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3641 lines
136 KiB
Python
3641 lines
136 KiB
Python
6 years ago
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""" Test functions for stats module
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"""
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from __future__ import division, print_function, absolute_import
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import warnings
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import re
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import sys
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import pickle
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import os
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from numpy.testing import (assert_equal, assert_array_equal,
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assert_almost_equal, assert_array_almost_equal,
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assert_allclose, assert_, assert_warns)
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import pytest
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from pytest import raises as assert_raises
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from scipy._lib._numpy_compat import suppress_warnings
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import numpy
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import numpy as np
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from numpy import typecodes, array
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from numpy.lib.recfunctions import rec_append_fields
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from scipy import special
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from scipy.integrate import IntegrationWarning
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import scipy.stats as stats
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from scipy.stats._distn_infrastructure import argsreduce
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import scipy.stats.distributions
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from scipy.special import xlogy
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from .test_continuous_basic import distcont
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# python -OO strips docstrings
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DOCSTRINGS_STRIPPED = sys.flags.optimize > 1
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# Generate test cases to test cdf and distribution consistency.
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# Note that this list does not include all distributions.
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dists = ['uniform', 'norm', 'lognorm', 'expon', 'beta',
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'powerlaw', 'bradford', 'burr', 'fisk', 'cauchy', 'halfcauchy',
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'foldcauchy', 'gamma', 'gengamma', 'loggamma',
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'alpha', 'anglit', 'arcsine', 'betaprime', 'dgamma', 'moyal',
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'exponnorm', 'exponweib', 'exponpow', 'frechet_l', 'frechet_r',
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'gilbrat', 'f', 'ncf', 'chi2', 'chi', 'nakagami', 'genpareto',
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'genextreme', 'genhalflogistic', 'pareto', 'lomax', 'halfnorm',
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'halflogistic', 'fatiguelife', 'foldnorm', 'ncx2', 't', 'nct',
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'weibull_min', 'weibull_max', 'dweibull', 'maxwell', 'rayleigh',
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'genlogistic', 'logistic', 'gumbel_l', 'gumbel_r', 'gompertz',
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'hypsecant', 'laplace', 'reciprocal', 'trapz', 'triang',
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'tukeylambda', 'vonmises', 'vonmises_line', 'pearson3', 'gennorm',
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'halfgennorm', 'rice', 'kappa4', 'kappa3', 'truncnorm', 'argus',
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'crystalball']
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def _assert_hasattr(a, b, msg=None):
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if msg is None:
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msg = '%s does not have attribute %s' % (a, b)
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assert_(hasattr(a, b), msg=msg)
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def test_api_regression():
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# https://github.com/scipy/scipy/issues/3802
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_assert_hasattr(scipy.stats.distributions, 'f_gen')
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# check function for test generator
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def check_distribution(dist, args, alpha):
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with suppress_warnings() as sup:
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# frechet_l and frechet_r are deprecated, so all their
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# methods generate DeprecationWarnings.
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sup.filter(category=DeprecationWarning, message=".*frechet_")
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D, pval = stats.kstest(dist, '', args=args, N=1000)
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if (pval < alpha):
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D, pval = stats.kstest(dist, '', args=args, N=1000)
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assert_(pval > alpha,
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msg="D = {}; pval = {}; alpha = {}; args = {}".format(
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D, pval, alpha, args))
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def cases_test_all_distributions():
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np.random.seed(1234)
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for dist in dists:
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distfunc = getattr(stats, dist)
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nargs = distfunc.numargs
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alpha = 0.01
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if dist == 'fatiguelife':
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alpha = 0.001
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if dist == 'trapz':
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args = tuple(np.sort(np.random.random(nargs)))
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elif dist == 'triang':
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args = tuple(np.random.random(nargs))
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elif dist == 'reciprocal' or dist == 'truncnorm':
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vals = np.random.random(nargs)
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vals[1] = vals[0] + 1.0
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args = tuple(vals)
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elif dist == 'vonmises':
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yield dist, (10,), alpha
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yield dist, (101,), alpha
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args = tuple(1.0 + np.random.random(nargs))
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else:
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args = tuple(1.0 + np.random.random(nargs))
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yield dist, args, alpha
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@pytest.mark.parametrize('dist,args,alpha', cases_test_all_distributions())
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def test_all_distributions(dist, args, alpha):
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check_distribution(dist, args, alpha)
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def check_vonmises_pdf_periodic(k, l, s, x):
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vm = stats.vonmises(k, loc=l, scale=s)
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assert_almost_equal(vm.pdf(x), vm.pdf(x % (2*numpy.pi*s)))
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def check_vonmises_cdf_periodic(k, l, s, x):
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vm = stats.vonmises(k, loc=l, scale=s)
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assert_almost_equal(vm.cdf(x) % 1, vm.cdf(x % (2*numpy.pi*s)) % 1)
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def test_vonmises_pdf_periodic():
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for k in [0.1, 1, 101]:
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for x in [0, 1, numpy.pi, 10, 100]:
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check_vonmises_pdf_periodic(k, 0, 1, x)
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check_vonmises_pdf_periodic(k, 1, 1, x)
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check_vonmises_pdf_periodic(k, 0, 10, x)
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check_vonmises_cdf_periodic(k, 0, 1, x)
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check_vonmises_cdf_periodic(k, 1, 1, x)
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check_vonmises_cdf_periodic(k, 0, 10, x)
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def test_vonmises_line_support():
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assert_equal(stats.vonmises_line.a, -np.pi)
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assert_equal(stats.vonmises_line.b, np.pi)
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def test_vonmises_numerical():
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vm = stats.vonmises(800)
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assert_almost_equal(vm.cdf(0), 0.5)
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@pytest.mark.parametrize('dist',
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['alpha', 'betaprime', 'burr', 'burr12',
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'fatiguelife', 'invgamma', 'invgauss', 'invweibull',
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'johnsonsb', 'levy', 'levy_l', 'lognorm', 'gilbrat',
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'powerlognorm', 'rayleigh', 'wald'])
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def test_support(dist):
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"""gh-6235"""
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dct = dict(distcont)
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args = dct[dist]
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dist = getattr(stats, dist)
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assert_almost_equal(dist.pdf(dist.a, *args), 0)
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assert_equal(dist.logpdf(dist.a, *args), -np.inf)
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assert_almost_equal(dist.pdf(dist.b, *args), 0)
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assert_equal(dist.logpdf(dist.b, *args), -np.inf)
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class TestRandInt(object):
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def setup_method(self):
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np.random.seed(1234)
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def test_rvs(self):
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vals = stats.randint.rvs(5, 30, size=100)
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assert_(numpy.all(vals < 30) & numpy.all(vals >= 5))
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assert_(len(vals) == 100)
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vals = stats.randint.rvs(5, 30, size=(2, 50))
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assert_(numpy.shape(vals) == (2, 50))
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assert_(vals.dtype.char in typecodes['AllInteger'])
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val = stats.randint.rvs(15, 46)
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assert_((val >= 15) & (val < 46))
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assert_(isinstance(val, numpy.ScalarType), msg=repr(type(val)))
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val = stats.randint(15, 46).rvs(3)
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assert_(val.dtype.char in typecodes['AllInteger'])
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def test_pdf(self):
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k = numpy.r_[0:36]
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out = numpy.where((k >= 5) & (k < 30), 1.0/(30-5), 0)
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vals = stats.randint.pmf(k, 5, 30)
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assert_array_almost_equal(vals, out)
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def test_cdf(self):
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x = np.linspace(0,36,100)
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k = numpy.floor(x)
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out = numpy.select([k >= 30, k >= 5], [1.0, (k-5.0+1)/(30-5.0)], 0)
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vals = stats.randint.cdf(x, 5, 30)
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assert_array_almost_equal(vals, out, decimal=12)
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class TestBinom(object):
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def setup_method(self):
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np.random.seed(1234)
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def test_rvs(self):
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vals = stats.binom.rvs(10, 0.75, size=(2, 50))
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assert_(numpy.all(vals >= 0) & numpy.all(vals <= 10))
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assert_(numpy.shape(vals) == (2, 50))
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assert_(vals.dtype.char in typecodes['AllInteger'])
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val = stats.binom.rvs(10, 0.75)
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assert_(isinstance(val, int))
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val = stats.binom(10, 0.75).rvs(3)
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assert_(isinstance(val, numpy.ndarray))
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assert_(val.dtype.char in typecodes['AllInteger'])
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def test_pmf(self):
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# regression test for Ticket #1842
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vals1 = stats.binom.pmf(100, 100, 1)
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vals2 = stats.binom.pmf(0, 100, 0)
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assert_allclose(vals1, 1.0, rtol=1e-15, atol=0)
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assert_allclose(vals2, 1.0, rtol=1e-15, atol=0)
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def test_entropy(self):
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# Basic entropy tests.
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b = stats.binom(2, 0.5)
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expected_p = np.array([0.25, 0.5, 0.25])
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expected_h = -sum(xlogy(expected_p, expected_p))
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h = b.entropy()
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assert_allclose(h, expected_h)
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b = stats.binom(2, 0.0)
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h = b.entropy()
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assert_equal(h, 0.0)
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b = stats.binom(2, 1.0)
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h = b.entropy()
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assert_equal(h, 0.0)
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def test_warns_p0(self):
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# no spurious warnigns are generated for p=0; gh-3817
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with warnings.catch_warnings():
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warnings.simplefilter("error", RuntimeWarning)
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assert_equal(stats.binom(n=2, p=0).mean(), 0)
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assert_equal(stats.binom(n=2, p=0).std(), 0)
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class TestBernoulli(object):
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def setup_method(self):
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np.random.seed(1234)
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def test_rvs(self):
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vals = stats.bernoulli.rvs(0.75, size=(2, 50))
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assert_(numpy.all(vals >= 0) & numpy.all(vals <= 1))
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assert_(numpy.shape(vals) == (2, 50))
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assert_(vals.dtype.char in typecodes['AllInteger'])
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val = stats.bernoulli.rvs(0.75)
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assert_(isinstance(val, int))
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val = stats.bernoulli(0.75).rvs(3)
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assert_(isinstance(val, numpy.ndarray))
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assert_(val.dtype.char in typecodes['AllInteger'])
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def test_entropy(self):
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# Simple tests of entropy.
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b = stats.bernoulli(0.25)
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expected_h = -0.25*np.log(0.25) - 0.75*np.log(0.75)
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h = b.entropy()
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assert_allclose(h, expected_h)
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b = stats.bernoulli(0.0)
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h = b.entropy()
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assert_equal(h, 0.0)
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b = stats.bernoulli(1.0)
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h = b.entropy()
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assert_equal(h, 0.0)
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class TestBradford(object):
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# gh-6216
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def test_cdf_ppf(self):
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c = 0.1
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x = np.logspace(-20, -4)
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q = stats.bradford.cdf(x, c)
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xx = stats.bradford.ppf(q, c)
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assert_allclose(x, xx)
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class TestNBinom(object):
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def setup_method(self):
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np.random.seed(1234)
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def test_rvs(self):
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vals = stats.nbinom.rvs(10, 0.75, size=(2, 50))
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assert_(numpy.all(vals >= 0))
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assert_(numpy.shape(vals) == (2, 50))
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assert_(vals.dtype.char in typecodes['AllInteger'])
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val = stats.nbinom.rvs(10, 0.75)
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assert_(isinstance(val, int))
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val = stats.nbinom(10, 0.75).rvs(3)
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assert_(isinstance(val, numpy.ndarray))
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assert_(val.dtype.char in typecodes['AllInteger'])
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def test_pmf(self):
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# regression test for ticket 1779
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assert_allclose(np.exp(stats.nbinom.logpmf(700, 721, 0.52)),
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stats.nbinom.pmf(700, 721, 0.52))
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# logpmf(0,1,1) shouldn't return nan (regression test for gh-4029)
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val = scipy.stats.nbinom.logpmf(0, 1, 1)
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assert_equal(val, 0)
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class TestNormInvGauss(object):
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def setup_method(self):
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np.random.seed(1234)
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def test_cdf_R(self):
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# test pdf and cdf vals against R
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# require("GeneralizedHyperbolic")
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# x_test <- c(-7, -5, 0, 8, 15)
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# r_cdf <- GeneralizedHyperbolic::pnig(x_test, mu = 0, a = 1, b = 0.5)
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# r_pdf <- GeneralizedHyperbolic::dnig(x_test, mu = 0, a = 1, b = 0.5)
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r_cdf = np.array([8.034920282e-07, 2.512671945e-05, 3.186661051e-01,
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9.988650664e-01, 9.999848769e-01])
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x_test = np.array([-7, -5, 0, 8, 15])
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vals_cdf = stats.norminvgauss.cdf(x_test, a=1, b=0.5)
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assert_allclose(vals_cdf, r_cdf, atol=1e-9)
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def test_pdf_R(self):
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# values from R as defined in test_cdf_R
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r_pdf = np.array([1.359600783e-06, 4.413878805e-05, 4.555014266e-01,
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7.450485342e-04, 8.917889931e-06])
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x_test = np.array([-7, -5, 0, 8, 15])
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vals_pdf = stats.norminvgauss.pdf(x_test, a=1, b=0.5)
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assert_allclose(vals_pdf, r_pdf, atol=1e-9)
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def test_stats(self):
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a, b = 1, 0.5
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|
|
gamma = np.sqrt(a**2 - b**2)
|
||
|
|
v_stats = (b / gamma, a**2 / gamma**3, 3.0 * b / (a * np.sqrt(gamma)),
|
||
|
|
3.0 * (1 + 4 * b**2 / a**2) / gamma)
|
||
|
|
assert_equal(v_stats, stats.norminvgauss.stats(a, b, moments='mvsk'))
|
||
|
|
|
||
|
|
def test_ppf(self):
|
||
|
|
a, b = 1, 0.5
|
||
|
|
x_test = np.array([0.001, 0.5, 0.999])
|
||
|
|
vals = stats.norminvgauss.ppf(x_test, a, b)
|
||
|
|
assert_allclose(x_test, stats.norminvgauss.cdf(vals, a, b))
|
||
|
|
|
||
|
|
|
||
|
|
class TestGeom(object):
|
||
|
|
def setup_method(self):
|
||
|
|
np.random.seed(1234)
|
||
|
|
|
||
|
|
def test_rvs(self):
|
||
|
|
vals = stats.geom.rvs(0.75, size=(2, 50))
|
||
|
|
assert_(numpy.all(vals >= 0))
|
||
|
|
assert_(numpy.shape(vals) == (2, 50))
|
||
|
|
assert_(vals.dtype.char in typecodes['AllInteger'])
|
||
|
|
val = stats.geom.rvs(0.75)
|
||
|
|
assert_(isinstance(val, int))
|
||
|
|
val = stats.geom(0.75).rvs(3)
|
||
|
|
assert_(isinstance(val, numpy.ndarray))
|
||
|
|
assert_(val.dtype.char in typecodes['AllInteger'])
|
||
|
|
|
||
|
|
def test_pmf(self):
|
||
|
|
vals = stats.geom.pmf([1, 2, 3], 0.5)
|
||
|
|
assert_array_almost_equal(vals, [0.5, 0.25, 0.125])
|
||
|
|
|
||
|
|
def test_logpmf(self):
|
||
|
|
# regression test for ticket 1793
|
||
|
|
vals1 = np.log(stats.geom.pmf([1, 2, 3], 0.5))
|
||
|
|
vals2 = stats.geom.logpmf([1, 2, 3], 0.5)
|
||
|
|
assert_allclose(vals1, vals2, rtol=1e-15, atol=0)
|
||
|
|
|
||
|
|
# regression test for gh-4028
|
||
|
|
val = stats.geom.logpmf(1, 1)
|
||
|
|
assert_equal(val, 0.0)
|
||
|
|
|
||
|
|
def test_cdf_sf(self):
|
||
|
|
vals = stats.geom.cdf([1, 2, 3], 0.5)
|
||
|
|
vals_sf = stats.geom.sf([1, 2, 3], 0.5)
|
||
|
|
expected = array([0.5, 0.75, 0.875])
|
||
|
|
assert_array_almost_equal(vals, expected)
|
||
|
|
assert_array_almost_equal(vals_sf, 1-expected)
|
||
|
|
|
||
|
|
def test_logcdf_logsf(self):
|
||
|
|
vals = stats.geom.logcdf([1, 2, 3], 0.5)
|
||
|
|
vals_sf = stats.geom.logsf([1, 2, 3], 0.5)
|
||
|
|
expected = array([0.5, 0.75, 0.875])
|
||
|
|
assert_array_almost_equal(vals, np.log(expected))
|
||
|
|
assert_array_almost_equal(vals_sf, np.log1p(-expected))
|
||
|
|
|
||
|
|
def test_ppf(self):
|
||
|
|
vals = stats.geom.ppf([0.5, 0.75, 0.875], 0.5)
|
||
|
|
expected = array([1.0, 2.0, 3.0])
|
||
|
|
assert_array_almost_equal(vals, expected)
|
||
|
|
|
||
|
|
def test_ppf_underflow(self):
|
||
|
|
# this should not underflow
|
||
|
|
assert_allclose(stats.geom.ppf(1e-20, 1e-20), 1.0, atol=1e-14)
|
||
|
|
|
||
|
|
|
||
|
|
class TestPlanck(object):
|
||
|
|
def setup_method(self):
|
||
|
|
np.random.seed(1234)
|
||
|
|
|
||
|
|
def test_sf(self):
|
||
|
|
vals = stats.planck.sf([1, 2, 3], 5.)
|
||
|
|
expected = array([4.5399929762484854e-05,
|
||
|
|
3.0590232050182579e-07,
|
||
|
|
2.0611536224385579e-09])
|
||
|
|
assert_array_almost_equal(vals, expected)
|
||
|
|
|
||
|
|
def test_logsf(self):
|
||
|
|
vals = stats.planck.logsf([1000., 2000., 3000.], 1000.)
|
||
|
|
expected = array([-1001000., -2001000., -3001000.])
