0.1, 0.9], *arg),
1.0 - distfn.sf([0.1, 0.9], *arg),
decimal=DECIMAL, err_msg=msg +
' - cdf-sf relationship')
def check_ppf_isf(distfn, arg, msg):
p = np.array([0.1, 0.9])
npt.assert_almost_equal(distfn.isf(p, *arg), distfn.ppf(1-p, *arg),
decimal=DECIMAL, err_msg=msg +
' - ppf-isf relationship')
def check_pdf(distfn, arg, msg):
# compares pdf at median with numerical derivative of cdf
median = distfn.ppf(0.5, *arg)
eps = 1e-6
pdfv = distfn.pdf(median, *arg)
if (pdfv < 1e-4) or (pdfv > 1e4):
# avoid checking a case where pdf is close to zero or
# huge (singularity)
median = median + 0.1
pdfv = distfn.pdf(median, *arg)
cdfdiff = (distfn.cdf(median + eps, *arg) -
distfn.cdf(median - eps, *arg))/eps/2.0
# replace with better diff and better test (more points),
# actually, this works pretty well
msg += ' - cdf-pdf relationship'
npt.assert_almost_equal(pdfv, cdfdiff, decimal=DECIMAL, err_msg=msg)
def check_pdf_logpdf(distfn, args, msg):
# compares pdf at several points with the log of the pdf
points = np.array([0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8])
vals = distfn.ppf(points, *args)
vals = vals[np.isfinite(vals)]
pdf = distfn.pdf(vals, *args)
logpdf = distfn.logpdf(vals, *args)
pdf = pdf[(pdf != 0) & np.isfinite(pdf)]
logpdf = logpdf[np.isfinite(logpdf)]
msg += " - logpdf-log(pdf) relationship"
npt.assert_almost_equal(np.log(pdf), logpdf, decimal=7, err_msg=msg)
def check_pdf_logpdf_at_endpoints(distfn, args, msg):
# compares pdf with the log of the pdf at the (finite) end points
points = np.array([0, 1])
vals = distfn.ppf(points, *args)
vals = vals[np.isfinite(vals)]
pdf = distfn.pdf(vals, *args)
logpdf = distfn.logpdf(vals, *args)
pdf = pdf[(pdf != 0) & np.isfinite(pdf)]
logpdf = logpdf[np.isfinite(logpdf)]
msg += " - logpdf-log(pdf) relationship"
npt.assert_almost_equal(np.log(pdf), logpdf, decimal=7, err_msg=msg)
def check_sf_logsf(distfn, args, msg):
# compares sf at several points with the log of the sf
points = np.array([0.0, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 1.0])
vals = distfn.ppf(points, *args)
vals = vals[np.isfinite(vals)]
sf = distfn.sf(vals, *args)
logsf = distfn.logsf(vals, *args)
sf = sf[sf != 0]
logsf = logsf[np.isfinite(logsf)]
msg += " - logsf-log(sf) relationship"
npt.assert_almost_equal(np.log(sf), logsf, decimal=7, err_msg=msg)
def check_cdf_logcdf(distfn, args, msg):
# compares cdf at several points with the log of the cdf
points = np.array([0, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 1.0])
vals = distfn.ppf(points, *args)
vals = vals[np.isfinite(vals)]
cdf = distfn.cdf(vals, *args)
logcdf = distfn.logcdf(vals, *args)
cdf = cdf[cdf != 0]
logcdf = logcdf[np.isfinite(logcdf)]
msg += " - logcdf-log(cdf) relationship"
npt.assert_almost_equal(np.log(cdf), logcdf, decimal=7, err_msg=msg)
def check_ppf_broadcast(distfn, arg, msg):
# compares ppf for multiple argsets.
num_repeats = 5
args = [] * num_repeats
if arg:
args = [np.array([_] * num_repeats) for _ in arg]
median = distfn.ppf(0.5, *arg)
medians = distfn.ppf(0.5, *args)
msg += " - ppf multiple"
npt.assert_almost_equal(medians, [median] * num_repeats, decimal=7, err_msg=msg)
def check_distribution_rvs(dist, args, alpha, rvs):
# dist is either a cdf function or name of a distribution in scipy.stats.
# args are the args for scipy.stats.dist(*args)
# alpha is a significance level, ~0.01
# rvs is array_like of random variables
# test from scipy.stats.tests
# this version reuses existing random variables
D, pval = stats.kstest(rvs, dist, args=args, N=1000)
if (pval < alpha):
