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__)