|
||
|
|
assert_array_almost_equal(vals, expected)
|
||
|
|
|
||
|
|
|
||
|
|
class TestGennorm(object):
|
||
|
|
def test_laplace(self):
|
||
|
|
# test against Laplace (special case for beta=1)
|
||
|
|
points = [1, 2, 3]
|
||
|
|
pdf1 = stats.gennorm.pdf(points, 1)
|
||
|
|
pdf2 = stats.laplace.pdf(points)
|
||
|
|
assert_almost_equal(pdf1, pdf2)
|
||
|
|
|
||
|
|
def test_norm(self):
|
||
|
|
# test against normal (special case for beta=2)
|
||
|
|
points = [1, 2, 3]
|
||
|
|
pdf1 = stats.gennorm.pdf(points, 2)
|
||
|
|
pdf2 = stats.norm.pdf(points, scale=2**-.5)
|
||
|
|
assert_almost_equal(pdf1, pdf2)
|
||
|
|
|
||
|
|
|
||
|
|
class TestHalfgennorm(object):
|
||
|
|
def test_expon(self):
|
||
|
|
# test against exponential (special case for beta=1)
|
||
|
|
points = [1, 2, 3]
|
||
|
|
pdf1 = stats.halfgennorm.pdf(points, 1)
|
||
|
|
pdf2 = stats.expon.pdf(points)
|
||
|
|
assert_almost_equal(pdf1, pdf2)
|
||
|
|
|
||
|
|
def test_halfnorm(self):
|
||
|
|
# test against half normal (special case for beta=2)
|
||
|
|
points = [1, 2, 3]
|
||
|
|
pdf1 = stats.halfgennorm.pdf(points, 2)
|
||
|
|
pdf2 = stats.halfnorm.pdf(points, scale=2**-.5)
|
||
|
|
assert_almost_equal(pdf1, pdf2)
|
||
|
|
|
||
|
|
def test_gennorm(self):
|
||
|
|
# test against generalized normal
|
||
|
|
points = [1, 2, 3]
|
||
|
|
pdf1 = stats.halfgennorm.pdf(points, .497324)
|
||
|
|
pdf2 = stats.gennorm.pdf(points, .497324)
|
||
|
|
assert_almost_equal(pdf1, 2*pdf2)
|
||
|
|
|
||
|
|
|
||
|
|
class TestTruncnorm(object):
|
||
|
|
def setup_method(self):
|
||
|
|
np.random.seed(1234)
|
||
|
|
|
||
|
|
def test_ppf_ticket1131(self):
|
||
|
|
vals = stats.truncnorm.ppf([-0.5, 0, 1e-4, 0.5, 1-1e-4, 1, 2], -1., 1.,
|
||
|
|
loc=[3]*7, scale=2)
|
||
|
|
expected = np.array([np.nan, 1, 1.00056419, 3, 4.99943581, 5, np.nan])
|
||
|
|
assert_array_almost_equal(vals, expected)
|
||
|
|
|
||
|
|
def test_isf_ticket1131(self):
|
||
|
|
vals = stats.truncnorm.isf([-0.5, 0, 1e-4, 0.5, 1-1e-4, 1, 2], -1., 1.,
|
||
|
|
loc=[3]*7, scale=2)
|
||
|
|
expected = np.array([np.nan, 5, 4.99943581, 3, 1.00056419, 1, np.nan])
|
||
|
|
assert_array_almost_equal(vals, expected)
|
||
|
|
|
||
|
|
def test_gh_2477_small_values(self):
|
||
|
|
# Check a case that worked in the original issue.
|
||
|
|
low, high = -11, -10
|
||
|
|
x = stats.truncnorm.rvs(low, high, 0, 1, size=10)
|
||
|
|
assert_(low < x.min() < x.max() < high)
|
||
|
|
# Check a case that failed in the original issue.
|
||
|
|
low, high = 10, 11
|
||
|
|
x = stats.truncnorm.rvs(low, high, 0, 1, size=10)
|
||
|
|
assert_(low < x.min() < x.max() < high)
|
||
|
|
|
||
|
|
@pytest.mark.xfail(reason="truncnorm rvs is know to fail at extreme tails")
|
||
|
|
def test_gh_2477_large_values(self):
|
||
|
|
# Check a case that fails because of extreme tailness.
|
||
|
|
low, high = 100, 101
|
||
|
|
with np.errstate(divide='ignore'):
|
||
|
|
x = stats.truncnorm.rvs(low, high, 0, 1, size=10)
|
||
|
|
assert_(low < x.min() < x.max() < high)
|
||
|
|
|
||
|
|
def test_gh_1489_trac_962_rvs(self):
|
||
|
|
# Check the original example.
|
||
|
|
low, high = 10, 15
|
||
|
|
x = stats.truncnorm.rvs(low, high, 0, 1, size=10)
|
||
|
|
assert_(low < x.min() < x.max() < high)
|
||
|
|
|
||
|
|
|
||
|
|
class TestHypergeom(object):
|
||
|
|
def setup_method(self):
|
||
|
|
np.random.seed(1234)
|
||
|
|
|
||
|
|
def test_rvs(self):
|
||
|
|
vals = stats.hypergeom.rvs(20, 10, 3, size=(2, 50))
|
||
|
|
assert_(numpy.all(vals >= 0) &
|
||
|
|
numpy.all(vals <= 3))
|
||
|
|
assert_(numpy.shape(vals) == (2, 50))
|
||
|
|
assert_(vals.dtype.char in typecodes['AllInteger'])
|
||
|
|
val = stats.hypergeom.rvs(20, 3, 10)
|
||
|
|
assert_(isinstance(val, int))
|
||
|
|
val = stats.hypergeom(20, 3, 10).rvs(3)
|
||
|
|
assert_(isinstance(val, numpy.ndarray))
|
||
|
|
assert_(val.dtype.char in typecodes['AllInteger'])
|
||
|
|
|
||
|
|
def test_precision(self):
|
||
|
|
# comparison number from mpmath
|
||
|
|
M = 2500
|
||
|
|
n = 50
|
||
|
|
N = 500
|
||
|
|
tot = M
|
||
|
|
good = n
|
||
|
|
hgpmf = stats.hypergeom.pmf(2, tot, good, N)
|
||
|
|
assert_almost_equal(hgpmf, 0.0010114963068932233, 11)
|
||
|
|
|
||
|
|
def test_args(self):
|
||
|
|
# test correct output for corner cases of arguments
|
||
|
|
# see gh-2325
|
||
|
|
assert_almost_equal(stats.hypergeom.pmf(0, 2, 1, 0), 1.0, 11)
|
||
|
|
assert_almost_equal(stats.hypergeom.pmf(1, 2, 1, 0), 0.0, 11)
|
||
|
|
|
||
|
|
assert_almost_equal(stats.hypergeom.pmf(0, 2, 0, 2), 1.0, 11)
|
||
|
|
assert_almost_equal(stats.hypergeom.pmf(1, 2, 1, 0), 0.0, 11)
|
||
|
|
|
||
|
|
def test_cdf_above_one(self):
|
||
|
|
# for some values of parameters, hypergeom cdf was >1, see gh-2238
|
||
|
|
assert_(0 <= stats.hypergeom.cdf(30, 13397950, 4363, 12390) <= 1.0)
|
||
|
|
|
||
|
|
def test_precision2(self):
|
||
|
|
# Test hypergeom precision for large numbers. See #1218.
|
||
|
|
# Results compared with those from R.
|
||
|
|
oranges = 9.9e4
|
||
|
|
pears = 1.1e5
|
||
|
|
fruits_eaten = np.array([3, 3.8, 3.9, 4, 4.1, 4.2, 5]) * 1e4
|
||
|
|
quantile = 2e4
|
||
|
|
res = []
|
||
|
|
for eaten in fruits_eaten:
|
||
|
|
res.append(stats.hypergeom.sf(quantile, oranges + pears, oranges,
|
||
|
|
eaten))
|
||
|
|
expected = np.array([0, 1.904153e-114, 2.752693e-66, 4.931217e-32,
|
||
|
|
8.265601e-11, 0.1237904, 1])
|
||
|
|
assert_allclose(res, expected, atol=0, rtol=5e-7)
|
||
|
|
|
||
|
|
# Test with array_like first argument
|
||
|
|
quantiles = [1.9e4, 2e4, 2.1e4, 2.15e4]
|
||
|
|
res2 = stats.hypergeom.sf(quantiles, oranges + pears, oranges, 4.2e4)
|
||
|
|
expected2 = [1, 0.1237904, 6.511452e-34, 3.277667e-69]
|
||
|
|
assert_allclose(res2, expected2, atol=0, rtol=5e-7)
|
||
|
|
|
||
|
|
def test_entropy(self):
|
||
|
|
# Simple tests of entropy.
|
||
|
|
hg = stats.hypergeom(4, 1, 1)
|
||
|
|
h = hg.entropy()
|
||
|
|
expected_p = np.array([0.75, 0.25])
|
||
|
|
expected_h = -np.sum(xlogy(expected_p, expected_p))
|
||
|
|
assert_allclose(h, expected_h)
|
||
|
|
|
||
|
|
hg = stats.hypergeom(1, 1, 1)
|
||
|
|
h = hg.entropy()
|
||
|
|
assert_equal(h, 0.0)
|
||
|
|
|
||
|
|
def test_logsf(self):
|
||
|
|
# Test logsf for very large numbers. See issue #4982
|
||
|
|
# Results compare with those from R (v3.2.0):
|
||
|
|
# phyper(k, n, M-n, N, lower.tail=FALSE, log.p=TRUE)
|
||
|
|
# -2239.771
|
||
|
|
|
||
|
|
k = 1e4
|
||
|
|
M = 1e7
|
||
|
|
n = 1e6
|
||
|
|
N = 5e4
|
||
|
|
|
||
|
|
result = stats.hypergeom.logsf(k, M, n, N)
|
||
|
|
exspected = -2239.771 # From R
|
||
|
|
assert_almost_equal(result, exspected, decimal=3)
|
||
|
|
|
||
|
|
|
||
|
|
class TestLoggamma(object):
|
||
|
|
|
||
|
|
def test_stats(self):
|
||
|
|
# The following precomputed values are from the table in section 2.2
|
||
|
|
# of "A Statistical Study of Log-Gamma Distribution", by Ping Shing
|
||
|
|
# Chan (thesis, McMaster University, 1993).
|
||
|
|
table = np.array([
|
||
|
|
# c, mean, var, skew, exc. kurt.
|
||
|
|
0.5, -1.9635, 4.9348, -1.5351, 4.0000,
|
||
|
|
1.0, -0.5772, 1.6449, -1.1395, 2.4000,
|
||
|
|
12.0, 2.4427, 0.0869, -0.2946, 0.1735,
|
||
|
|
]).reshape(-1, 5)
|
||
|
|
for c, mean, var, skew, kurt in table:
|
||
|
|
computed = stats.loggamma.stats(c, moments='msvk')
|
||
|
|
assert_array_almost_equal(computed, [mean, var, skew, kurt],
|
||
|
|
decimal=4)
|
||
|
|
|
||
|
|
|
||
|
|
class TestLogistic(object):
|
||
|
|
# gh-6226
|
||
|
|
def test_cdf_ppf(self):
|
||
|
|
x = np.linspace(-20, 20)
|
||
|
|
y = stats.logistic.cdf(x)
|
||
|
|
xx = stats.logistic.ppf(y)
|
||
|
|
assert_allclose(x, xx)
|
||
|
|
|
||
|
|
def test_sf_isf(self):
|
||
|
|
x = np.linspace(-20, 20)
|
||
|
|
y = stats.logistic.sf(x)
|
||
|
|
xx = stats.logistic.isf(y)
|
||
|
|
assert_allclose(x, xx)
|
||
|
|
|
||
|
|
def test_extreme_values(self):
|
||
|
|
# p is chosen so that 1 - (1 - p) == p in double precision
|
||
|
|
p = 9.992007221626409e-16
|
||
|
|
desired = 34.53957599234088
|
||
|
|
assert_allclose(stats.logistic.ppf(1 - p), desired)
|
||
|
|
assert_allclose(stats.logistic.isf(p), desired)
|
||
|
|
|
||
|
|
|
||
|
|
class TestLogser(object):
|
||
|
|
def setup_method(self):
|
||
|
|
np.random.seed(1234)
|
||
|
|
|
||
|
|
def test_rvs(self):
|
||
|
|
vals = stats.logser.rvs(0.75, size=(2, 50))
|
||
|
|
assert_(numpy.all(vals >= 1))
|
||
|
|
assert_(numpy.shape(vals) == (2, 50))
|
||
|
|
assert_(vals.dtype.char in typecodes['AllInteger'])
|
||
|
|
val = stats.logser.rvs(0.75)
|
||
|
|
assert_(isinstance(val, int))
|
||
|
|
val = stats.logser(0.75).rvs(3)
|
||
|
|
assert_(isinstance(val, numpy.ndarray))
|
||
|
|
assert_(val.dtype.char in typecodes['AllInteger'])
|
||
|
|
|
||
|
|
def test_pmf_small_p(self):
|
||
|
|
m = stats.logser.pmf(4, 1e-20)
|
||
|
|
# The expected value was computed using mpmath:
|
||
|
|
# >>> import mpmath
|
||
|
|
# >>> mpmath.mp.dps = 64
|
||
|
|
# >>> k = 4
|
||
|
|
# >>> p = mpmath.mpf('1e-20')
|
||
|
|
# >>> float(-(p**k)/k/mpmath.log(1-p))
|
||
|
|
# 2.5e-61
|
||
|
|
# It is also clear from noticing that for very small p,
|
||
|
|
# log(1-p) is approximately -p, and the formula becomes
|
||
|
|
# p**(k-1) / k
|
||
|
|
assert_allclose(m, 2.5e-61)
|
||
|
|
|
||
|
|
def test_mean_small_p(self):
|
||
|
|
m = stats.logser.mean(1e-8)
|
||
|
|
# The expected mean was computed using mpmath:
|
||
|
|
# >>> import mpmath
|
||
|
|
# >>> mpmath.dps = 60
|
||
|
|
# >>> p = mpmath.mpf('1e-8')
|
||
|
|
# >>> float(-p / ((1 - p)*mpmath.log(1 - p)))
|
||
|
|
# 1.000000005
|
||
|
|
assert_allclose(m, 1.000000005)
|
||
|
|
|
||
|
|
|
||
|
|
class TestPareto(object):
|
||
|
|
def test_stats(self):
|
||
|
|
# Check the stats() method with some simple values. Also check
|
||
|
|
# that the calculations do not trigger RuntimeWarnings.
|
||
|
|
with warnings.catch_warnings():
|
||
|
|
warnings.simplefilter("error", RuntimeWarning)
|
||
|
|
|
||
|
|
m, v, s, k = stats.pareto.stats(0.5, moments='mvsk')
|
||
|
|
assert_equal(m, np.inf)
|
||
|
|
assert_equal(v, np.inf)
|
||
|
|
assert_equal(s, np.nan)
|
||
|
|
assert_equal(k, np.nan)
|
||
|
|
|
||
|
|
m, v, s, k = stats.pareto.stats(1.0, moments='mvsk')
|
||
|
|
assert_equal(m, np.inf)
|
||
|
|
assert_equal(v, np.inf)
|
||
|
|
assert_equal(s, np.nan)
|
||
|
|
assert_equal(k, np.nan)
|
||
|
|
|
||
|
|
m, v, s, k = stats.pareto.stats(1.5, moments='mvsk')
|
||
|
|
assert_equal(m, 3.0)
|
||
|
|
assert_equal(v, np.inf)
|
||
|
|
assert_equal(s, np.nan)
|
||
|
|
assert_equal(k, np.nan)
|
||
|
|
|
||
|
|
m, v, s, k = stats.pareto.stats(2.0, moments='mvsk')
|
||
|
|
assert_equal(m, 2.0)
|
||
|
|
assert_equal(v, np.inf)
|
||
|
|
assert_equal(s, np.nan)
|
||
|
|
assert_equal(k, np.nan)
|
||
|
|
|
||
|
|
m, v, s, k = stats.pareto.stats(2.5, moments='mvsk')
|
||
|
|
assert_allclose(m, 2.5 / 1.5)
|
||
|
|
assert_allclose(v, 2.5 / (1.5*1.5*0.5))
|
||
|
|
assert_equal(s, np.nan)
|
||
|
|
assert_equal(k, np.nan)
|
||
|
|
|
||
|
|
m, v, s, k = stats.pareto.stats(3.0, moments='mvsk')
|
||
|
|
assert_allclose(m, 1.5)
|
||
|
|
assert_allclose(v, 0.75)
|
||
|
|
assert_equal(s, np.nan)
|
||
|
|
assert_equal(k, np.nan)
|
||
|
|
|
||
|
|
m, v, s, k = stats.pareto.stats(3.5, moments='mvsk')
|
||
|
|
assert_allclose(m, 3.5 / 2.5)
|
||
|
|
assert_allclose(v, 3.5 / (2.5*2.5*1.5))
|
||
|
|
assert_allclose(s, (2*4.5/0.5)*np.sqrt(1.5/3.5))
|
||
|
|
assert_equal(k, np.nan)
|
||
|
|
|
||
|
|
m, v, s, k = stats.pareto.stats(4.0, moments='mvsk')
|
||
|
|
assert_allclose(m, 4.0 / 3.0)
|
||
|
|
assert_allclose(v, 4.0 / 18.0)
|
||
|
|
assert_allclose(s, 2*(1+4.0)/(4.0-3) * np.sqrt((4.0-2)/4.0))
|
||
|
|
assert_equal(k, np.nan)
|
||
|
|
|
||
|
|
m, v, s, k = stats.pareto.stats(4.5, moments='mvsk')
|
||
|
|
assert_allclose(m, 4.5 / 3.5)
|
||
|
|
assert_allclose(v, 4.5 / (3.5*3.5*2.5))
|
||
|
|
assert_allclose(s, (2*5.5/1.5) * np.sqrt(2.5/4.5))
|
||
|
|
assert_allclose(k, 6*(4.5**3 + 4.5**2 - 6*4.5 - 2)/(4.5*1.5*0.5))
|
||
|
|
|
||
|
|
def test_sf(self):
|
||
|
|
x = 1e9
|
||
|
|
b = 2
|
||
|
|
scale = 1.5
|
||
|
|
p = stats.pareto.sf(x, b, loc=0, scale=scale)
|
||
|
|
expected = (scale/x)**b # 2.25e-18
|
||
|
|
assert_allclose(p, expected)
|
||
|
|
|
||
|
|
|
||
|
|
class TestGenpareto(object):
|
||
|
|
def test_ab(self):
|
||
|
|
# c >= 0: a, b = [0, inf]
|
||
|
|
for c in [1., 0.]:
|
||
|
|
c = np.asarray(c)
|
||
|
|
stats.genpareto._argcheck(c) # ugh
|
||
|
|
assert_equal(stats.genpareto.a, 0.)
|
||
|
|
assert_(np.isposinf(stats.genpareto.b))
|
||
|
|
|
||
|
|
# c < 0: a=0, b=1/|c|
|
||
|
|
c = np.asarray(-2.)
|
||
|
|
stats.genpareto._argcheck(c)
|
||
|
|
assert_allclose([stats.genpareto.a, stats.genpareto.b], [0., 0.5])
|
||
|
|
|
||
|
|
def test_c0(self):
|
||
|
|
# with c=0, genpareto reduces to the exponential distribution
|
||
|
|
rv = stats.genpareto(c=0.)