# The rvs passed in failed the K-S test, which _could_ happen
# but is unlikely if alpha is small enough.
# Repeat the test with a new sample of rvs.
# Generate 1000 rvs, perform a K-S test that the new sample of rvs
# are distributed according to the distribution.
D, pval = stats.kstest(dist, dist, args=args, N=1000)
npt.assert_(pval > alpha, "D = " + str(D) + "; pval = " + str(pval) +
"; alpha = " + str(alpha) + "\nargs = " + str(args))
def check_vecentropy(distfn, args):
npt.assert_equal(distfn.vecentropy(*args), distfn._entropy(*args))
def check_loc_scale(distfn, arg, m, v, msg):
# Make `loc` and `scale` arrays to catch bugs like gh-13580 where
# `loc` and `scale` arrays improperly broadcast with shapes.
loc, scale = np.array([10.0, 20.0]), np.array([10.0, 20.0])
mt, vt = distfn.stats(*arg, loc=loc, scale=scale)
npt.assert_allclose(m*scale + loc, mt)
npt.assert_allclose(v*scale*scale, vt)
def check_ppf_private(distfn, arg, msg):
# fails by design for truncnorm self.nb not defined
ppfs = distfn._ppf(np.array([0.1, 0.5, 0.9]), *arg)
npt.assert_(not np.any(np.isnan(ppfs)), msg + 'ppf private is nan')
def check_retrieving_support(distfn, args):
loc, scale = 1, 2
supp = distfn.support(*args)
supp_loc_scale = distfn.support(*args, loc=loc, scale=scale)
npt.assert_almost_equal(np.array(supp)*scale + loc,
np.array(supp_loc_scale))
def check_fit_args(distfn, arg, rvs, method):
with np.errstate(all='ignore'), npt.suppress_warnings() as sup:
sup.filter(category=RuntimeWarning,
message="The shape parameter of the erlang")
sup.filter(category=RuntimeWarning,
message="floating point number truncated")
vals = distfn.fit(rvs, method=method)
vals2 = distfn.fit(rvs, optimizer='powell', method=method)
# Only check the length of the return; accuracy tested in test_fit.py
npt.assert_(len(vals) == 2+len(arg))
npt.assert_(len(vals2) == 2+len(arg))
def check_fit_args_fix(distfn, arg, rvs, method):
with np.errstate(all='ignore'), npt.suppress_warnings() as sup:
sup.filter(category=RuntimeWarning,
message="The shape parameter of the erlang")
vals = distfn.fit(rvs, floc=0, method=method)
vals2 = distfn.fit(rvs, fscale=1, method=method)
npt.assert_(len(vals) == 2+len(arg))
npt.assert_(vals[-2] == 0)
npt.assert_(vals2[-1] == 1)
npt.assert_(len(vals2) == 2+len(arg))
if len(arg) > 0:
vals3 = distfn.fit(rvs, f0=arg[0], method=method)
npt.assert_(len(vals3) == 2+len(arg))
npt.assert_(vals3[0] == arg[0])
if len(arg) > 1:
vals4 = distfn.fit(rvs, f1=arg[1], method=method)
npt.assert_(len(vals4) == 2+len(arg))
npt.assert_(vals4[1] == arg[1])
if len(arg) > 2:
vals5 = distfn.fit(rvs, f2=arg[2], method=method)
npt.assert_(len(vals5) == 2+len(arg))
npt.assert_(vals5[2] == arg[2])
@pytest.mark.parametrize('method', ['pdf', 'logpdf', 'cdf', 'logcdf',
'sf', 'logsf', 'ppf', 'isf'])
@pytest.mark.parametrize('distname, args', distcont)
def test_methods_with_lists(method, distname, args):
# Test that the continuous distributions can accept Python lists
# as arguments.
dist = getattr(stats, distname)
f = getattr(dist, method)
if distname == 'invweibull' and method.startswith('log'):
x = [1.5, 2]
else:
x = [0.1, 0.2]
shape2 = [[a]*2 for a in args]
loc = [0, 0.1]
scale = [1, 1.01]
result = f(x, *shape2, loc=loc, scale=scale)
npt.assert_allclose(result,
[f(*v) for v in zip(x, *shape2, loc, scale)],
rtol=1e-14, atol=5e-14)
def test_burr_fisk_moment_gh13234_regression():
vals0 = stats.burr.moment(1, 5, 4)
assert isinstance(vals0, float)
vals1 = stats.fisk.moment(1, 8)
assert isinstance(vals1, float)
def test_moments_with_array_gh12192_regression():
# array loc and scalar scale
vals0 = stats.norm.moment(order=1, loc=np.array([1, 2, 3]), scale=1)
expected0 = np.array([1., 2., 3.])
