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from __future__ import division, print_function, absolute_import
import numpy.testing as npt
import numpy as np
from scipy._lib.six import xrange
import pytest
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_edge_support,
check_named_args, check_random_state_property,
check_pickling, check_rvs_broadcast)
from scipy.stats._distr_params import distdiscrete
vals = ([1, 2, 3, 4], [0.1, 0.2, 0.3, 0.4])
distdiscrete += [[stats.rv_discrete(values=vals), ()]]
def cases_test_discrete_basic():
seen = set()
for distname, arg in distdiscrete:
yield distname, arg, distname not in seen
seen.add(distname)
@pytest.mark.parametrize('distname,arg,first_case', cases_test_discrete_basic())
def test_discrete_basic(distname, arg, first_case):
try:
distfn = getattr(stats, distname)
except TypeError:
distfn = distname
distname = 'sample distribution'
np.random.seed(9765456)
rvs = distfn.rvs(size=2000, *arg)
supp = np.unique(rvs)
m, v = distfn.stats(*arg)
check_cdf_ppf(distfn, arg, supp, distname + ' cdf_ppf')
check_pmf_cdf(distfn, arg, distname)
check_oth(distfn, arg, supp, distname + ' oth')
check_edge_support(distfn, arg)
alpha = 0.01
check_discrete_chisquare(distfn, arg, rvs, alpha,
distname + ' chisquare')
if first_case:
locscale_defaults = (0,)
meths = [distfn.pmf, distfn.logpmf, distfn.cdf, distfn.logcdf,
distfn.logsf]
# make sure arguments are within support
spec_k = {'randint': 11, 'hypergeom': 4, 'bernoulli': 0, }
k = spec_k.get(distname, 1)
check_named_args(distfn, k, arg, locscale_defaults, meths)
if distname != 'sample distribution':
check_scale_docstring(distfn)
check_random_state_property(distfn, arg)
check_pickling(distfn, arg)
# Entropy
check_entropy(distfn, arg, distname)
if distfn.__class__._entropy != stats.rv_discrete._entropy:
check_private_entropy(distfn, arg, stats.rv_discrete)
@pytest.mark.parametrize('distname,arg', distdiscrete)
def test_moments(distname, arg):
try:
distfn = getattr(stats, distname)
except TypeError:
distfn = distname
distname = 'sample distribution'
m, v, s, k = distfn.stats(*arg, moments='mvsk')
check_normalization(distfn, arg, distname)
# compare `stats` and `moment` methods
check_moment(distfn, arg, m, v, distname)
check_mean_expect(distfn, arg, m, distname)
check_var_expect(distfn, arg, m, v, distname)
check_skew_expect(distfn, arg, m, v, s, distname)
if distname not in ['zipf']:
check_kurt_expect(distfn, arg, m, v, k, distname)
# frozen distr moments
check_moment_frozen(distfn, arg, m, 1)
check_moment_frozen(distfn, arg, v+m*m, 2)
@pytest.mark.parametrize('dist,shape_args', distdiscrete)
def test_rvs_broadcast(dist, shape_args):
# 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 ['skellam']
try:
distfunc = getattr(stats, dist)
except TypeError:
distfunc = dist
dist = 'rv_discrete(values=(%r, %r))' % (dist.xk, dist.pk)
loc = np.zeros(2)
nargs = distfunc.numargs
allargs = []
bshape = []
# Generate shape parameter arguments...
for k in range(nargs):
shp = (k + 3,) + (1,)*(k + 1)
param_val = shape_args[k]
allargs.append(param_val*np.ones(shp, dtype=np.array(param_val).dtype))
bshape.insert(0, shp[0])
allargs.append(loc)
bshape.append(loc.size)
# 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, [np.int_])
def check_cdf_ppf(distfn, arg, supp, msg):
# cdf is a step function, and ppf(q) = min{k : cdf(k) >= q, k integer}
npt.assert_array_equal(distfn.ppf(distfn.cdf(supp, *arg), *arg),
supp, msg + '-roundtrip')
npt.assert_array_equal(distfn.ppf(distfn.cdf(supp, *arg) - 1e-8, *arg),
supp, msg + '-roundtrip')
if not hasattr(distfn, 'xk'):
supp1 = supp[supp < distfn.b]
npt.assert_array_equal(distfn.ppf(distfn.cdf(supp1, *arg) + 1e-8, *arg),
supp1 + distfn.inc, msg + ' ppf-cdf-next')
# -1e-8 could cause an error if pmf < 1e-8
def check_pmf_cdf(distfn, arg, distname):
if hasattr(distfn, 'xk'):
index = distfn.xk
else:
startind = int(distfn.ppf(0.01, *arg) - 1)
index = list(range(startind, startind + 10))
cdfs = distfn.cdf(index, *arg)
pmfs_cum = distfn.pmf(index, *arg).cumsum()
atol, rtol = 1e-10, 1e-10
if distname == 'skellam': # ncx2 accuracy
atol, rtol = 1e-5, 1e-5
npt.assert_allclose(cdfs - cdfs[0], pmfs_cum - pmfs_cum[0],
atol=atol, rtol=rtol)
def check_moment_frozen(distfn, arg, m, k):
npt.assert_allclose(distfn(*arg).moment(k), m,
atol=1e-10, rtol=1e-10)
def check_oth(distfn, arg, supp, msg):
# checking other methods of distfn
npt.assert_allclose(distfn.sf(supp, *arg), 1. - distfn.cdf(supp, *arg),
atol=1e-10, rtol=1e-10)
q = np.linspace(0.01, 0.99, 20)
npt.assert_allclose(distfn.isf(q, *arg), distfn.ppf(1. - q, *arg),
atol=1e-10, rtol=1e-10)
median_sf = distfn.isf(0.5, *arg)
npt.assert_(distfn.sf(median_sf - 1, *arg) > 0.5)
npt.assert_(distfn.cdf(median_sf + 1, *arg) > 0.5)
def check_discrete_chisquare(distfn, arg, rvs, alpha, msg):
"""Perform chisquare test for random sample of a discrete distribution
Parameters
----------
distname : string
name of distribution function
arg : sequence
parameters of distribution
alpha : float
significance level, threshold for p-value
Returns
-------
result : bool
0 if test passes, 1 if test fails
"""
wsupp = 0.05
# construct intervals with minimum mass `wsupp`.
# intervals are left-half-open as in a cdf difference
lo = int(max(distfn.a, -1000))
distsupport = xrange(lo, int(min(distfn.b, 1000)) + 1)
last = 0
distsupp = [lo]
distmass = []
for ii in distsupport:
current = distfn.cdf(ii, *arg)
if current - last >= wsupp - 1e-14:
distsupp.append(ii)
distmass.append(current - last)
last = current
if current > (1 - wsupp):
break
if distsupp[-1] < distfn.b:
distsupp.append(distfn.b)
distmass.append(1 - last)
distsupp = np.array(distsupp)
distmass = np.array(distmass)
# convert intervals to right-half-open as required by histogram
histsupp = distsupp + 1e-8
histsupp[0] = distfn.a
# find sample frequencies and perform chisquare test
freq, hsupp = np.histogram(rvs, histsupp)
chis, pval = stats.chisquare(np.array(freq), len(rvs)*distmass)
npt.assert_(pval > alpha,
'chisquare - test for %s at arg = %s with pval = %s' %
(msg, str(arg), str(pval)))
def check_scale_docstring(distfn):
if distfn.__doc__ is not None:
# Docstrings can be stripped if interpreter is run with -OO
npt.assert_('scale' not in distfn.__doc__)
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