|
||
|
|
x = np.linspace(0, 10., 30)
|
||
|
|
assert_allclose(rv.pdf(x), stats.expon.pdf(x))
|
||
|
|
assert_allclose(rv.cdf(x), stats.expon.cdf(x))
|
||
|
|
assert_allclose(rv.sf(x), stats.expon.sf(x))
|
||
|
|
|
||
|
|
q = np.linspace(0., 1., 10)
|
||
|
|
assert_allclose(rv.ppf(q), stats.expon.ppf(q))
|
||
|
|
|
||
|
|
def test_cm1(self):
|
||
|
|
# with c=-1, genpareto reduces to the uniform distr on [0, 1]
|
||
|
|
rv = stats.genpareto(c=-1.)
|
||
|
|
x = np.linspace(0, 10., 30)
|
||
|
|
assert_allclose(rv.pdf(x), stats.uniform.pdf(x))
|
||
|
|
assert_allclose(rv.cdf(x), stats.uniform.cdf(x))
|
||
|
|
assert_allclose(rv.sf(x), stats.uniform.sf(x))
|
||
|
|
|
||
|
|
q = np.linspace(0., 1., 10)
|
||
|
|
assert_allclose(rv.ppf(q), stats.uniform.ppf(q))
|
||
|
|
|
||
|
|
# logpdf(1., c=-1) should be zero
|
||
|
|
assert_allclose(rv.logpdf(1), 0)
|
||
|
|
|
||
|
|
def test_x_inf(self):
|
||
|
|
# make sure x=inf is handled gracefully
|
||
|
|
rv = stats.genpareto(c=0.1)
|
||
|
|
assert_allclose([rv.pdf(np.inf), rv.cdf(np.inf)], [0., 1.])
|
||
|
|
assert_(np.isneginf(rv.logpdf(np.inf)))
|
||
|
|
|
||
|
|
rv = stats.genpareto(c=0.)
|
||
|
|
assert_allclose([rv.pdf(np.inf), rv.cdf(np.inf)], [0., 1.])
|
||
|
|
assert_(np.isneginf(rv.logpdf(np.inf)))
|
||
|
|
|
||
|
|
rv = stats.genpareto(c=-1.)
|
||
|
|
assert_allclose([rv.pdf(np.inf), rv.cdf(np.inf)], [0., 1.])
|
||
|
|
assert_(np.isneginf(rv.logpdf(np.inf)))
|
||
|
|
|
||
|
|
def test_c_continuity(self):
|
||
|
|
# pdf is continuous at c=0, -1
|
||
|
|
x = np.linspace(0, 10, 30)
|
||
|
|
for c in [0, -1]:
|
||
|
|
pdf0 = stats.genpareto.pdf(x, c)
|
||
|
|
for dc in [1e-14, -1e-14]:
|
||
|
|
pdfc = stats.genpareto.pdf(x, c + dc)
|
||
|
|
assert_allclose(pdf0, pdfc, atol=1e-12)
|
||
|
|
|
||
|
|
cdf0 = stats.genpareto.cdf(x, c)
|
||
|
|
for dc in [1e-14, 1e-14]:
|
||
|
|
cdfc = stats.genpareto.cdf(x, c + dc)
|
||
|
|
assert_allclose(cdf0, cdfc, atol=1e-12)
|
||
|
|
|
||
|
|
def test_c_continuity_ppf(self):
|
||
|
|
q = np.r_[np.logspace(1e-12, 0.01, base=0.1),
|
||
|
|
np.linspace(0.01, 1, 30, endpoint=False),
|
||
|
|
1. - np.logspace(1e-12, 0.01, base=0.1)]
|
||
|
|
for c in [0., -1.]:
|
||
|
|
ppf0 = stats.genpareto.ppf(q, c)
|
||
|
|
for dc in [1e-14, -1e-14]:
|
||
|
|
ppfc = stats.genpareto.ppf(q, c + dc)
|
||
|
|
assert_allclose(ppf0, ppfc, atol=1e-12)
|
||
|
|
|
||
|
|
def test_c_continuity_isf(self):
|
||
|
|
q = np.r_[np.logspace(1e-12, 0.01, base=0.1),
|
||
|
|
np.linspace(0.01, 1, 30, endpoint=False),
|
||
|
|
1. - np.logspace(1e-12, 0.01, base=0.1)]
|
||
|
|
for c in [0., -1.]:
|
||
|
|
isf0 = stats.genpareto.isf(q, c)
|
||
|
|
for dc in [1e-14, -1e-14]:
|
||
|
|
isfc = stats.genpareto.isf(q, c + dc)
|
||
|
|
assert_allclose(isf0, isfc, atol=1e-12)
|
||
|
|
|
||
|
|
def test_cdf_ppf_roundtrip(self):
|
||
|
|
# this should pass with machine precision. hat tip @pbrod
|
||
|
|
q = np.r_[np.logspace(1e-12, 0.01, base=0.1),
|
||
|
|
np.linspace(0.01, 1, 30, endpoint=False),
|
||
|
|
1. - np.logspace(1e-12, 0.01, base=0.1)]
|
||
|
|
for c in [1e-8, -1e-18, 1e-15, -1e-15]:
|
||
|
|
assert_allclose(stats.genpareto.cdf(stats.genpareto.ppf(q, c), c),
|
||
|
|
q, atol=1e-15)
|
||
|
|
|
||
|
|
def test_logsf(self):
|
||
|
|
logp = stats.genpareto.logsf(1e10, .01, 0, 1)
|
||
|
|
assert_allclose(logp, -1842.0680753952365)
|
||
|
|
|
||
|
|
|
||
|
|
class TestPearson3(object):
|
||
|
|
def setup_method(self):
|
||
|
|
np.random.seed(1234)
|
||
|
|
|
||
|
|
def test_rvs(self):
|
||
|
|
vals = stats.pearson3.rvs(0.1, size=(2, 50))
|
||
|
|
assert_(numpy.shape(vals) == (2, 50))
|
||
|
|
assert_(vals.dtype.char in typecodes['AllFloat'])
|
||
|
|
val = stats.pearson3.rvs(0.5)
|
||
|
|
assert_(isinstance(val, float))
|
||
|
|
val = stats.pearson3(0.5).rvs(3)
|
||
|
|
assert_(isinstance(val, numpy.ndarray))
|
||
|
|
assert_(val.dtype.char in typecodes['AllFloat'])
|
||
|
|
assert_(len(val) == 3)
|
||
|
|
|
||
|
|
def test_pdf(self):
|
||
|
|
vals = stats.pearson3.pdf(2, [0.0, 0.1, 0.2])
|
||
|
|
assert_allclose(vals, np.array([0.05399097, 0.05555481, 0.05670246]),
|
||
|
|
atol=1e-6)
|
||
|
|
vals = stats.pearson3.pdf(-3, 0.1)
|
||
|
|
assert_allclose(vals, np.array([0.00313791]), atol=1e-6)
|
||
|
|
vals = stats.pearson3.pdf([-3, -2, -1, 0, 1], 0.1)
|
||
|
|
assert_allclose(vals, np.array([0.00313791, 0.05192304, 0.25028092,
|
||
|
|
0.39885918, 0.23413173]), atol=1e-6)
|
||
|
|
|
||
|
|
def test_cdf(self):
|
||
|
|
vals = stats.pearson3.cdf(2, [0.0, 0.1, 0.2])
|
||
|
|
assert_allclose(vals, np.array([0.97724987, 0.97462004, 0.97213626]),
|
||
|
|
atol=1e-6)
|
||
|
|
vals = stats.pearson3.cdf(-3, 0.1)
|
||
|
|
assert_allclose(vals, [0.00082256], atol=1e-6)
|
||
|
|
vals = stats.pearson3.cdf([-3, -2, -1, 0, 1], 0.1)
|
||
|
|
assert_allclose(vals, [8.22563821e-04, 1.99860448e-02, 1.58550710e-01,
|
||
|
|
5.06649130e-01, 8.41442111e-01], atol=1e-6)
|
||
|
|
|
||
|
|
|
||
|
|
class TestKappa4(object):
|
||
|
|
def test_cdf_genpareto(self):
|
||
|
|
# h = 1 and k != 0 is generalized Pareto
|
||
|
|
x = [0.0, 0.1, 0.2, 0.5]
|
||
|
|
h = 1.0
|
||
|
|
for k in [-1.9, -1.0, -0.5, -0.2, -0.1, 0.1, 0.2, 0.5, 1.0,
|
||
|
|
1.9]:
|
||
|
|
vals = stats.kappa4.cdf(x, h, k)
|
||
|
|
# shape parameter is opposite what is expected
|
||
|
|
vals_comp = stats.genpareto.cdf(x, -k)
|
||
|
|
assert_allclose(vals, vals_comp)
|
||
|
|
|
||
|
|
def test_cdf_genextreme(self):
|
||
|
|
# h = 0 and k != 0 is generalized extreme value
|
||
|
|
x = np.linspace(-5, 5, 10)
|
||
|
|
h = 0.0
|
||
|
|
k = np.linspace(-3, 3, 10)
|
||
|
|
vals = stats.kappa4.cdf(x, h, k)
|
||
|
|
vals_comp = stats.genextreme.cdf(x, k)
|
||
|
|
assert_allclose(vals, vals_comp)
|
||
|
|
|
||
|
|
def test_cdf_expon(self):
|
||
|
|
# h = 1 and k = 0 is exponential
|
||
|
|
x = np.linspace(0, 10, 10)
|
||
|
|
h = 1.0
|
||
|
|
k = 0.0
|
||
|
|
vals = stats.kappa4.cdf(x, h, k)
|
||
|
|
vals_comp = stats.expon.cdf(x)
|
||
|
|
assert_allclose(vals, vals_comp)
|
||
|
|
|
||
|
|
def test_cdf_gumbel_r(self):
|
||
|
|
# h = 0 and k = 0 is gumbel_r
|
||
|
|
x = np.linspace(-5, 5, 10)
|
||
|
|
h = 0.0
|
||
|
|
k = 0.0
|
||
|
|
vals = stats.kappa4.cdf(x, h, k)
|
||
|
|
vals_comp = stats.gumbel_r.cdf(x)
|
||
|
|
assert_allclose(vals, vals_comp)
|
||
|
|
|
||
|
|
def test_cdf_logistic(self):
|
||
|
|
# h = -1 and k = 0 is logistic
|
||
|
|
x = np.linspace(-5, 5, 10)
|
||
|
|
h = -1.0
|
||
|
|
k = 0.0
|
||
|
|
vals = stats.kappa4.cdf(x, h, k)
|
||
|
|
vals_comp = stats.logistic.cdf(x)
|
||
|
|
assert_allclose(vals, vals_comp)
|
||
|
|
|
||
|
|
def test_cdf_uniform(self):
|
||
|
|
# h = 1 and k = 1 is uniform
|
||
|
|
x = np.linspace(-5, 5, 10)
|
||
|
|
h = 1.0
|
||
|
|
k = 1.0
|
||
|
|
vals = stats.kappa4.cdf(x, h, k)
|
||
|
|
vals_comp = stats.uniform.cdf(x)
|
||
|
|
assert_allclose(vals, vals_comp)
|
||
|
|
|
||
|
|
def test_integers_ctor(self):
|
||
|
|
# regression test for gh-7416: _argcheck fails for integer h and k
|
||
|
|
# in numpy 1.12
|
||
|
|
stats.kappa4(1, 2)
|
||
|
|
|
||
|
|
|
||
|
|
class TestPoisson(object):
|
||
|
|
def setup_method(self):
|
||
|
|
np.random.seed(1234)
|
||
|
|
|
||
|
|
def test_pmf_basic(self):
|
||
|
|
# Basic case
|
||
|
|
ln2 = np.log(2)
|
||
|
|
vals = stats.poisson.pmf([0, 1, 2], ln2)
|
||
|
|
expected = [0.5, ln2/2, ln2**2/4]
|
||
|
|
assert_allclose(vals, expected)
|
||
|
|
|
||
|
|
def test_mu0(self):
|
||
|
|
# Edge case: mu=0
|
||
|
|
vals = stats.poisson.pmf([0, 1, 2], 0)
|
||
|
|
expected = [1, 0, 0]
|
||
|
|
assert_array_equal(vals, expected)
|
||
|
|
|
||
|
|
interval = stats.poisson.interval(0.95, 0)
|
||
|
|
assert_equal(interval, (0, 0))
|
||
|
|
|
||
|
|
def test_rvs(self):
|
||
|
|
vals = stats.poisson.rvs(0.5, size=(2, 50))
|
||
|
|
assert_(numpy.all(vals >= 0))
|
||
|
|
assert_(numpy.shape(vals) == (2, 50))
|
||
|
|
assert_(vals.dtype.char in typecodes['AllInteger'])
|
||
|
|
val = stats.poisson.rvs(0.5)
|
||
|
|
assert_(isinstance(val, int))
|
||
|
|
val = stats.poisson(0.5).rvs(3)
|
||
|
|
assert_(isinstance(val, numpy.ndarray))
|
||
|
|
assert_(val.dtype.char in typecodes['AllInteger'])
|
||
|
|
|
||
|
|
def test_stats(self):
|
||
|
|
mu = 16.0
|
||
|
|
result = stats.poisson.stats(mu, moments='mvsk')
|
||
|
|
assert_allclose(result, [mu, mu, np.sqrt(1.0/mu), 1.0/mu])
|
||
|
|
|
||
|
|
mu = np.array([0.0, 1.0, 2.0])
|
||
|
|
result = stats.poisson.stats(mu, moments='mvsk')
|
||
|
|
expected = (mu, mu, [np.inf, 1, 1/np.sqrt(2)], [np.inf, 1, 0.5])
|
||
|
|
assert_allclose(result, expected)
|
||
|
|
|
||
|
|
|
||
|
|
class TestZipf(object):
|
||
|
|
def setup_method(self):
|
||
|
|
np.random.seed(1234)
|
||
|
|
|
||
|
|
def test_rvs(self):
|
||
|
|
vals = stats.zipf.rvs(1.5, size=(2, 50))
|
||
|
|
assert_(numpy.all(vals >= 1))
|
||
|
|
assert_(numpy.shape(vals) == (2, 50))
|
||
|
|
assert_(vals.dtype.char in typecodes['AllInteger'])
|
||
|
|
val = stats.zipf.rvs(1.5)
|
||
|
|
assert_(isinstance(val, int))
|
||
|
|
val = stats.zipf(1.5).rvs(3)
|
||
|
|
assert_(isinstance(val, numpy.ndarray))
|
||
|
|
assert_(val.dtype.char in typecodes['AllInteger'])
|
||
|
|
|
||
|
|
def test_moments(self):
|
||
|
|
# n-th moment is finite iff a > n + 1
|
||
|
|
m, v = stats.zipf.stats(a=2.8)
|
||
|
|
assert_(np.isfinite(m))
|
||
|
|
assert_equal(v, np.inf)
|
||
|
|
|
||
|
|
s, k = stats.zipf.stats(a=4.8, moments='sk')
|
||
|
|
assert_(not np.isfinite([s, k]).all())
|
||
|
|
|
||
|
|
|
||
|
|
class TestDLaplace(object):
|
||
|
|
def setup_method(self):
|
||
|
|
np.random.seed(1234)
|
||
|
|
|
||
|
|
def test_rvs(self):
|
||
|
|
vals = stats.dlaplace.rvs(1.5, size=(2, 50))
|
||
|
|
assert_(numpy.shape(vals) == (2, 50))
|
||
|
|
assert_(vals.dtype.char in typecodes['AllInteger'])
|
||
|
|
val = stats.dlaplace.rvs(1.5)
|
||
|
|
assert_(isinstance(val, int))
|
||
|
|
val = stats.dlaplace(1.5).rvs(3)
|
||
|
|
assert_(isinstance(val, numpy.ndarray))
|
||
|
|
assert_(val.dtype.char in typecodes['AllInteger'])
|
||
|
|
assert_(stats.dlaplace.rvs(0.8) is not None)
|
||
|
|
|
||
|
|
def test_stats(self):
|
||
|
|
# compare the explicit formulas w/ direct summation using pmf
|
||
|
|
a = 1.
|
||
|
|
dl = stats.dlaplace(a)
|
||
|
|
m, v, s, k = dl.stats('mvsk')
|
||
|
|
|
||
|
|
N = 37
|
||
|
|
xx = np.arange(-N, N+1)
|
||
|
|
pp = dl.pmf(xx)
|
||
|
|
m2, m4 = np.sum(pp*xx**2), np.sum(pp*xx**4)
|
||
|
|
assert_equal((m, s), (0, 0))
|
||
|
|
assert_allclose((v, k), (m2, m4/m2**2 - 3.), atol=1e-14, rtol=1e-8)
|
||
|
|
|
||
|
|
def test_stats2(self):
|
||
|
|
a = np.log(2.)
|
||
|
|
dl = stats.dlaplace(a)
|
||
|
|
m, v, s, k = dl.stats('mvsk')
|
||
|
|
assert_equal((m, s), (0., 0.))