npt.assert_equal(vals0, expected0)
# array loc and invalid scalar scale
vals1 = stats.norm.moment(order=1, loc=np.array([1, 2, 3]), scale=-1)
expected1 = np.array([np.nan, np.nan, np.nan])
npt.assert_equal(vals1, expected1)
# array loc and array scale with invalid entries
vals2 = stats.norm.moment(order=1, loc=np.array([1, 2, 3]),
scale=[-3, 1, 0])
expected2 = np.array([np.nan, 2., np.nan])
npt.assert_equal(vals2, expected2)
# (loc == 0) & (scale < 0)
vals3 = stats.norm.moment(order=2, loc=0, scale=-4)
expected3 = np.nan
npt.assert_equal(vals3, expected3)
assert isinstance(vals3, expected3.__class__)
# array loc with 0 entries and scale with invalid entries
vals4 = stats.norm.moment(order=2, loc=[1, 0, 2], scale=[3, -4, -5])
expected4 = np.array([10., np.nan, np.nan])
npt.assert_equal(vals4, expected4)
# all(loc == 0) & (array scale with invalid entries)
vals5 = stats.norm.moment(order=2, loc=[0, 0, 0], scale=[5., -2, 100.])
expected5 = np.array([25., np.nan, 10000.])
npt.assert_equal(vals5, expected5)
# all( (loc == 0) & (scale < 0) )
vals6 = stats.norm.moment(order=2, loc=[0, 0, 0], scale=[-5., -2, -100.])
expected6 = np.array([np.nan, np.nan, np.nan])
npt.assert_equal(vals6, expected6)
# scalar args, loc, and scale
vals7 = stats.chi.moment(order=2, df=1, loc=0, scale=0)
expected7 = np.nan
npt.assert_equal(vals7, expected7)
assert isinstance(vals7, expected7.__class__)
# array args, scalar loc, and scalar scale
vals8 = stats.chi.moment(order=2, df=[1, 2, 3], loc=0, scale=0)
expected8 = np.array([np.nan, np.nan, np.nan])
npt.assert_equal(vals8, expected8)
# array args, array loc, and array scale
vals9 = stats.chi.moment(order=2, df=[1, 2, 3], loc=[1., 0., 2.],
scale=[1., -3., 0.])
expected9 = np.array([3.59576912, np.nan, np.nan])
npt.assert_allclose(vals9, expected9, rtol=1e-8)
# (n > 4), all(loc != 0), and all(scale != 0)
vals10 = stats.norm.moment(5, [1., 2.], [1., 2.])
expected10 = np.array([26., 832.])
npt.assert_allclose(vals10, expected10, rtol=1e-13)
# test broadcasting and more
a = [-1.1, 0, 1, 2.2, np.pi]
b = [-1.1, 0, 1, 2.2, np.pi]
loc = [-1.1, 0, np.sqrt(2)]
scale = [-2.1, 0, 1, 2.2, np.pi]
a = np.array(a).reshape((-1, 1, 1, 1))
b = np.array(b).reshape((-1, 1, 1))
loc = np.array(loc).reshape((-1, 1))
scale = np.array(scale)
vals11 = stats.beta.moment(order=2, a=a, b=b, loc=loc, scale=scale)
a, b, loc, scale = np.broadcast_arrays(a, b, loc, scale)
for i in np.ndenumerate(a):
with np.errstate(invalid='ignore', divide='ignore'):
i = i[0] # just get the index
# check against same function with scalar input
expected = stats.beta.moment(order=2, a=a[i], b=b[i],
loc=loc[i], scale=scale[i])
np.testing.assert_equal(vals11[i], expected)
def test_broadcasting_in_moments_gh12192_regression():
vals0 = stats.norm.moment(order=1, loc=np.array([1, 2, 3]), scale=[[1]])
expected0 = np.array([[1., 2., 3.]])
npt.assert_equal(vals0, expected0)
assert vals0.shape == expected0.shape
vals1 = stats.norm.moment(order=1, loc=np.array([[1], [2], [3]]),
scale=[1, 2, 3])
expected1 = np.array([[1., 1., 1.], [2., 2., 2.], [3., 3., 3.]])
npt.assert_equal(vals1, expected1)
assert vals1.shape == expected1.shape
vals2 = stats.chi.moment(order=1, df=[1., 2., 3.], loc=0., scale=1.)
expected2 = np.array([0.79788456, 1.25331414, 1.59576912])
npt.assert_allclose(vals2, expected2, rtol=1e-8)
assert vals2.shape == expected2.shape
vals3 = stats.chi.moment(order=1, df=[[1.], [2.], [3.]], loc=[0., 1., 2.],
scale=[-1., 0., 3.])