|
||
|
|
assert_allclose((v, k), (4., 3.25))
|
||
|
|
|
||
|
|
|
||
|
|
class TestInvGamma(object):
|
||
|
|
def test_invgamma_inf_gh_1866(self):
|
||
|
|
# invgamma's moments are only finite for a>n
|
||
|
|
# specific numbers checked w/ boost 1.54
|
||
|
|
with warnings.catch_warnings():
|
||
|
|
warnings.simplefilter('error', RuntimeWarning)
|
||
|
|
mvsk = stats.invgamma.stats(a=19.31, moments='mvsk')
|
||
|
|
expected = [0.05461496450, 0.0001723162534, 1.020362676,
|
||
|
|
2.055616582]
|
||
|
|
assert_allclose(mvsk, expected)
|
||
|
|
|
||
|
|
a = [1.1, 3.1, 5.6]
|
||
|
|
mvsk = stats.invgamma.stats(a=a, moments='mvsk')
|
||
|
|
expected = ([10., 0.476190476, 0.2173913043], # mmm
|
||
|
|
[np.inf, 0.2061430632, 0.01312749422], # vvv
|
||
|
|
[np.nan, 41.95235392, 2.919025532], # sss
|
||
|
|
[np.nan, np.nan, 24.51923076]) # kkk
|
||
|
|
for x, y in zip(mvsk, expected):
|
||
|
|
assert_almost_equal(x, y)
|
||
|
|
|
||
|
|
def test_cdf_ppf(self):
|
||
|
|
# gh-6245
|
||
|
|
x = np.logspace(-2.6, 0)
|
||
|
|
y = stats.invgamma.cdf(x, 1)
|
||
|
|
xx = stats.invgamma.ppf(y, 1)
|
||
|
|
assert_allclose(x, xx)
|
||
|
|
|
||
|
|
def test_sf_isf(self):
|
||
|
|
# gh-6245
|
||
|
|
if sys.maxsize > 2**32:
|
||
|
|
x = np.logspace(2, 100)
|
||
|
|
else:
|
||
|
|
# Invgamme roundtrip on 32-bit systems has relative accuracy
|
||
|
|
# ~1e-15 until x=1e+15, and becomes inf above x=1e+18
|
||
|
|
x = np.logspace(2, 18)
|
||
|
|
|
||
|
|
y = stats.invgamma.sf(x, 1)
|
||
|
|
xx = stats.invgamma.isf(y, 1)
|
||
|
|
assert_allclose(x, xx, rtol=1.0)
|
||
|
|
|
||
|
|
|
||
|
|
class TestF(object):
|
||
|
|
def test_f_moments(self):
|
||
|
|
# n-th moment of F distributions is only finite for n < dfd / 2
|
||
|
|
m, v, s, k = stats.f.stats(11, 6.5, moments='mvsk')
|
||
|
|
assert_(np.isfinite(m))
|
||
|
|
assert_(np.isfinite(v))
|
||
|
|
assert_(np.isfinite(s))
|
||
|
|
assert_(not np.isfinite(k))
|
||
|
|
|
||
|
|
def test_moments_warnings(self):
|
||
|
|
# no warnings should be generated for dfd = 2, 4, 6, 8 (div by zero)
|
||
|
|
with warnings.catch_warnings():
|
||
|
|
warnings.simplefilter('error', RuntimeWarning)
|
||
|
|
stats.f.stats(dfn=[11]*4, dfd=[2, 4, 6, 8], moments='mvsk')
|
||
|
|
|
||
|
|
@pytest.mark.xfail(reason='f stats does not properly broadcast')
|
||
|
|
def test_stats_broadcast(self):
|
||
|
|
# stats do not fully broadcast just yet
|
||
|
|
mv = stats.f.stats(dfn=11, dfd=[11, 12])
|
||
|
|
|
||
|
|
|
||
|
|
def test_rvgeneric_std():
|
||
|
|
# Regression test for #1191
|
||
|
|
assert_array_almost_equal(stats.t.std([5, 6]), [1.29099445, 1.22474487])
|
||
|
|
|
||
|
|
|
||
|
|
def test_moments_t():
|
||
|
|
# regression test for #8786
|
||
|
|
assert_equal(stats.t.stats(df=1, moments='mvsk'),
|
||
|
|
(np.inf, np.nan, np.nan, np.nan))
|
||
|
|
assert_equal(stats.t.stats(df=1.01, moments='mvsk'),
|
||
|
|
(0.0, np.inf, np.nan, np.nan))
|
||
|
|
assert_equal(stats.t.stats(df=2, moments='mvsk'),
|
||
|
|
(0.0, np.inf, np.nan, np.nan))
|
||
|
|
assert_equal(stats.t.stats(df=2.01, moments='mvsk'),
|
||
|
|
(0.0, 2.01/(2.01-2.0), np.nan, np.inf))
|
||
|
|
assert_equal(stats.t.stats(df=3, moments='sk'), (np.nan, np.inf))
|
||
|
|
assert_equal(stats.t.stats(df=3.01, moments='sk'), (0.0, np.inf))
|
||
|
|
assert_equal(stats.t.stats(df=4, moments='sk'), (0.0, np.inf))
|
||
|
|
assert_equal(stats.t.stats(df=4.01, moments='sk'), (0.0, 6.0/(4.01 - 4.0)))
|
||
|
|
|
||
|
|
|
||
|
|
class TestRvDiscrete(object):
|
||
|
|
def setup_method(self):
|
||
|
|
np.random.seed(1234)
|
||
|
|
|
||
|
|
def test_rvs(self):
|
||
|
|
states = [-1, 0, 1, 2, 3, 4]
|
||
|
|
probability = [0.0, 0.3, 0.4, 0.0, 0.3, 0.0]
|
||
|
|
samples = 1000
|
||
|
|
r = stats.rv_discrete(name='sample', values=(states, probability))
|
||
|
|
x = r.rvs(size=samples)
|
||
|
|
assert_(isinstance(x, numpy.ndarray))
|
||
|
|
|
||
|
|
for s, p in zip(states, probability):
|
||
|
|
assert_(abs(sum(x == s)/float(samples) - p) < 0.05)
|
||
|
|
|
||
|
|
x = r.rvs()
|
||
|
|
assert_(isinstance(x, int))
|
||
|
|
|
||
|
|
def test_entropy(self):
|
||
|
|
# Basic tests of entropy.
|
||
|
|
pvals = np.array([0.25, 0.45, 0.3])
|
||
|
|
p = stats.rv_discrete(values=([0, 1, 2], pvals))
|
||
|
|
expected_h = -sum(xlogy(pvals, pvals))
|
||
|
|
h = p.entropy()
|
||
|
|
assert_allclose(h, expected_h)
|
||
|
|
|
||
|
|
p = stats.rv_discrete(values=([0, 1, 2], [1.0, 0, 0]))
|
||
|
|
h = p.entropy()
|
||
|
|
assert_equal(h, 0.0)
|
||
|
|
|
||
|
|
def test_pmf(self):
|
||
|
|
xk = [1, 2, 4]
|
||
|
|
pk = [0.5, 0.3, 0.2]
|
||
|
|
rv = stats.rv_discrete(values=(xk, pk))
|
||
|
|
|
||
|
|
x = [[1., 4.],
|
||
|
|
[3., 2]]
|
||
|
|
assert_allclose(rv.pmf(x),
|
||
|
|
[[0.5, 0.2],
|
||
|
|
[0., 0.3]], atol=1e-14)
|
||
|
|
|
||
|
|
def test_cdf(self):
|
||
|
|
xk = [1, 2, 4]
|
||
|
|
pk = [0.5, 0.3, 0.2]
|
||
|
|
rv = stats.rv_discrete(values=(xk, pk))
|
||
|
|
|
||
|
|
x_values = [-2, 1., 1.1, 1.5, 2.0, 3.0, 4, 5]
|
||
|
|
expected = [0, 0.5, 0.5, 0.5, 0.8, 0.8, 1, 1]
|
||
|
|
assert_allclose(rv.cdf(x_values), expected, atol=1e-14)
|
||
|
|
|
||
|
|
# also check scalar arguments
|
||
|
|
assert_allclose([rv.cdf(xx) for xx in x_values],
|
||
|
|
expected, atol=1e-14)
|
||
|
|
|
||
|
|
def test_ppf(self):
|
||
|
|
xk = [1, 2, 4]
|
||
|
|
pk = [0.5, 0.3, 0.2]
|
||
|
|
rv = stats.rv_discrete(values=(xk, pk))
|
||
|
|
|
||
|
|
q_values = [0.1, 0.5, 0.6, 0.8, 0.9, 1.]
|
||
|
|
expected = [1, 1, 2, 2, 4, 4]
|
||
|
|
assert_allclose(rv.ppf(q_values), expected, atol=1e-14)
|
||
|
|
|
||
|
|
# also check scalar arguments
|
||
|
|
assert_allclose([rv.ppf(q) for q in q_values],
|
||
|
|
expected, atol=1e-14)
|
||
|
|
|
||
|
|
def test_cdf_ppf_next(self):
|
||
|
|
# copied and special cased from test_discrete_basic
|
||
|
|
vals = ([1, 2, 4, 7, 8], [0.1, 0.2, 0.3, 0.3, 0.1])
|
||
|
|
rv = stats.rv_discrete(values=vals)
|
||
|
|
|
||
|
|
assert_array_equal(rv.ppf(rv.cdf(rv.xk[:-1]) + 1e-8),
|
||
|
|
rv.xk[1:])
|
||
|
|
|
||
|
|
def test_expect(self):
|
||
|
|
xk = [1, 2, 4, 6, 7, 11]
|
||
|
|
pk = [0.1, 0.2, 0.2, 0.2, 0.2, 0.1]
|
||
|
|
rv = stats.rv_discrete(values=(xk, pk))
|
||
|
|
|
||
|
|
assert_allclose(rv.expect(), np.sum(rv.xk * rv.pk), atol=1e-14)
|
||
|
|
|
||
|
|
def test_bad_input(self):
|
||
|
|
xk = [1, 2, 3]
|
||
|
|
pk = [0.5, 0.5]
|
||
|
|
assert_raises(ValueError, stats.rv_discrete, **dict(values=(xk, pk)))
|
||
|
|
|
||
|
|
pk = [1, 2, 3]
|
||
|
|
assert_raises(ValueError, stats.rv_discrete, **dict(values=(xk, pk)))
|
||
|
|
|
||
|
|
|
||
|
|
class TestSkewNorm(object):
|
||
|
|
def setup_method(self):
|
||
|
|
np.random.seed(1234)
|
||
|
|
|
||
|
|
def test_normal(self):
|
||
|
|
# When the skewness is 0 the distribution is normal
|
||
|
|
x = np.linspace(-5, 5, 100)
|
||
|
|
assert_array_almost_equal(stats.skewnorm.pdf(x, a=0),
|
||
|
|
stats.norm.pdf(x))
|
||
|
|
|
||
|
|
def test_rvs(self):
|
||
|
|
shape = (3, 4, 5)
|
||
|
|
x = stats.skewnorm.rvs(a=0.75, size=shape)
|
||
|
|
assert_equal(shape, x.shape)
|
||
|
|
|
||
|
|
x = stats.skewnorm.rvs(a=-3, size=shape)
|
||
|
|
assert_equal(shape, x.shape)
|
||
|
|
|
||
|
|
def test_moments(self):
|
||
|
|
X = stats.skewnorm.rvs(a=4, size=int(1e6), loc=5, scale=2)
|
||
|
|
expected = [np.mean(X), np.var(X), stats.skew(X), stats.kurtosis(X)]
|
||
|
|
computed = stats.skewnorm.stats(a=4, loc=5, scale=2, moments='mvsk')
|
||
|
|
assert_array_almost_equal(computed, expected, decimal=2)
|
||
|
|
|
||
|
|
X = stats.skewnorm.rvs(a=-4, size=int(1e6), loc=5, scale=2)
|
||
|
|
expected = [np.mean(X), np.var(X), stats.skew(X), stats.kurtosis(X)]
|
||
|
|
computed = stats.skewnorm.stats(a=-4, loc=5, scale=2, moments='mvsk')
|
||
|
|
assert_array_almost_equal(computed, expected, decimal=2)
|
||
|
|
|
||
|
|
def test_cdf_large_x(self):
|
||
|
|
# Regression test for gh-7746.
|
||
|
|
# The x values are large enough that the closest 64 bit floating
|
||
|
|
# point representation of the exact CDF is 1.0.
|
||
|
|
p = stats.skewnorm.cdf([10, 20, 30], -1)
|
||
|
|
assert_allclose(p, np.ones(3), rtol=1e-14)
|
||
|
|
p = stats.skewnorm.cdf(25, 2.5)
|
||
|
|
assert_allclose(p, 1.0, rtol=1e-14)
|
||
|
|
|
||
|
|
def test_cdf_sf_small_values(self):
|
||
|
|
# Triples are [x, a, cdf(x, a)]. These values were computed
|
||
|
|
# using CDF[SkewNormDistribution[0, 1, a], x] in Wolfram Alpha.
|
||
|
|
cdfvals = [
|
||
|
|
[-8, 1, 3.870035046664392611e-31],
|
||
|
|
[-4, 2, 8.1298399188811398e-21],
|
||
|
|
[-2, 5, 1.55326826787106273e-26],
|
||
|
|
[-9, -1, 2.257176811907681295e-19],
|
||
|
|
[-10, -4, 1.523970604832105213e-23],
|
||
|
|
]
|
||
|
|
for x, a, cdfval in cdfvals:
|
||
|
|
p = stats.skewnorm.cdf(x, a)
|
||
|
|
assert_allclose(p, cdfval, rtol=1e-8)
|
||
|
|
# For the skew normal distribution, sf(-x, -a) = cdf(x, a).
|
||
|
|
p = stats.skewnorm.sf(-x, -a)
|
||
|
|
assert_allclose(p, cdfval, rtol=1e-8)
|
||
|
|
|
||
|
|
|
||
|
|
class TestExpon(object):
|
||
|
|
def test_zero(self):
|
||
|
|
assert_equal(stats.expon.pdf(0), 1)
|
||
|
|
|
||
|
|
def test_tail(self): # Regression test for ticket 807
|
||
|
|
assert_equal(stats.expon.cdf(1e-18), 1e-18)
|
||
|
|
assert_equal(stats.expon.isf(stats.expon.sf(40)), 40)
|
||
|
|
|
||
|
|
|
||
|
|
class TestExponNorm(object):
|
||
|
|
def test_moments(self):
|
||
|
|
# Some moment test cases based on non-loc/scaled formula
|
||
|
|
def get_moms(lam, sig, mu):
|
||
|
|
# See wikipedia for these formulae
|
||
|
|
# where it is listed as an exponentially modified gaussian
|
||
|
|
opK2 = 1.0 + 1 / (lam*sig)**2
|
||
|
|
exp_skew = 2 / (lam * sig)**3 * opK2**(-1.5)
|
||
|
|
exp_kurt = 6.0 * (1 + (lam * sig)**2)**(-2)
|
||
|
|
return [mu + 1/lam, sig*sig + 1.0/(lam*lam), exp_skew, exp_kurt]
|
||
|
|
|
||
|
|
mu, sig, lam = 0, 1, 1
|
||
|
|
K = 1.0 / (lam * sig)
|
||
|
|
sts = stats.exponnorm.stats(K, loc=mu, scale=sig, moments='mvsk')
|
||
|
|
assert_almost_equal(sts, get_moms(lam, sig, mu))
|
||
|
|
mu, sig, lam = -3, 2, 0.1
|
||
|
|
K = 1.0 / (lam * sig)
|
||
|
|
sts = stats.exponnorm.stats(K, loc=mu, scale=sig, moments='mvsk')
|
||
|
|
assert_almost_equal(sts, get_moms(lam, sig, mu))
|
||
|
|
mu, sig, lam = 0, 3, 1
|
||
|
|
K = 1.0 / (lam * sig)
|
||
|
|
sts = stats.exponnorm.stats(K, loc=mu, scale=sig, moments='mvsk')
|
||
|
|
assert_almost_equal(sts, get_moms(lam, sig, mu))
|
||
|
|
mu, sig, lam = -5, 11, 3.5
|
||
|
|
K = 1.0 / (lam * sig)
|
||
|
|
sts = stats.exponnorm.stats(K, loc=mu, scale=sig, moments='mvsk')
|
||
|
|
assert_almost_equal(sts, get_moms(lam, sig, mu))
|
||
|
|
|
||
|
|
def test_extremes_x(self):
|
||
|
|
# Test for extreme values against overflows
|
||
|
|
assert_almost_equal(stats.exponnorm.pdf(-900, 1), 0.0)
|
||
|
|
assert_almost_equal(stats.exponnorm.pdf(+900, 1), 0.0)
|
||
|
|
|
||
|
|
|
||
|
|
class TestGenExpon(object):
|
||
|
|
def test_pdf_unity_area(self):
|
||
|
|
from scipy.integrate import simps
|
||
|
|
# PDF should integrate to one
|
||
|
|
p = stats.genexpon.pdf(numpy.arange(0, 10, 0.01), 0.5, 0.5, 2.0)
|
||
|
|
assert_almost_equal(simps(p, dx=0.01), 1, 1)
|
||
|
|
|
||
|
|
def test_cdf_bounds(self):
|
||
|
|
# CDF should always be positive
|
||
|
|
cdf = stats.genexpon.cdf(numpy.arange(0, 10, 0.01), 0.5, 0.5, 2.0)
|
||
|
|
assert_(numpy.all((0 <= cdf) & (cdf <= 1)))
|
||
|
|
|
||
|
|
|
||
|
|
class TestExponpow(object):
|
||
|
|
def test_tail(self):
|
||
|
|
assert_almost_equal(stats.exponpow.cdf(1e-10, 2.), 1e-20)
|
||
|
|
assert_almost_equal(stats.exponpow.isf(stats.exponpow.sf(5, .8), .8),
|
||
|
|
5)
|
||
|
|
|
||
|
|
|
||
|
|
class TestSkellam(object):
|
||
|
|
def test_pmf(self):
|
||
|
|
# comparison to R
|
||
|
|
k = numpy.arange(-10, 15)
|
||
|
|
mu1, mu2 = 10, 5
|
||
|
|
skpmfR = numpy.array(
|
||
|
|
[4.2254582961926893e-005, 1.1404838449648488e-004,
|
||
|
|
2.8979625801752660e-004, 6.9177078182101231e-004,
|
||
|
|
1.5480716105844708e-003, 3.2412274963433889e-003,
|
||
|
|
6.3373707175123292e-003, 1.1552351566696643e-002,
|
||
|
|
1.9606152375042644e-002, 3.0947164083410337e-002,
|
||
|
|
4.5401737566767360e-002, 6.1894328166820688e-002,
|
||
|
|
7.8424609500170578e-002, 9.2418812533573133e-002,
|
||
|
|
1.0139793148019728e-001, 1.0371927988298846e-001,
|
||
|
|
9.9076583077406091e-002, 8.8546660073089561e-002,
|
||
|
|
7.4187842052486810e-002, 5.8392772862200251e-002,
|
||
|
|
4.3268692953013159e-002, 3.0248159818374226e-002,
|
||
|
|
1.9991434305603021e-002, 1.2516877303301180e-002,
|
||
|
|
7.4389876226229707e-003])
|
||
|
|
|
||
|
|
assert_almost_equal(stats.skellam.pmf(k, mu1, mu2), skpmfR, decimal=15)
|
||
|
|
|
||
|
|
def test_cdf(self):
|
||
|
|
# comparison to R, only 5 decimals
|
||
|
|
k = numpy.arange(-10, 15)
|
||
|
|
mu1, mu2 = 10, 5
|
||
|
|
skcdfR = numpy.array(
|
||
|
|
[6.4061475386192104e-005, 1.7810985988267694e-004,
|
||
|
|
4.6790611790020336e-004, 1.1596768997212152e-003,
|
||
|
|
2.7077485103056847e-003, 5.9489760066490718e-003,
|
||
|
|
1.2286346724161398e-002, 2.3838698290858034e-002,
|
||
|
|
4.3444850665900668e-002, 7.4392014749310995e-002,
|
||
|
|
1.1979375231607835e-001, 1.8168808048289900e-001,
|
||
|
|
2.6011268998306952e-001, 3.5253150251664261e-001,
|
||
|
|
4.5392943399683988e-001, 5.5764871387982828e-001,
|
||
|
|
6.5672529695723436e-001, 7.4527195703032389e-001,
|
||
|
|
8.1945979908281064e-001, 8.7785257194501087e-001,
|
||
|
|
9.2112126489802404e-001, 9.5136942471639818e-001,
|
||
|
|
9.7136085902200120e-001, 9.8387773632530240e-001,
|
||
|
|
9.9131672394792536e-001])
|
||
|
|
|
||
|
|
assert_almost_equal(stats.skellam.cdf(k, mu1, mu2), skcdfR, decimal=5)
|
||
|
|
|
||
|
|
|
||
|
|
class TestLognorm(object):
|
||
|
|
def test_pdf(self):
|
||
|
|
# Regression test for Ticket #1471: avoid nan with 0/0 situation
|
||
|
|
# Also make sure there are no warnings at x=0, cf gh-5202
|
||
|
|
with warnings.catch_warnings():
|
||
|
|
warnings.simplefilter('error', RuntimeWarning)
|
||
|
|
pdf = stats.lognorm.pdf([0, 0.5, 1], 1)
|
||
|
|
assert_array_almost_equal(pdf, [0.0, 0.62749608, 0.39894228])
|
||
|
|
|
||
|
|
def test_logcdf(self):
|
||
|
|
# Regression test for gh-5940: sf et al would underflow too early
|
||
|
|
x2, mu, sigma = 201.68, 195, 0.149
|
||
|
|
assert_allclose(stats.lognorm.sf(x2-mu, s=sigma),
|
||
|
|
stats.norm.sf(np.log(x2-mu)/sigma))
|
||
|
|
assert_allclose(stats.lognorm.logsf(x2-mu, s=sigma),
|
||
|
|
stats.norm.logsf(np.log(x2-mu)/sigma))
|
||
|
|
|
||
|
|
|
||
|
|
class TestBeta(object):
|
||
|
|
def test_logpdf(self):
|
||
|
|
# Regression test for Ticket #1326: avoid nan with 0*log(0) situation
|
||
|
|
logpdf = stats.beta.logpdf(0, 1, 0.5)
|
||
|
|
assert_almost_equal(logpdf, -0.69314718056)
|
||
|
|
logpdf = stats.beta.logpdf(0, 0.5, 1)
|
||
|
|
assert_almost_equal(logpdf, np.inf)
|
||
|
|
|
||
|
|
def test_logpdf_ticket_1866(self):
|
||
|
|
alpha, beta = 267, 1472
|
||
|
|
x = np.array([0.2, 0.5, 0.6])
|
||
|
|
b = stats.beta(alpha, beta)
|
||
|
|
assert_allclose(b.logpdf(x).sum(), -1201.699061824062)
|
||
|
|
assert_allclose(b.pdf(x), np.exp(b.logpdf(x)))
|
||
|
|
|
||
|
|
|
||
|
|
class TestBetaPrime(object):
|
||
|
|
def test_logpdf(self):
|
||
|
|
alpha, beta = 267, 1472
|
||
|
|
x = np.array([0.2, 0.5, 0.6])
|
||
|
|
b = stats.betaprime(alpha, beta)
|
||
|
|
assert_(np.isfinite(b.logpdf(x)).all())
|
||
|
|
assert_allclose(b.pdf(x), np.exp(b.logpdf(x)))
|
||
|
|
|
||
|
|
def test_cdf(self):
|
||
|
|
# regression test for gh-4030: Implementation of
|
||
|
|
# scipy.stats.betaprime.cdf()
|
||
|
|
x = stats.betaprime.cdf(0, 0.2, 0.3)
|
||
|
|
assert_equal(x, 0.0)
|
||
|
|
|
||
|
|
alpha, beta = 267, 1472
|
||
|
|
x = np.array([0.2, 0.5, 0.6])
|
||
|
|
cdfs = stats.betaprime.cdf(x, alpha, beta)
|
||
|
|
assert_(np.isfinite(cdfs).all())
|
||
|
|
|
||
|
|
# check the new cdf implementation vs generic one:
|
||
|
|
gen_cdf = stats.rv_continuous._cdf_single
|
||
|
|
cdfs_g = [gen_cdf(stats.betaprime, val, alpha, beta) for val in x]
|
||
|
|
assert_allclose(cdfs, cdfs_g, atol=0, rtol=2e-12)
|
||
|
|
|
||
|
|
|
||
|
|
class TestGamma(object):
|
||
|
|
def test_pdf(self):
|
||
|
|
# a few test cases to compare with R
|
||
|
|
pdf = stats.gamma.pdf(90, 394, scale=1./5)
|
||
|
|
assert_almost_equal(pdf, 0.002312341)
|
||
|
|
|
||
|
|
pdf = stats.gamma.pdf(3, 10, scale=1./5)
|
||
|
|
assert_almost_equal(pdf, 0.1620358)
|
||
|
|
|
||
|
|
def test_logpdf(self):
|
||
|
|
# Regression test for Ticket #1326: cornercase avoid nan with 0*log(0)
|
||
|
|
# situation
|
||
|
|
logpdf = stats.gamma.logpdf(0, 1)
|
||
|
|
assert_almost_equal(logpdf, 0)
|
||
|
|
|
||
|
|
|
||
|
|
class TestChi2(object):
|
||
|
|
# regression tests after precision improvements, ticket:1041, not verified
|
||
|
|
def test_precision(self):
|
||
|
|
assert_almost_equal(stats.chi2.pdf(1000, 1000), 8.919133934753128e-003,
|
||
|
|
decimal=14)
|
||
|
|
assert_almost_equal(stats.chi2.pdf(100, 100), 0.028162503162596778,
|
||
|
|
decimal=14)
|
||
|
|
|
||
|
|
|
||
|
|
class TestGumbelL(object):
|
||
|
|
# gh-6228
|
||
|
|
def test_cdf_ppf(self):
|
||
|
|
x = np.linspace(-100, -4)
|
||
|
|
y = stats.gumbel_l.cdf(x)
|
||
|
|
xx = stats.gumbel_l.ppf(y)
|
||
|
|
assert_allclose(x, xx)
|
||
|
|
|
||
|
|
def test_logcdf_logsf(self):
|
||
|
|
x = np.linspace(-100, -4)
|
||
|
|
y = stats.gumbel_l.logcdf(x)
|
||
|
|
z = stats.gumbel_l.logsf(x)
|
||
|
|
u = np.exp(y)
|
||
|
|
v = -special.expm1(z)
|
||
|
|
assert_allclose(u, v)
|
||
|
|
|
||
|
|
def test_sf_isf(self):
|
||
|
|
x = np.linspace(-20, 5)
|
||
|
|
y = stats.gumbel_l.sf(x)
|
||
|
|
xx = stats.gumbel_l.isf(y)
|
||
|
|
assert_allclose(x, xx)
|
||
|
|
|
||
|
|
class TestLevyStable(object):
|
||
|
|
|
||
|
|
def test_fit(self):
|
||
|
|
# construct data to have percentiles that match
|
||
|
|
# example in McCulloch 1986.
|
||
|
|
x = [-.05413,-.05413,
|
||
|
|
0.,0.,0.,0.,
|
||
|
|
.00533,.00533,.00533,.00533,.00533,
|
||
|
|
.03354,.03354,.03354,.03354,.03354,
|
||
|
|
.05309,.05309,.05309,.05309,.05309]
|
||
|
|
alpha1, beta1, loc1, scale1 = stats.levy_stable._fitstart(x)
|
||
|
|
assert_allclose(alpha1, 1.48, rtol=0, atol=0.01)
|
||
|
|
assert_almost_equal(beta1, -.22, 2)
|
||
|
|
assert_almost_equal(scale1, 0.01717, 4)
|
||
|
|
assert_almost_equal(loc1, 0.00233, 2) # to 2 dps due to rounding error in McCulloch86
|
||
|
|
|
||
|
|
# cover alpha=2 scenario
|
||
|
|
x2 = x + [.05309,.05309,.05309,.05309,.05309]
|
||
|
|
alpha2, beta2, loc2, scale2 = stats.levy_stable._fitstart(x2)
|
||
|
|
assert_equal(alpha2, 2)
|
||
|
|
assert_equal(beta2, -1)
|
||
|
|
assert_almost_equal(scale2, .02503, 4)
|
||
|
|
assert_almost_equal(loc2, .03354, 4)
|
||
|
|
|
||
|
|
@pytest.mark.slow
|
||
|
|
def test_pdf_nolan_samples(self):
|
||
|
|
""" Test pdf values against Nolan's stablec.exe output
|
||
|
|
see - http://fs2.american.edu/jpnolan/www/stable/stable.html
|
||
|
|
|
||
|
|
There's a known limitation of Nolan's executable for alpha < 0.2.
|
||
|
|
|
||
|
|
Repeat following with beta = -1, -.5, 0, .5 and 1
|
||
|
|
stablec.exe <<
|
||
|
|
1 # pdf
|
||
|
|
1 # Nolan S equivalent to S0 in scipy
|
||
|
|
.25,2,.25 # alpha
|
||
|
|
-1,-1,0 # beta
|
||
|
|
-10,10,1 # x
|
||
|
|
1,0 # gamma, delta
|
||
|
|
2 # output file
|
||
|
|
"""
|
||
|
|
data = np.load(os.path.abspath(os.path.join(os.path.dirname(__file__),
|
||
|
|
'data/stable-pdf-sample-data.npy')))
|
||
|
|
|
||
|
|
data = np.core.records.fromarrays(data.T, names='x,p,alpha,beta')
|
||
|
|
|
||
|
|
# support numpy 1.8.2 for travis
|
||
|
|
npisin = np.isin if hasattr(np, "isin") else np.in1d
|
||
|
|
|
||
|
|
tests = [
|
||
|
|
# best selects
|
||
|
|
['best', None, 8, None],
|
||
|
|
|
||
|
|
# quadrature is accurate for most alpha except 0.25; perhaps limitation of Nolan stablec?
|
||
|
|
# we reduce size of x to speed up computation as numerical integration slow.
|
||
|
|
['quadrature', None, 8, lambda r: (r['alpha'] > 0.25) & (npisin(r['x'], [-10,-5,0,5,10]))],
|
||
|
|
|
||
|
|
# zolatarev is accurate except at alpha==1, beta != 0
|
||
|
|
['zolotarev', None, 8, lambda r: r['alpha'] != 1],
|
||
|
|
['zolotarev', None, 8, lambda r: (r['alpha'] == 1) & (r['beta'] == 0)],
|
||
|
|
['zolotarev', None, 1, lambda r: (r['alpha'] == 1) & (r['beta'] != 0)],
|
||
|
|
|
||
|
|
# fft accuracy reduces as alpha decreases, fails at low values of alpha and x=0
|
||
|
|
['fft', 0, 4, lambda r: r['alpha'] > 1],
|
||
|
|
['fft', 0, 3, lambda r: (r['alpha'] < 1) & (r['alpha'] > 0.25)],
|
||
|
|
['fft', 0, 1, lambda r: (r['alpha'] == 0.25) & (r['x'] != 0)], # not useful here
|
||
|
|
]
|
||
|
|
for ix, (default_method, fft_min_points, decimal_places, filter_func) in enumerate(tests):
|
||
|
|
stats.levy_stable.pdf_default_method = default_method
|
||
|
|
stats.levy_stable.pdf_fft_min_points_threshold = fft_min_points
|
||
|
|
subdata = data[filter_func(data)] if filter_func is not None else data
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.record(RuntimeWarning, "Density calculation unstable for alpha=1 and beta!=0.*")
|
||
|
|
sup.record(RuntimeWarning, "Density calculations experimental for FFT method.*")
|
||
|
|
p = stats.levy_stable.pdf(subdata['x'], subdata['alpha'], subdata['beta'], scale=1, loc=0)
|
||
|
|
subdata2 = rec_append_fields(subdata, 'calc', p)
|
||
|
|
failures = subdata2[(np.abs(p-subdata['p']) >= 1.5*10.**(-decimal_places)) | np.isnan(p)]
|
||
|
|
assert_almost_equal(p, subdata['p'], decimal_places, "pdf test %s failed with method '%s'\n%s" % (ix, default_method, failures), verbose=False)
|
||
|
|
|
||
|
|
@pytest.mark.slow
|
||
|
|
def test_cdf_nolan_samples(self):
|
||
|
|
""" Test cdf values against Nolan's stablec.exe output
|
||
|
|
see - http://fs2.american.edu/jpnolan/www/stable/stable.html
|
||
|
|
|
||
|
|
There's a known limitation of Nolan's executable for alpha < 0.2.
|
||
|
|
|
||
|
|
Repeat following with beta = -1, -.5, 0, .5 and 1
|
||
|
|
stablec.exe <<
|
||
|
|
2 # cdf
|
||
|
|
1 # Nolan S equivalent to S0 in scipy
|
||
|
|
.25,2,.25 # alpha
|
||
|
|
-1,-1,0 # beta
|
||
|
|
-10,10,1 # x
|
||
|
|
1,0 # gamma, delta
|
||
|
|
2 # output file
|
||
|
|
"""
|
||
|
|
data = np.load(os.path.abspath(os.path.join(os.path.dirname(__file__),
|
||
|
|
'data/stable-cdf-sample-data.npy')))
|
||
|
|
|
||
|
|
data = np.core.records.fromarrays(data.T, names='x,p,alpha,beta')
|
||
|
|
|
||
|
|
tests = [
|
||
|
|
# zolatarev is accurate for all values
|
||
|
|
['zolotarev', None, 8, None],
|
||
|
|
|
||
|
|
# fft accuracy poor, very poor alpha < 1
|
||
|
|
['fft', 0, 2, lambda r: r['alpha'] > 1],
|
||
|
|
]
|
||
|
|
for ix, (default_method, fft_min_points, decimal_places, filter_func) in enumerate(tests):
|
||
|
|
stats.levy_stable.pdf_default_method = default_method
|
||
|
|
stats.levy_stable.pdf_fft_min_points_threshold = fft_min_points
|
||
|
|
subdata = data[filter_func(data)] if filter_func is not None else data
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.record(RuntimeWarning, 'FFT method is considered ' +
|
||
|
|
'experimental for cumulative distribution ' +
|
||
|
|
'function evaluations.*')
|
||
|
|
p = stats.levy_stable.cdf(subdata['x'], subdata['alpha'], subdata['beta'], scale=1, loc=0)
|
||
|
|
subdata2 = rec_append_fields(subdata, 'calc', p)
|
||
|
|
failures = subdata2[(np.abs(p-subdata['p']) >= 1.5*10.**(-decimal_places)) | np.isnan(p)]
|
||
|
|
assert_almost_equal(p, subdata['p'], decimal_places, "cdf test %s failed with method '%s'\n%s" % (ix, default_method, failures), verbose=False)
|
||
|
|
|
||
|
|
def test_pdf_alpha_equals_one_beta_non_zero(self):
|
||
|
|
""" sample points extracted from Tables and Graphs of Stable Probability
|
||
|
|
Density Functions - Donald R Holt - 1973 - p 187.
|
||
|
|
"""
|
||
|
|
xs = np.array([0, 0, 0, 0,
|
||
|
|
1, 1, 1, 1,
|
||
|
|
2, 2, 2, 2,
|
||
|
|
3, 3, 3, 3,
|
||
|
|
4, 4, 4, 4])
|
||
|
|
density = np.array([.3183, .3096, .2925, .2622,
|
||
|
|
.1591, .1587, .1599, .1635,
|
||
|
|
.0637, .0729, .0812, .0955,
|
||
|
|
.0318, .0390, .0458, .0586,
|
||
|
|
.0187, .0236, .0285, .0384])
|
||
|
|
betas = np.array([0, .25, .5, 1,
|
||
|
|
0, .25, .5, 1,
|
||
|
|
0, .25, .5, 1,
|
||
|
|
0, .25, .5, 1,
|
||
|
|
0, .25, .5, 1])
|
||
|
|
|
||
|
|
tests = [
|
||
|
|
['quadrature', None, 4],
|
||
|
|
#['fft', 0, 4],
|
||
|
|
['zolotarev', None, 1],
|
||
|
|
]
|
||
|
|
|
||
|
|
with np.errstate(all='ignore'), suppress_warnings() as sup:
|
||
|
|
sup.filter(category=RuntimeWarning, message="Density calculation unstable.*")
|
||
|
|
for default_method, fft_min_points, decimal_places in tests:
|
||
|
|
stats.levy_stable.pdf_default_method = default_method
|
||
|
|
stats.levy_stable.pdf_fft_min_points_threshold = fft_min_points
|
||
|
|
#stats.levy_stable.fft_grid_spacing = 0.0001
|
||
|
|
pdf = stats.levy_stable.pdf(xs, 1, betas, scale=1, loc=0)
|
||
|
|
assert_almost_equal(pdf, density, decimal_places, default_method)
|
||
|
|
|
||
|
|
def test_stats(self):
|
||
|
|
param_sets = [
|
||
|
|
[(1.48,-.22, 0, 1), (0,np.inf,np.NaN,np.NaN)],
|
||
|
|
[(2,.9, 10, 1.5), (10,4.5,0,0)]
|
||
|
|
]
|
||
|
|
for args, exp_stats in param_sets:
|
||
|
|
calc_stats = stats.levy_stable.stats(args[0], args[1], loc=args[2], scale=args[3], moments='mvsk')
|
||
|
|
assert_almost_equal(calc_stats, exp_stats)
|
||
|
|
|
||
|
|
class TestArrayArgument(object): # test for ticket:992
|
||
|
|
def setup_method(self):
|
||
|
|
np.random.seed(1234)
|
||
|
|
|
||
|
|
def test_noexception(self):
|
||
|
|
rvs = stats.norm.rvs(loc=(np.arange(5)), scale=np.ones(5),
|
||
|
|
size=(10, 5))
|
||
|
|
assert_equal(rvs.shape, (10, 5))
|
||
|
|
|
||
|
|
|
||
|
|
class TestDocstring(object):
|
||
|
|
def test_docstrings(self):
|
||
|
|
# See ticket #761
|
||
|
|
if stats.rayleigh.__doc__ is not None:
|
||
|
|
assert_("rayleigh" in stats.rayleigh.__doc__.lower())
|
||
|
|
if stats.bernoulli.__doc__ is not None:
|
||
|
|
assert_("bernoulli" in stats.bernoulli.__doc__.lower())
|
||
|
|
|
||
|
|
def test_no_name_arg(self):
|
||
|
|
# If name is not given, construction shouldn't fail. See #1508.
|
||
|
|
stats.rv_continuous()
|
||
|
|
stats.rv_discrete()
|
||
|
|
|
||
|
|
|
||
|
|
class TestEntropy(object):
|
||
|
|
def test_entropy_positive(self):
|
||
|
|
# See ticket #497
|
||
|
|
pk = [0.5, 0.2, 0.3]
|
||
|
|
qk = [0.1, 0.25, 0.65]
|
||
|
|
eself = stats.entropy(pk, pk)
|
||
|
|
edouble = stats.entropy(pk, qk)
|
||
|
|
assert_(0.0 == eself)
|
||
|
|
assert_(edouble >= 0.0)
|
||
|
|
|
||
|
|
def test_entropy_base(self):
|
||
|
|
pk = np.ones(16, float)
|
||
|
|
S = stats.entropy(pk, base=2.)
|
||
|
|
assert_(abs(S - 4.) < 1.e-5)
|
||
|
|
|
||
|
|
qk = np.ones(16, float)
|
||
|
|
qk[:8] = 2.
|
||
|
|
S = stats.entropy(pk, qk)
|
||
|
|
S2 = stats.entropy(pk, qk, base=2.)