expected3 = np.array([[np.nan, np.nan, 4.39365368],
[np.nan, np.nan, 5.75994241],
[np.nan, np.nan, 6.78730736]])
npt.assert_allclose(vals3, expected3, rtol=1e-8)
assert vals3.shape == expected3.shape
def test_kappa3_array_gh13582():
# https://github.com/scipy/scipy/pull/15140#issuecomment-994958241
shapes = [0.5, 1.5, 2.5, 3.5, 4.5]
moments = 'mvsk'
res = np.array([[stats.kappa3.stats(shape, moments=moment)
for shape in shapes] for moment in moments])
res2 = np.array(stats.kappa3.stats(shapes, moments=moments))
npt.assert_allclose(res, res2)
@pytest.mark.xslow
def test_kappa4_array_gh13582():
h = np.array([-0.5, 2.5, 3.5, 4.5, -3])
k = np.array([-0.5, 1, -1.5, 0, 3.5])
moments = 'mvsk'
res = np.array([[stats.kappa4.stats(h[i], k[i], moments=moment)
for i in range(5)] for moment in moments])
res2 = np.array(stats.kappa4.stats(h, k, moments=moments))
npt.assert_allclose(res, res2)
# https://github.com/scipy/scipy/pull/15250#discussion_r775112913
h = np.array([-1, -1/4, -1/4, 1, -1, 0])
k = np.array([1, 1, 1/2, -1/3, -1, 0])
res = np.array([[stats.kappa4.stats(h[i], k[i], moments=moment)
for i in range(6)] for moment in moments])
res2 = np.array(stats.kappa4.stats(h, k, moments=moments))
npt.assert_allclose(res, res2)
# https://github.com/scipy/scipy/pull/15250#discussion_r775115021
h = np.array([-1, -0.5, 1])
k = np.array([-1, -0.5, 0, 1])[:, None]
res2 = np.array(stats.kappa4.stats(h, k, moments=moments))
assert res2.shape == (4, 4, 3)
def test_frozen_attributes():
# gh-14827 reported that all frozen distributions had both pmf and pdf
# attributes; continuous should have pdf and discrete should have pmf.
message = "'rv_continuous_frozen' object has no attribute"
with pytest.raises(AttributeError, match=message):
stats.norm().pmf
with pytest.raises(AttributeError, match=message):
stats.norm().logpmf
stats.norm.pmf = "herring"
frozen_norm = stats.norm()
assert isinstance(frozen_norm, rv_continuous_frozen)
delattr(stats.norm, 'pmf')
def test_skewnorm_pdf_gh16038():
rng = np.random.default_rng(0)
x, a = -np.inf, 0
npt.assert_equal(stats.skewnorm.pdf(x, a), stats.norm.pdf(x))
x, a = rng.random(size=(3, 3)), rng.random(size=(3, 3))
mask = rng.random(size=(3, 3)) < 0.5
a[mask] = 0
x_norm = x[mask]
res = stats.skewnorm.pdf(x, a)
npt.assert_equal(res[mask], stats.norm.pdf(x_norm))
npt.assert_equal(res[~mask], stats.skewnorm.pdf(x[~mask], a[~mask]))
# for scalar input, these functions should return scalar output
scalar_out = [['rvs', []], ['pdf', [0]], ['logpdf', [0]], ['cdf', [0]],
['logcdf', [0]], ['sf', [0]], ['logsf', [0]], ['ppf', [0]],
['isf', [0]], ['moment', [1]], ['entropy', []], ['expect', []],
['median', []], ['mean', []], ['std', []], ['var', []]]
scalars_out = [['interval', [0.95]], ['support', []], ['stats', ['mv']]]
@pytest.mark.parametrize('case', scalar_out + scalars_out)
def test_scalar_for_scalar(case):
# Some rv_continuous functions returned 0d array instead of NumPy scalar
# Guard against regression
method_name, args = case
method = getattr(stats.norm(), method_name)
res = method(*args)
if case in scalar_out:
assert isinstance(res, np.number)
else:
assert isinstance(res[0], np.number)
assert isinstance(res[1], np.number)
def test_scalar_for_scalar2():
# test methods that are not attributes of frozen distributions
res = stats.norm.fit([1, 2, 3])
assert isinstance(res[0], np.number)
assert isinstance(res[1], np.number)
res = stats.norm.fit_loc_scale([1, 2, 3])
assert isinstance(res[0], np.number)
assert isinstance(res[1], np.number)
res = stats.norm.nnlf((0, 1), [1, 2, 3])
assert isinstance(res, np.number)
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