|
||
|
|
assert_(abs(S/S2 - np.log(2.)) < 1.e-5)
|
||
|
|
|
||
|
|
def test_entropy_zero(self):
|
||
|
|
# Test for PR-479
|
||
|
|
assert_almost_equal(stats.entropy([0, 1, 2]), 0.63651416829481278,
|
||
|
|
decimal=12)
|
||
|
|
|
||
|
|
def test_entropy_2d(self):
|
||
|
|
pk = [[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]]
|
||
|
|
qk = [[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]]
|
||
|
|
assert_array_almost_equal(stats.entropy(pk, qk),
|
||
|
|
[0.1933259, 0.18609809])
|
||
|
|
|
||
|
|
def test_entropy_2d_zero(self):
|
||
|
|
pk = [[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]]
|
||
|
|
qk = [[0.0, 0.1], [0.3, 0.6], [0.5, 0.3]]
|
||
|
|
assert_array_almost_equal(stats.entropy(pk, qk),
|
||
|
|
[np.inf, 0.18609809])
|
||
|
|
|
||
|
|
pk[0][0] = 0.0
|
||
|
|
assert_array_almost_equal(stats.entropy(pk, qk),
|
||
|
|
[0.17403988, 0.18609809])
|
||
|
|
|
||
|
|
|
||
|
|
def TestArgsreduce():
|
||
|
|
a = array([1, 3, 2, 1, 2, 3, 3])
|
||
|
|
b, c = argsreduce(a > 1, a, 2)
|
||
|
|
|
||
|
|
assert_array_equal(b, [3, 2, 2, 3, 3])
|
||
|
|
assert_array_equal(c, [2, 2, 2, 2, 2])
|
||
|
|
|
||
|
|
b, c = argsreduce(2 > 1, a, 2)
|
||
|
|
assert_array_equal(b, a[0])
|
||
|
|
assert_array_equal(c, [2])
|
||
|
|
|
||
|
|
b, c = argsreduce(a > 0, a, 2)
|
||
|
|
assert_array_equal(b, a)
|
||
|
|
assert_array_equal(c, [2] * numpy.size(a))
|
||
|
|
|
||
|
|
|
||
|
|
class TestFitMethod(object):
|
||
|
|
skip = ['ncf']
|
||
|
|
|
||
|
|
def setup_method(self):
|
||
|
|
np.random.seed(1234)
|
||
|
|
|
||
|
|
@pytest.mark.slow
|
||
|
|
@pytest.mark.parametrize('dist,args,alpha', cases_test_all_distributions())
|
||
|
|
def test_fit(self, dist, args, alpha):
|
||
|
|
if dist in self.skip:
|
||
|
|
pytest.skip("%s fit known to fail" % dist)
|
||
|
|
distfunc = getattr(stats, dist)
|
||
|
|
with np.errstate(all='ignore'), suppress_warnings() as sup:
|
||
|
|
sup.filter(category=DeprecationWarning, message=".*frechet_")
|
||
|
|
res = distfunc.rvs(*args, **{'size': 200})
|
||
|
|
vals = distfunc.fit(res)
|
||
|
|
vals2 = distfunc.fit(res, optimizer='powell')
|
||
|
|
# Only check the length of the return
|
||
|
|
# FIXME: should check the actual results to see if we are 'close'
|
||
|
|
# to what was created --- but what is 'close' enough
|
||
|
|
assert_(len(vals) == 2+len(args))
|
||
|
|
assert_(len(vals2) == 2+len(args))
|
||
|
|
|
||
|
|
@pytest.mark.slow
|
||
|
|
@pytest.mark.parametrize('dist,args,alpha', cases_test_all_distributions())
|
||
|
|
def test_fix_fit(self, dist, args, alpha):
|
||
|
|
# Not sure why 'ncf', and 'beta' are failing
|
||
|
|
# frechet has different len(args) than distfunc.numargs
|
||
|
|
if dist in self.skip + ['frechet']:
|
||
|
|
pytest.skip("%s fit known to fail" % dist)
|
||
|
|
distfunc = getattr(stats, dist)
|
||
|
|
with np.errstate(all='ignore'), suppress_warnings() as sup:
|
||
|
|
sup.filter(category=DeprecationWarning, message=".*frechet_")
|
||
|
|
res = distfunc.rvs(*args, **{'size': 200})
|
||
|
|
vals = distfunc.fit(res, floc=0)
|
||
|
|
vals2 = distfunc.fit(res, fscale=1)
|
||
|
|
assert_(len(vals) == 2+len(args))
|
||
|
|
assert_(vals[-2] == 0)
|
||
|
|
assert_(vals2[-1] == 1)
|
||
|
|
assert_(len(vals2) == 2+len(args))
|
||
|
|
if len(args) > 0:
|
||
|
|
vals3 = distfunc.fit(res, f0=args[0])
|
||
|
|
assert_(len(vals3) == 2+len(args))
|
||
|
|
assert_(vals3[0] == args[0])
|
||
|
|
if len(args) > 1:
|
||
|
|
vals4 = distfunc.fit(res, f1=args[1])
|
||
|
|
assert_(len(vals4) == 2+len(args))
|
||
|
|
assert_(vals4[1] == args[1])
|
||
|
|
if len(args) > 2:
|
||
|
|
vals5 = distfunc.fit(res, f2=args[2])
|
||
|
|
assert_(len(vals5) == 2+len(args))
|
||
|
|
assert_(vals5[2] == args[2])
|
||
|
|
|
||
|
|
def test_fix_fit_2args_lognorm(self):
|
||
|
|
# Regression test for #1551.
|
||
|
|
np.random.seed(12345)
|
||
|
|
with np.errstate(all='ignore'):
|
||
|
|
x = stats.lognorm.rvs(0.25, 0., 20.0, size=20)
|
||
|
|
expected_shape = np.sqrt(((np.log(x) - np.log(20))**2).mean())
|
||
|
|
assert_allclose(np.array(stats.lognorm.fit(x, floc=0, fscale=20)),
|
||
|
|
[expected_shape, 0, 20], atol=1e-8)
|
||
|
|
|
||
|
|
def test_fix_fit_norm(self):
|
||
|
|
x = np.arange(1, 6)
|
||
|
|
|
||
|
|
loc, scale = stats.norm.fit(x)
|
||
|
|
assert_almost_equal(loc, 3)
|
||
|
|
assert_almost_equal(scale, np.sqrt(2))
|
||
|
|
|
||
|
|
loc, scale = stats.norm.fit(x, floc=2)
|
||
|
|
assert_equal(loc, 2)
|
||
|
|
assert_equal(scale, np.sqrt(3))
|
||
|
|
|
||
|
|
loc, scale = stats.norm.fit(x, fscale=2)
|
||
|
|
assert_almost_equal(loc, 3)
|
||
|
|
assert_equal(scale, 2)
|
||
|
|
|
||
|
|
def test_fix_fit_gamma(self):
|
||
|
|
x = np.arange(1, 6)
|
||
|
|
meanlog = np.log(x).mean()
|
||
|
|
|
||
|
|
# A basic test of gamma.fit with floc=0.
|
||
|
|
floc = 0
|
||
|
|
a, loc, scale = stats.gamma.fit(x, floc=floc)
|
||
|
|
s = np.log(x.mean()) - meanlog
|
||
|
|
assert_almost_equal(np.log(a) - special.digamma(a), s, decimal=5)
|
||
|
|
assert_equal(loc, floc)
|
||
|
|
assert_almost_equal(scale, x.mean()/a, decimal=8)
|
||
|
|
|
||
|
|
# Regression tests for gh-2514.
|
||
|
|
# The problem was that if `floc=0` was given, any other fixed
|
||
|
|
# parameters were ignored.
|
||
|
|
f0 = 1
|
||
|
|
floc = 0
|
||
|
|
a, loc, scale = stats.gamma.fit(x, f0=f0, floc=floc)
|
||
|
|
assert_equal(a, f0)
|
||
|
|
assert_equal(loc, floc)
|
||
|
|
assert_almost_equal(scale, x.mean()/a, decimal=8)
|
||
|
|
|
||
|
|
f0 = 2
|
||
|
|
floc = 0
|
||
|
|
a, loc, scale = stats.gamma.fit(x, f0=f0, floc=floc)
|
||
|
|
assert_equal(a, f0)
|
||
|
|
assert_equal(loc, floc)
|
||
|
|
assert_almost_equal(scale, x.mean()/a, decimal=8)
|
||
|
|
|
||
|
|
# loc and scale fixed.
|
||
|
|
floc = 0
|
||
|
|
fscale = 2
|
||
|
|
a, loc, scale = stats.gamma.fit(x, floc=floc, fscale=fscale)
|
||
|
|
assert_equal(loc, floc)
|
||
|
|
assert_equal(scale, fscale)
|
||
|
|
c = meanlog - np.log(fscale)
|
||
|
|
assert_almost_equal(special.digamma(a), c)
|
||
|
|
|
||
|
|
def test_fix_fit_beta(self):
|
||
|
|
# Test beta.fit when both floc and fscale are given.
|
||
|
|
|
||
|
|
def mlefunc(a, b, x):
|
||
|
|
# Zeros of this function are critical points of
|
||
|
|
# the maximum likelihood function.
|
||
|
|
n = len(x)
|
||
|
|
s1 = np.log(x).sum()
|
||
|
|
s2 = np.log(1-x).sum()
|
||
|
|
psiab = special.psi(a + b)
|
||
|
|
func = [s1 - n * (-psiab + special.psi(a)),
|
||
|
|
s2 - n * (-psiab + special.psi(b))]
|
||
|
|
return func
|
||
|
|
|
||
|
|
# Basic test with floc and fscale given.
|
||
|
|
x = np.array([0.125, 0.25, 0.5])
|
||
|
|
a, b, loc, scale = stats.beta.fit(x, floc=0, fscale=1)
|
||
|
|
assert_equal(loc, 0)
|
||
|
|
assert_equal(scale, 1)
|
||
|
|
assert_allclose(mlefunc(a, b, x), [0, 0], atol=1e-6)
|
||
|
|
|
||
|
|
# Basic test with f0, floc and fscale given.
|
||
|
|
# This is also a regression test for gh-2514.
|
||
|
|
x = np.array([0.125, 0.25, 0.5])
|
||
|
|
a, b, loc, scale = stats.beta.fit(x, f0=2, floc=0, fscale=1)
|
||
|
|
assert_equal(a, 2)
|
||
|
|
assert_equal(loc, 0)
|
||
|
|
assert_equal(scale, 1)
|
||
|
|
da, db = mlefunc(a, b, x)
|
||
|
|
assert_allclose(db, 0, atol=1e-5)
|
||
|
|
|
||
|
|
# Same floc and fscale values as above, but reverse the data
|
||
|
|
# and fix b (f1).
|
||
|
|
x2 = 1 - x
|
||
|
|
a2, b2, loc2, scale2 = stats.beta.fit(x2, f1=2, floc=0, fscale=1)
|
||
|
|
assert_equal(b2, 2)
|
||
|
|
assert_equal(loc2, 0)
|
||
|
|
assert_equal(scale2, 1)
|
||
|
|
da, db = mlefunc(a2, b2, x2)
|
||
|
|
assert_allclose(da, 0, atol=1e-5)
|
||
|
|
# a2 of this test should equal b from above.
|
||
|
|
assert_almost_equal(a2, b)
|
||
|
|
|
||
|
|
# Check for detection of data out of bounds when floc and fscale
|
||
|
|
# are given.
|
||
|
|
assert_raises(ValueError, stats.beta.fit, x, floc=0.5, fscale=1)
|
||
|
|
y = np.array([0, .5, 1])
|
||
|
|
assert_raises(ValueError, stats.beta.fit, y, floc=0, fscale=1)
|
||
|
|
assert_raises(ValueError, stats.beta.fit, y, floc=0, fscale=1, f0=2)
|
||
|
|
assert_raises(ValueError, stats.beta.fit, y, floc=0, fscale=1, f1=2)
|
||
|
|
|
||
|
|
# Check that attempting to fix all the parameters raises a ValueError.
|
||
|
|
assert_raises(ValueError, stats.beta.fit, y, f0=0, f1=1,
|
||
|
|
floc=2, fscale=3)
|
||
|
|
|
||
|
|
def test_expon_fit(self):
|
||
|
|
x = np.array([2, 2, 4, 4, 4, 4, 4, 8])
|
||
|
|
|
||
|
|
loc, scale = stats.expon.fit(x)
|
||
|
|
assert_equal(loc, 2) # x.min()
|
||
|
|
assert_equal(scale, 2) # x.mean() - x.min()
|
||
|
|
|
||
|
|
loc, scale = stats.expon.fit(x, fscale=3)
|
||
|
|
assert_equal(loc, 2) # x.min()
|
||
|
|
assert_equal(scale, 3) # fscale
|
||
|
|
|
||
|
|
loc, scale = stats.expon.fit(x, floc=0)
|
||
|
|
assert_equal(loc, 0) # floc
|
||
|
|
assert_equal(scale, 4) # x.mean() - loc
|
||
|
|
|
||
|
|
def test_lognorm_fit(self):
|
||
|
|
x = np.array([1.5, 3, 10, 15, 23, 59])
|
||
|
|
lnxm1 = np.log(x - 1)
|
||
|
|
|
||
|
|
shape, loc, scale = stats.lognorm.fit(x, floc=1)
|
||
|
|
assert_allclose(shape, lnxm1.std(), rtol=1e-12)
|
||
|
|
assert_equal(loc, 1)
|
||
|
|
assert_allclose(scale, np.exp(lnxm1.mean()), rtol=1e-12)
|
||
|
|
|
||
|
|
shape, loc, scale = stats.lognorm.fit(x, floc=1, fscale=6)
|
||
|
|
assert_allclose(shape, np.sqrt(((lnxm1 - np.log(6))**2).mean()),
|
||
|
|
rtol=1e-12)
|
||
|
|
assert_equal(loc, 1)
|
||
|
|
assert_equal(scale, 6)
|
||
|
|
|
||
|
|
shape, loc, scale = stats.lognorm.fit(x, floc=1, fix_s=0.75)
|
||
|
|
assert_equal(shape, 0.75)
|
||
|
|
assert_equal(loc, 1)
|
||
|
|
assert_allclose(scale, np.exp(lnxm1.mean()), rtol=1e-12)
|
||
|
|
|
||
|
|
def test_uniform_fit(self):
|
||
|
|
x = np.array([1.0, 1.1, 1.2, 9.0])
|
||
|
|
|
||
|
|
loc, scale = stats.uniform.fit(x)
|
||
|
|
assert_equal(loc, x.min())
|
||
|
|
assert_equal(scale, x.ptp())
|
||
|
|
|
||
|
|
loc, scale = stats.uniform.fit(x, floc=0)
|
||
|
|
assert_equal(loc, 0)
|
||
|
|
assert_equal(scale, x.max())
|
||
|
|
|
||
|
|
loc, scale = stats.uniform.fit(x, fscale=10)
|
||
|
|
assert_equal(loc, 0)
|
||
|
|
assert_equal(scale, 10)
|
||
|
|
|
||
|
|
assert_raises(ValueError, stats.uniform.fit, x, floc=2.0)
|
||
|
|
assert_raises(ValueError, stats.uniform.fit, x, fscale=5.0)
|
||
|
|
|
||
|
|
def test_fshapes(self):
|
||
|
|
# take a beta distribution, with shapes='a, b', and make sure that
|
||
|
|
# fa is equivalent to f0, and fb is equivalent to f1
|
||
|
|
a, b = 3., 4.
|
||
|
|
x = stats.beta.rvs(a, b, size=100, random_state=1234)
|
||
|
|
res_1 = stats.beta.fit(x, f0=3.)
|
||
|
|
res_2 = stats.beta.fit(x, fa=3.)
|
||
|
|
assert_allclose(res_1, res_2, atol=1e-12, rtol=1e-12)
|
||
|
|
|
||
|
|
res_2 = stats.beta.fit(x, fix_a=3.)
|
||
|
|
assert_allclose(res_1, res_2, atol=1e-12, rtol=1e-12)
|
||
|
|
|
||
|
|
res_3 = stats.beta.fit(x, f1=4.)
|
||
|
|
res_4 = stats.beta.fit(x, fb=4.)
|
||
|
|
assert_allclose(res_3, res_4, atol=1e-12, rtol=1e-12)
|
||
|
|
|
||
|
|
res_4 = stats.beta.fit(x, fix_b=4.)
|
||
|
|
assert_allclose(res_3, res_4, atol=1e-12, rtol=1e-12)
|
||
|
|
|
||
|
|
# cannot specify both positional and named args at the same time
|
||
|
|
assert_raises(ValueError, stats.beta.fit, x, fa=1, f0=2)
|
||
|
|
|
||
|
|
# check that attempting to fix all parameters raises a ValueError
|
||
|
|
assert_raises(ValueError, stats.beta.fit, x, fa=0, f1=1,
|
||
|
|
floc=2, fscale=3)
|
||
|
|
|
||
|
|
# check that specifying floc, fscale and fshapes works for
|
||
|
|
# beta and gamma which override the generic fit method
|
||
|
|
res_5 = stats.beta.fit(x, fa=3., floc=0, fscale=1)
|
||
|
|
aa, bb, ll, ss = res_5
|
||
|
|
assert_equal([aa, ll, ss], [3., 0, 1])
|
||
|
|
|
||
|
|
# gamma distribution
|
||
|
|
a = 3.
|
||
|
|
data = stats.gamma.rvs(a, size=100)
|
||
|
|
aa, ll, ss = stats.gamma.fit(data, fa=a)
|
||
|
|
assert_equal(aa, a)
|
||
|
|
|
||
|
|
def test_extra_params(self):
|
||
|
|
# unknown parameters should raise rather than be silently ignored
|
||
|
|
dist = stats.exponnorm
|
||
|
|
data = dist.rvs(K=2, size=100)
|
||
|
|
dct = dict(enikibeniki=-101)
|
||
|
|
assert_raises(TypeError, dist.fit, data, **dct)
|
||
|
|
|
||
|
|
|
||
|
|
class TestFrozen(object):
|
||
|
|
def setup_method(self):
|
||
|
|
np.random.seed(1234)
|
||
|
|
|
||
|
|
# Test that a frozen distribution gives the same results as the original
|
||
|
|
# object.
|
||
|
|
#
|
||
|
|
# Only tested for the normal distribution (with loc and scale specified)
|
||
|
|
# and for the gamma distribution (with a shape parameter specified).
|
||
|
|
def test_norm(self):
|
||
|
|
dist = stats.norm
|
||
|
|
frozen = stats.norm(loc=10.0, scale=3.0)
|
||
|
|
|
||
|
|
result_f = frozen.pdf(20.0)
|
||
|
|
result = dist.pdf(20.0, loc=10.0, scale=3.0)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.cdf(20.0)
|
||
|
|
result = dist.cdf(20.0, loc=10.0, scale=3.0)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.ppf(0.25)
|
||
|
|
result = dist.ppf(0.25, loc=10.0, scale=3.0)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.isf(0.25)
|
||
|
|
result = dist.isf(0.25, loc=10.0, scale=3.0)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.sf(10.0)
|
||
|
|
result = dist.sf(10.0, loc=10.0, scale=3.0)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.median()
|
||
|
|
result = dist.median(loc=10.0, scale=3.0)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.mean()
|
||
|
|
result = dist.mean(loc=10.0, scale=3.0)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.var()
|
||
|
|
result = dist.var(loc=10.0, scale=3.0)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.std()
|
||
|
|
result = dist.std(loc=10.0, scale=3.0)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.entropy()
|
||
|
|
result = dist.entropy(loc=10.0, scale=3.0)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.moment(2)
|
||
|
|
result = dist.moment(2, loc=10.0, scale=3.0)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
assert_equal(frozen.a, dist.a)
|
||
|
|
assert_equal(frozen.b, dist.b)
|
||
|
|
|
||
|
|
def test_gamma(self):
|
||
|
|
a = 2.0
|
||
|
|
dist = stats.gamma
|
||
|
|
frozen = stats.gamma(a)
|
||
|
|
|
||
|
|
result_f = frozen.pdf(20.0)
|
||
|
|
result = dist.pdf(20.0, a)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.cdf(20.0)
|
||
|
|
result = dist.cdf(20.0, a)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.ppf(0.25)
|
||
|
|
result = dist.ppf(0.25, a)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.isf(0.25)
|
||
|
|
result = dist.isf(0.25, a)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.sf(10.0)
|
||
|
|
result = dist.sf(10.0, a)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.median()
|
||
|
|
result = dist.median(a)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.mean()
|
||
|
|
result = dist.mean(a)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.var()
|
||
|
|
result = dist.var(a)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.std()
|
||
|
|
result = dist.std(a)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.entropy()
|
||
|
|
result = dist.entropy(a)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
result_f = frozen.moment(2)
|
||
|
|
result = dist.moment(2, a)
|
||
|
|
assert_equal(result_f, result)
|
||
|
|
|
||
|
|
assert_equal(frozen.a, frozen.dist.a)
|
||
|
|
assert_equal(frozen.b, frozen.dist.b)
|
||
|
|
|
||
|
|
def test_regression_ticket_1293(self):
|
||
|
|
# Create a frozen distribution.
|
||
|
|
frozen = stats.lognorm(1)
|
||
|
|
# Call one of its methods that does not take any keyword arguments.
|
||
|
|
m1 = frozen.moment(2)
|
||
|
|
# Now call a method that takes a keyword argument.
|
||
|
|
frozen.stats(moments='mvsk')
|
||
|
|
# Call moment(2) again.
|
||
|
|
# After calling stats(), the following was raising an exception.
|
||
|
|
# So this test passes if the following does not raise an exception.
|
||
|
|
m2 = frozen.moment(2)
|
||
|
|
# The following should also be true, of course. But it is not
|
||
|
|
# the focus of this test.
|
||
|
|
assert_equal(m1, m2)
|
||
|
|
|
||
|
|
def test_ab(self):
|
||
|
|
# test that the support of a frozen distribution
|
||
|
|
# (i) remains frozen even if it changes for the original one
|
||
|
|
# (ii) is actually correct if the shape parameters are such that
|
||
|
|
# the values of [a, b] are not the default [0, inf]
|
||
|
|
# take a genpareto as an example where the support
|
||
|
|
# depends on the value of the shape parameter:
|
||
|
|
# for c > 0: a, b = 0, inf
|
||
|
|
# for c < 0: a, b = 0, -1/c
|
||
|
|
rv = stats.genpareto(c=-0.1)
|
||
|
|
a, b = rv.dist.a, rv.dist.b
|
||
|
|
assert_equal([a, b], [0., 10.])
|
||
|
|
assert_equal([rv.a, rv.b], [0., 10.])
|
||
|
|
|
||
|
|
stats.genpareto.pdf(0, c=0.1) # this changes genpareto.b
|
||
|
|
assert_equal([rv.dist.a, rv.dist.b], [a, b])
|
||
|
|
assert_equal([rv.a, rv.b], [a, b])
|
||
|
|
|
||
|
|
rv1 = stats.genpareto(c=0.1)
|
||
|
|
assert_(rv1.dist is not rv.dist)
|
||
|
|
|
||
|
|
def test_rv_frozen_in_namespace(self):
|
||
|
|
# Regression test for gh-3522
|
||
|
|
assert_(hasattr(stats.distributions, 'rv_frozen'))
|
||
|
|
|
||
|
|
def test_random_state(self):
|
||
|
|
# only check that the random_state attribute exists,
|
||
|
|
frozen = stats.norm()
|
||
|
|
assert_(hasattr(frozen, 'random_state'))
|
||
|
|
|
||
|
|
# ... that it can be set,
|
||
|
|
frozen.random_state = 42
|
||
|
|
assert_equal(frozen.random_state.get_state(),
|
||
|
|
np.random.RandomState(42).get_state())
|
||
|
|
|
||
|
|
# ... and that .rvs method accepts it as an argument
|
||
|
|
rndm = np.random.RandomState(1234)
|
||
|
|
frozen.rvs(size=8, random_state=rndm)
|
||
|
|
|
||
|
|
def test_pickling(self):
|
||
|
|
# test that a frozen instance pickles and unpickles
|
||
|
|
# (this method is a clone of common_tests.check_pickling)
|
||
|
|
beta = stats.beta(2.3098496451481823, 0.62687954300963677)
|
||
|
|
poiss = stats.poisson(3.)
|
||
|
|
sample = stats.rv_discrete(values=([0, 1, 2, 3],
|
||
|
|
[0.1, 0.2, 0.3, 0.4]))
|
||
|
|
|
||
|
|
for distfn in [beta, poiss, sample]:
|
||
|
|
distfn.random_state = 1234
|
||
|
|
distfn.rvs(size=8)
|
||
|
|
s = pickle.dumps(distfn)
|
||
|
|
r0 = distfn.rvs(size=8)
|
||
|
|
|
||
|
|
unpickled = pickle.loads(s)
|
||
|
|
r1 = unpickled.rvs(size=8)
|
||
|
|
assert_equal(r0, r1)
|
||
|
|
|
||
|
|
# also smoke test some methods
|
||
|
|
medians = [distfn.ppf(0.5), unpickled.ppf(0.5)]
|
||
|
|
assert_equal(medians[0], medians[1])
|
||
|
|
assert_equal(distfn.cdf(medians[0]),
|
||
|
|
unpickled.cdf(medians[1]))
|
||
|
|
|
||
|
|
def test_expect(self):
|
||
|
|
# smoke test the expect method of the frozen distribution
|
||
|
|
# only take a gamma w/loc and scale and poisson with loc specified
|
||
|
|
def func(x):
|
||
|
|
return x
|
||
|
|
|
||
|
|
gm = stats.gamma(a=2, loc=3, scale=4)
|
||
|
|
gm_val = gm.expect(func, lb=1, ub=2, conditional=True)
|
||
|
|
gamma_val = stats.gamma.expect(func, args=(2,), loc=3, scale=4,
|
||
|
|
lb=1, ub=2, conditional=True)
|
||
|
|
assert_allclose(gm_val, gamma_val)
|
||
|
|
|
||
|
|
p = stats.poisson(3, loc=4)
|
||
|
|
p_val = p.expect(func)
|
||
|
|
poisson_val = stats.poisson.expect(func, args=(3,), loc=4)
|
||
|
|
assert_allclose(p_val, poisson_val)
|
||
|
|
|
||
|
|
|
||
|
|
class TestExpect(object):
|
||
|
|
# Test for expect method.
|
||
|
|
#
|
||
|
|
# Uses normal distribution and beta distribution for finite bounds, and
|
||
|
|
# hypergeom for discrete distribution with finite support
|
||
|
|
def test_norm(self):
|
||
|
|
v = stats.norm.expect(lambda x: (x-5)*(x-5), loc=5, scale=2)
|
||
|
|
assert_almost_equal(v, 4, decimal=14)
|
||
|
|
|
||
|
|
m = stats.norm.expect(lambda x: (x), loc=5, scale=2)
|
||
|
|
assert_almost_equal(m, 5, decimal=14)
|
||
|
|
|
||
|
|
lb = stats.norm.ppf(0.05, loc=5, scale=2)
|
||
|
|
ub = stats.norm.ppf(0.95, loc=5, scale=2)
|
||
|
|
prob90 = stats.norm.expect(lambda x: 1, loc=5, scale=2, lb=lb, ub=ub)
|
||
|
|
assert_almost_equal(prob90, 0.9, decimal=14)
|
||
|
|
|
||
|
|
prob90c = stats.norm.expect(lambda x: 1, loc=5, scale=2, lb=lb, ub=ub,
|
||
|
|
conditional=True)
|
||
|
|
assert_almost_equal(prob90c, 1., decimal=14)
|
||
|
|
|
||
|
|
def test_beta(self):
|
||
|
|
# case with finite support interval
|
||
|
|
v = stats.beta.expect(lambda x: (x-19/3.)*(x-19/3.), args=(10, 5),
|
||
|
|
loc=5, scale=2)
|
||
|
|
assert_almost_equal(v, 1./18., decimal=13)
|
||
|
|
|
||
|
|
m = stats.beta.expect(lambda x: x, args=(10, 5), loc=5., scale=2.)
|
||
|
|
assert_almost_equal(m, 19/3., decimal=13)
|
||
|
|
|
||
|
|
ub = stats.beta.ppf(0.95, 10, 10, loc=5, scale=2)
|
||
|
|
lb = stats.beta.ppf(0.05, 10, 10, loc=5, scale=2)
|
||
|
|
prob90 = stats.beta.expect(lambda x: 1., args=(10, 10), loc=5.,
|
||
|
|
scale=2., lb=lb, ub=ub, conditional=False)
|
||
|
|
assert_almost_equal(prob90, 0.9, decimal=13)
|
||
|
|
|
||
|
|
prob90c = stats.beta.expect(lambda x: 1, args=(10, 10), loc=5,
|
||
|
|
scale=2, lb=lb, ub=ub, conditional=True)
|
||
|
|
assert_almost_equal(prob90c, 1., decimal=13)
|
||
|
|
|
||
|
|
def test_hypergeom(self):
|
||
|
|
# test case with finite bounds
|
||
|
|
|
||
|
|
# without specifying bounds
|
||
|
|
m_true, v_true = stats.hypergeom.stats(20, 10, 8, loc=5.)
|
||
|
|
m = stats.hypergeom.expect(lambda x: x, args=(20, 10, 8), loc=5.)
|
||
|
|
assert_almost_equal(m, m_true, decimal=13)
|
||
|
|
|
||
|
|
v = stats.hypergeom.expect(lambda x: (x-9.)**2, args=(20, 10, 8),
|
||
|
|
loc=5.)
|
||
|
|
assert_almost_equal(v, v_true, decimal=14)
|
||
|
|
|
||
|
|
# with bounds, bounds equal to shifted support
|
||
|
|
v_bounds = stats.hypergeom.expect(lambda x: (x-9.)**2,
|
||
|
|
args=(20, 10, 8),
|
||
|
|
loc=5., lb=5, ub=13)
|
||
|
|
assert_almost_equal(v_bounds, v_true, decimal=14)
|
||
|
|
|
||
|
|
# drop boundary points
|
||
|
|
prob_true = 1-stats.hypergeom.pmf([5, 13], 20, 10, 8, loc=5).sum()
|
||
|
|
prob_bounds = stats.hypergeom.expect(lambda x: 1, args=(20, 10, 8),
|
||
|
|
loc=5., lb=6, ub=12)
|
||
|
|
assert_almost_equal(prob_bounds, prob_true, decimal=13)
|
||
|
|
|
||
|
|
# conditional
|
||
|
|
prob_bc = stats.hypergeom.expect(lambda x: 1, args=(20, 10, 8), loc=5.,
|
||
|
|
lb=6, ub=12, conditional=True)
|
||
|
|
assert_almost_equal(prob_bc, 1, decimal=14)
|
||
|
|
|
||
|
|
# check simple integral
|
||
|
|
prob_b = stats.hypergeom.expect(lambda x: 1, args=(20, 10, 8),
|
||
|
|
lb=0, ub=8)
|
||
|
|
assert_almost_equal(prob_b, 1, decimal=13)
|
||
|
|
|
||
|
|
def test_poisson(self):
|
||
|
|
# poisson, use lower bound only
|
||
|
|
prob_bounds = stats.poisson.expect(lambda x: 1, args=(2,), lb=3,
|
||
|
|
conditional=False)
|
||
|
|
prob_b_true = 1-stats.poisson.cdf(2, 2)
|
||
|
|
assert_almost_equal(prob_bounds, prob_b_true, decimal=14)
|
||
|
|
|
||
|
|
prob_lb = stats.poisson.expect(lambda x: 1, args=(2,), lb=2,
|
||
|
|
conditional=True)
|
||
|
|
assert_almost_equal(prob_lb, 1, decimal=14)
|
||
|
|
|
||
|
|
def test_genhalflogistic(self):
|
||
|
|
# genhalflogistic, changes upper bound of support in _argcheck
|
||
|
|
# regression test for gh-2622
|
||
|
|
halflog = stats.genhalflogistic
|
||
|
|
# check consistency when calling expect twice with the same input
|
||
|
|
res1 = halflog.expect(args=(1.5,))
|
||
|
|
halflog.expect(args=(0.5,))
|
||
|
|
res2 = halflog.expect(args=(1.5,))
|
||
|
|
assert_almost_equal(res1, res2, decimal=14)
|
||
|
|
|
||
|
|
def test_rice_overflow(self):
|
||
|
|
# rice.pdf(999, 0.74) was inf since special.i0 silentyly overflows
|
||
|
|
# check that using i0e fixes it
|
||
|
|
assert_(np.isfinite(stats.rice.pdf(999, 0.74)))
|
||
|
|
|
||
|
|
assert_(np.isfinite(stats.rice.expect(lambda x: 1, args=(0.74,))))
|
||
|
|
assert_(np.isfinite(stats.rice.expect(lambda x: 2, args=(0.74,))))
|
||
|
|
assert_(np.isfinite(stats.rice.expect(lambda x: 3, args=(0.74,))))
|
||
|
|
|
||
|
|
def test_logser(self):
|
||
|
|
# test a discrete distribution with infinite support and loc
|
||
|
|
p, loc = 0.3, 3
|
||
|
|
res_0 = stats.logser.expect(lambda k: k, args=(p,))
|
||
|
|
# check against the correct answer (sum of a geom series)
|
||
|
|
assert_allclose(res_0,
|
||
|
|
p / (p - 1.) / np.log(1. - p), atol=1e-15)
|
||
|
|
|
||
|
|
# now check it with `loc`
|
||
|
|
res_l = stats.logser.expect(lambda k: k, args=(p,), loc=loc)
|
||
|
|
assert_allclose(res_l, res_0 + loc, atol=1e-15)
|
||
|
|
|
||
|
|
def test_skellam(self):
|
||
|
|
# Use a discrete distribution w/ bi-infinite support. Compute two first
|
||
|
|
# moments and compare to known values (cf skellam.stats)
|
||
|
|
p1, p2 = 18, 22
|
||
|
|
m1 = stats.skellam.expect(lambda x: x, args=(p1, p2))
|
||
|
|
m2 = stats.skellam.expect(lambda x: x**2, args=(p1, p2))
|
||
|
|
assert_allclose(m1, p1 - p2, atol=1e-12)
|
||
|
|
assert_allclose(m2 - m1**2, p1 + p2, atol=1e-12)
|
||
|
|
|
||
|
|
def test_randint(self):
|
||
|
|
# Use a discrete distribution w/ parameter-dependent support, which
|
||
|
|
# is larger than the default chunksize
|
||
|
|
lo, hi = 0, 113
|
||
|
|
res = stats.randint.expect(lambda x: x, (lo, hi))
|
||
|
|
assert_allclose(res,
|
||
|
|
sum(_ for _ in range(lo, hi)) / (hi - lo), atol=1e-15)
|
||
|
|
|
||
|
|
def test_zipf(self):
|
||
|
|
# Test that there is no infinite loop even if the sum diverges
|
||
|
|
assert_warns(RuntimeWarning, stats.zipf.expect,
|
||
|
|
lambda x: x**2, (2,))
|
||
|
|
|
||
|
|
def test_discrete_kwds(self):
|
||
|
|
# check that discrete expect accepts keywords to control the summation
|
||
|
|
n0 = stats.poisson.expect(lambda x: 1, args=(2,))
|
||
|
|
n1 = stats.poisson.expect(lambda x: 1, args=(2,),
|
||
|
|
maxcount=1001, chunksize=32, tolerance=1e-8)
|
||
|
|
assert_almost_equal(n0, n1, decimal=14)
|
||
|
|
|
||
|
|
def test_moment(self):
|
||
|
|
# test the .moment() method: compute a higher moment and compare to
|
||
|
|
# a known value
|
||
|
|
def poiss_moment5(mu):
|
||
|
|
return mu**5 + 10*mu**4 + 25*mu**3 + 15*mu**2 + mu
|
||
|
|
|
||
|
|
for mu in [5, 7]:
|
||
|
|
m5 = stats.poisson.moment(5, mu)
|
||
|
|
assert_allclose(m5, poiss_moment5(mu), rtol=1e-10)
|
||
|
|
|
||
|
|
|
||
|
|
class TestNct(object):
|
||
|
|
def test_nc_parameter(self):
|
||
|
|
# Parameter values c<=0 were not enabled (gh-2402).
|
||
|
|
# For negative values c and for c=0 results of rv.cdf(0) below were nan
|
||
|
|
rv = stats.nct(5, 0)
|
||
|
|
assert_equal(rv.cdf(0), 0.5)
|
||
|
|
rv = stats.nct(5, -1)
|
||
|
|
assert_almost_equal(rv.cdf(0), 0.841344746069, decimal=10)
|
||
|
|
|
||
|
|
def test_broadcasting(self):
|
||
|
|
res = stats.nct.pdf(5, np.arange(4, 7)[:, None],
|
||
|
|
np.linspace(0.1, 1, 4))
|
||
|
|
expected = array([[0.00321886, 0.00557466, 0.00918418, 0.01442997],
|
||
|
|
[0.00217142, 0.00395366, 0.00683888, 0.01126276],
|
||
|
|
[0.00153078, 0.00291093, 0.00525206, 0.00900815]])
|
||
|
|
assert_allclose(res, expected, rtol=1e-5)
|
||
|
|
|
||
|
|
def test_variance_gh_issue_2401(self):
|
||
|
|
# Computation of the variance of a non-central t-distribution resulted
|
||
|
|
# in a TypeError: ufunc 'isinf' not supported for the input types,
|
||
|
|
# and the inputs could not be safely coerced to any supported types
|
||
|
|
# according to the casting rule 'safe'
|
||
|
|
rv = stats.nct(4, 0)
|
||
|
|
assert_equal(rv.var(), 2.0)
|
||
|
|
|
||
|
|
def test_nct_inf_moments(self):
|
||
|
|
# n-th moment of nct only exists for df > n
|
||
|
|
m, v, s, k = stats.nct.stats(df=1.9, nc=0.3, moments='mvsk')
|
||
|
|
assert_(np.isfinite(m))
|
||
|
|
assert_equal([v, s, k], [np.inf, np.nan, np.nan])
|
||
|
|
|
||
|
|
m, v, s, k = stats.nct.stats(df=3.1, nc=0.3, moments='mvsk')
|
||
|
|
assert_(np.isfinite([m, v, s]).all())
|
||
|
|
assert_equal(k, np.nan)
|
||
|
|
|
||
|
|
|
||
|
|
class TestRice(object):
|
||
|
|
def test_rice_zero_b(self):
|
||
|
|
# rice distribution should work with b=0, cf gh-2164
|
||
|
|
x = [0.2, 1., 5.]
|
||
|
|
assert_(np.isfinite(stats.rice.pdf(x, b=0.)).all())
|
||
|
|
assert_(np.isfinite(stats.rice.logpdf(x, b=0.)).all())
|
||
|
|
assert_(np.isfinite(stats.rice.cdf(x, b=0.)).all())
|
||
|
|
assert_(np.isfinite(stats.rice.logcdf(x, b=0.)).all())
|
||
|
|
|
||
|
|
q = [0.1, 0.1, 0.5, 0.9]
|
||
|
|
assert_(np.isfinite(stats.rice.ppf(q, b=0.)).all())
|
||
|
|
|
||
|
|
mvsk = stats.rice.stats(0, moments='mvsk')
|
||
|
|
assert_(np.isfinite(mvsk).all())
|
||
|
|
|
||
|
|
# furthermore, pdf is continuous as b\to 0
|
||
|
|
# rice.pdf(x, b\to 0) = x exp(-x^2/2) + O(b^2)
|
||
|
|
# see e.g. Abramovich & Stegun 9.6.7 & 9.6.10
|
||
|
|
b = 1e-8
|
||
|
|
assert_allclose(stats.rice.pdf(x, 0), stats.rice.pdf(x, b),
|
||
|
|
atol=b, rtol=0)
|
||
|
|
|
||
|
|
def test_rice_rvs(self):
|
||
|
|
rvs = stats.rice.rvs
|
||
|
|
assert_equal(rvs(b=3.).size, 1)
|
||
|
|
assert_equal(rvs(b=3., size=(3, 5)).shape, (3, 5))
|
||
|
|
|
||
|
|
|
||
|
|
class TestErlang(object):
|
||
|
|
def setup_method(self):
|
||
|
|
np.random.seed(1234)
|
||
|
|
|
||
|
|
def test_erlang_runtimewarning(self):
|
||
|
|
# erlang should generate a RuntimeWarning if a non-integer
|
||
|
|
# shape parameter is used.
|
||
|
|
with warnings.catch_warnings():
|
||
|
|
warnings.simplefilter("error", RuntimeWarning)
|
||
|
|
|
||
|
|
# The non-integer shape parameter 1.3 should trigger a
|
||
|
|
# RuntimeWarning
|
||
|
|
assert_raises(RuntimeWarning,
|
||
|
|
stats.erlang.rvs, 1.3, loc=0, scale=1, size=4)
|
||
|
|
|
||
|
|
# Calling the fit method with `f0` set to an integer should
|
||
|
|
# *not* trigger a RuntimeWarning. It should return the same
|
||
|
|
# values as gamma.fit(...).
|
||
|
|
data = [0.5, 1.0, 2.0, 4.0]
|
||
|
|
result_erlang = stats.erlang.fit(data, f0=1)
|
||
|
|
result_gamma = stats.gamma.fit(data, f0=1)
|
||
|
|
assert_allclose(result_erlang, result_gamma, rtol=1e-3)
|
||
|
|
|
||
|
|
|
||
|
|
class TestRayleigh(object):
|
||
|
|
# gh-6227
|
||
|
|
def test_logpdf(self):
|
||
|
|
y = stats.rayleigh.logpdf(50)
|
||
|
|
assert_allclose(y, -1246.0879769945718)
|
||
|
|
|
||
|
|
def test_logsf(self):
|
||
|
|
y = stats.rayleigh.logsf(50)
|
||
|
|
assert_allclose(y, -1250)
|
||
|
|
|
||
|
|
|
||
|
|
class TestExponWeib(object):
|
||
|
|
|
||
|
|
def test_pdf_logpdf(self):
|
||
|
|
# Regression test for gh-3508.
|
||
|
|
x = 0.1
|
||
|
|
a = 1.0
|
||
|
|
c = 100.0
|
||
|
|
p = stats.exponweib.pdf(x, a, c)
|
||
|
|
logp = stats.exponweib.logpdf(x, a, c)
|
||
|
|
# Expected values were computed with mpmath.
|
||
|
|
assert_allclose([p, logp],
|
||
|
|
[1.0000000000000054e-97, -223.35075402042244])
|
||
|
|
|
||
|
|
def test_a_is_1(self):
|
||
|
|
# For issue gh-3508.
|
||
|
|
# Check that when a=1, the pdf and logpdf methods of exponweib are the
|
||
|
|
# same as those of weibull_min.
|
||
|
|
x = np.logspace(-4, -1, 4)
|
||
|
|
a = 1
|
||
|
|
c = 100
|
||
|
|
|
||
|
|
p = stats.exponweib.pdf(x, a, c)
|
||
|
|
expected = stats.weibull_min.pdf(x, c)
|
||
|
|
assert_allclose(p, expected)
|
||
|
|
|
||
|
|
logp = stats.exponweib.logpdf(x, a, c)
|
||
|
|
expected = stats.weibull_min.logpdf(x, c)
|
||
|
|
assert_allclose(logp, expected)
|
||
|
|
|
||
|
|
def test_a_is_1_c_is_1(self):
|
||
|
|
# When a = 1 and c = 1, the distribution is exponential.
|
||
|
|
x = np.logspace(-8, 1, 10)
|
||
|
|
a = 1
|
||
|
|
c = 1
|
||
|
|
|
||
|
|
p = stats.exponweib.pdf(x, a, c)
|
||
|
|
expected = stats.expon.pdf(x)
|
||
|
|
assert_allclose(p, expected)
|
||
|
|
|
||
|
|
logp = stats.exponweib.logpdf(x, a, c)
|
||
|
|
expected = stats.expon.logpdf(x)
|
||
|
|
assert_allclose(logp, expected)
|
||
|
|
|
||
|
|
|
||
|
|
class TestWeibull(object):
|
||
|
|
|
||
|
|
def test_logpdf(self):
|
||
|
|
# gh-6217
|
||
|
|
y = stats.weibull_min.logpdf(0, 1)
|
||
|
|
assert_equal(y, 0)
|
||
|
|
|
||
|
|
def test_with_maxima_distrib(self):
|
||
|
|
# Tests for weibull_min and weibull_max.
|
||
|
|
# The expected values were computed using the symbolic algebra
|
||
|
|
# program 'maxima' with the package 'distrib', which has
|
||
|
|
# 'pdf_weibull' and 'cdf_weibull'. The mapping between the
|
||
|
|
# scipy and maxima functions is as follows:
|
||
|
|
# -----------------------------------------------------------------
|
||
|
|
# scipy maxima
|
||
|
|
# --------------------------------- ------------------------------
|
||
|
|
# weibull_min.pdf(x, a, scale=b) pdf_weibull(x, a, b)
|
||
|
|
# weibull_min.logpdf(x, a, scale=b) log(pdf_weibull(x, a, b))
|
||
|
|
# weibull_min.cdf(x, a, scale=b) cdf_weibull(x, a, b)
|
||
|
|
# weibull_min.logcdf(x, a, scale=b) log(cdf_weibull(x, a, b))
|
||
|
|
# weibull_min.sf(x, a, scale=b) 1 - cdf_weibull(x, a, b)
|
||
|
|
# weibull_min.logsf(x, a, scale=b) log(1 - cdf_weibull(x, a, b))
|
||
|
|
#
|
||
|
|
# weibull_max.pdf(x, a, scale=b) pdf_weibull(-x, a, b)
|
||
|
|
# weibull_max.logpdf(x, a, scale=b) log(pdf_weibull(-x, a, b))
|
||
|
|
# weibull_max.cdf(x, a, scale=b) 1 - cdf_weibull(-x, a, b)
|
||
|
|
# weibull_max.logcdf(x, a, scale=b) log(1 - cdf_weibull(-x, a, b))
|
||
|
|
# weibull_max.sf(x, a, scale=b) cdf_weibull(-x, a, b)
|
||
|
|
# weibull_max.logsf(x, a, scale=b) log(cdf_weibull(-x, a, b))
|
||
|
|
# -----------------------------------------------------------------
|
||
|
|
x = 1.5
|
||
|
|
a = 2.0
|
||
|
|
b = 3.0
|
||
|
|
|
||
|
|
# weibull_min
|
||
|
|
|
||
|
|
p = stats.weibull_min.pdf(x, a, scale=b)
|
||
|
|
assert_allclose(p, np.exp(-0.25)/3)
|
||
|
|
|
||
|
|
lp = stats.weibull_min.logpdf(x, a, scale=b)
|
||
|
|
assert_allclose(lp, -0.25 - np.log(3))
|
||
|
|
|
||
|
|
c = stats.weibull_min.cdf(x, a, scale=b)
|
||
|
|
assert_allclose(c, -special.expm1(-0.25))
|
||
|
|
|
||
|
|
lc = stats.weibull_min.logcdf(x, a, scale=b)
|
||
|
|
assert_allclose(lc, np.log(-special.expm1(-0.25)))
|
||
|
|
|
||
|
|
s = stats.weibull_min.sf(x, a, scale=b)
|
||
|
|
assert_allclose(s, np.exp(-0.25))
|
||
|
|
|
||
|
|
ls = stats.weibull_min.logsf(x, a, scale=b)
|
||
|
|
assert_allclose(ls, -0.25)
|
||
|
|
|
||
|
|
# Also test using a large value x, for which computing the survival
|
||
|
|
# function using the CDF would result in 0.
|
||
|
|
s = stats.weibull_min.sf(30, 2, scale=3)
|
||
|
|
assert_allclose(s, np.exp(-100))
|
||
|
|
|
||
|
|
ls = stats.weibull_min.logsf(30, 2, scale=3)
|
||
|
|
assert_allclose(ls, -100)
|
||
|
|
|
||
|
|
# weibull_max
|
||
|
|
x = -1.5
|
||
|
|
|
||
|
|
p = stats.weibull_max.pdf(x, a, scale=b)
|
||
|
|
assert_allclose(p, np.exp(-0.25)/3)
|
||
|
|
|
||
|
|
lp = stats.weibull_max.logpdf(x, a, scale=b)
|
||
|
|
assert_allclose(lp, -0.25 - np.log(3))
|
||
|
|
|
||
|
|
c = stats.weibull_max.cdf(x, a, scale=b)
|
||
|
|
assert_allclose(c, np.exp(-0.25))
|
||
|
|
|
||
|
|
lc = stats.weibull_max.logcdf(x, a, scale=b)
|
||
|
|
assert_allclose(lc, -0.25)
|
||
|
|
|
||
|
|
s = stats.weibull_max.sf(x, a, scale=b)
|
||
|
|
assert_allclose(s, -special.expm1(-0.25))
|
||
|
|
|
||
|
|
ls = stats.weibull_max.logsf(x, a, scale=b)
|
||
|
|
assert_allclose(ls, np.log(-special.expm1(-0.25)))
|
||
|
|
|
||
|
|
# Also test using a value of x close to 0, for which computing the
|
||
|
|
# survival function using the CDF would result in 0.
|
||
|
|
s = stats.weibull_max.sf(-1e-9, 2, scale=3)
|
||
|
|
assert_allclose(s, -special.expm1(-1/9000000000000000000))
|
||
|
|
|
||
|
|
ls = stats.weibull_max.logsf(-1e-9, 2, scale=3)
|
||
|
|
assert_allclose(ls, np.log(-special.expm1(-1/9000000000000000000)))
|
||
|
|
|
||
|
|
|
||
|
|
class TestRdist(object):
|
||
|
|
@pytest.mark.slow
|
||
|
|
def test_rdist_cdf_gh1285(self):
|
||
|
|
# check workaround in rdist._cdf for issue gh-1285.
|
||
|
|
distfn = stats.rdist
|
||
|
|
values = [0.001, 0.5, 0.999]
|
||
|
|
assert_almost_equal(distfn.cdf(distfn.ppf(values, 541.0), 541.0),
|
||
|
|
values, decimal=5)
|
||
|
|
|
||
|
|
|
||
|
|
class TestTrapz(object):
|
||
|
|
def test_reduces_to_triang(self):
|
||
|
|
modes = [0, 0.3, 0.5, 1]
|
||
|
|
for mode in modes:
|
||
|
|
x = [0, mode, 1]
|
||
|
|
assert_almost_equal(stats.trapz.pdf(x, mode, mode),
|
||
|
|
stats.triang.pdf(x, mode))
|
||
|
|
assert_almost_equal(stats.trapz.cdf(x, mode, mode),
|
||
|
|
stats.triang.cdf(x, mode))
|
||
|
|
|
||
|
|
def test_reduces_to_uniform(self):
|
||
|
|
x = np.linspace(0, 1, 10)
|
||
|
|
assert_almost_equal(stats.trapz.pdf(x, 0, 1), stats.uniform.pdf(x))
|
||
|
|
assert_almost_equal(stats.trapz.cdf(x, 0, 1), stats.uniform.cdf(x))
|
||
|
|
|
||
|
|
def test_cases(self):
|
||
|
|
# edge cases
|
||
|
|
assert_almost_equal(stats.trapz.pdf(0, 0, 0), 2)
|
||
|
|
assert_almost_equal(stats.trapz.pdf(1, 1, 1), 2)
|
||
|
|
assert_almost_equal(stats.trapz.pdf(0.5, 0, 0.8),
|
||
|
|
1.11111111111111111)
|
||
|
|
assert_almost_equal(stats.trapz.pdf(0.5, 0.2, 1.0),
|
||
|
|
1.11111111111111111)
|
||
|
|
|
||
|
|
# straightforward case
|
||
|
|
assert_almost_equal(stats.trapz.pdf(0.1, 0.2, 0.8), 0.625)
|
||
|
|
assert_almost_equal(stats.trapz.pdf(0.5, 0.2, 0.8), 1.25)
|
||
|
|
assert_almost_equal(stats.trapz.pdf(0.9, 0.2, 0.8), 0.625)
|
||
|
|
|
||
|
|
assert_almost_equal(stats.trapz.cdf(0.1, 0.2, 0.8), 0.03125)
|
||
|
|
assert_almost_equal(stats.trapz.cdf(0.2, 0.2, 0.8), 0.125)
|
||
|
|
assert_almost_equal(stats.trapz.cdf(0.5, 0.2, 0.8), 0.5)
|
||
|
|
assert_almost_equal(stats.trapz.cdf(0.9, 0.2, 0.8), 0.96875)
|
||
|
|
assert_almost_equal(stats.trapz.cdf(1.0, 0.2, 0.8), 1.0)
|
||
|
|
|
||
|
|
def test_trapz_vect(self):
|
||
|
|
# test that array-valued shapes and arguments are handled
|
||
|
|
c = np.array([0.1, 0.2, 0.3])
|
||
|
|
d = np.array([0.5, 0.6])[:, None]
|
||
|
|
x = np.array([0.15, 0.25, 0.9])
|
||
|
|
v = stats.trapz.pdf(x, c, d)
|
||
|
|
|
||
|
|
cc, dd, xx = np.broadcast_arrays(c, d, x)
|
||
|
|
|
||
|
|
res = np.empty(xx.size, dtype=xx.dtype)
|
||
|
|
ind = np.arange(xx.size)
|
||
|
|
for i, x1, c1, d1 in zip(ind, xx.ravel(), cc.ravel(), dd.ravel()):
|
||
|
|
res[i] = stats.trapz.pdf(x1, c1, d1)
|
||
|
|
|
||
|
|
assert_allclose(v, res.reshape(v.shape), atol=1e-15)
|
||
|
|
|
||
|
|
|
||
|
|
class TestTriang(object):
|
||
|
|
def test_edge_cases(self):
|
||
|
|
with np.errstate(all='raise'):
|
||
|
|
assert_equal(stats.triang.pdf(0, 0), 2.)
|
||
|
|
assert_equal(stats.triang.pdf(0.5, 0), 1.)
|
||
|
|
assert_equal(stats.triang.pdf(1, 0), 0.)
|
||
|
|
|
||
|
|
assert_equal(stats.triang.pdf(0, 1), 0)
|
||
|
|
assert_equal(stats.triang.pdf(0.5, 1), 1.)
|
||
|
|
assert_equal(stats.triang.pdf(1, 1), 2)
|
||
|
|
|
||
|
|
assert_equal(stats.triang.cdf(0., 0.), 0.)
|
||
|
|
assert_equal(stats.triang.cdf(0.5, 0.), 0.75)
|
||
|
|
assert_equal(stats.triang.cdf(1.0, 0.), 1.0)
|
||
|
|
|
||
|
|
assert_equal(stats.triang.cdf(0., 1.), 0.)
|
||
|
|
assert_equal(stats.triang.cdf(0.5, 1.), 0.25)
|
||
|
|
assert_equal(stats.triang.cdf(1., 1.), 1)
|
||
|
|
|
||
|
|
|
||
|
|
def test_540_567():
|
||
|
|
# test for nan returned in tickets 540, 567
|
||
|
|
assert_almost_equal(stats.norm.cdf(-1.7624320982), 0.03899815971089126,
|
||
|
|
decimal=10, err_msg='test_540_567')
|
||
|
|
assert_almost_equal(stats.norm.cdf(-1.7624320983), 0.038998159702449846,
|
||
|
|
decimal=10, err_msg='test_540_567')
|
||
|
|
assert_almost_equal(stats.norm.cdf(1.38629436112, loc=0.950273420309,
|
||
|
|
scale=0.204423758009),
|
||
|
|
0.98353464004309321,
|
||
|
|
decimal=10, err_msg='test_540_567')
|
||
|
|
|
||
|
|
|
||
|
|
def test_regression_ticket_1316():
|
||
|
|
# The following was raising an exception, because _construct_default_doc()
|
||
|
|
# did not handle the default keyword extradoc=None. See ticket #1316.
|
||
|
|
g = stats._continuous_distns.gamma_gen(name='gamma')
|
||
|
|
|
||
|
|
|
||
|
|
def test_regression_ticket_1326():
|
||
|
|
# adjust to avoid nan with 0*log(0)
|
||
|
|
assert_almost_equal(stats.chi2.pdf(0.0, 2), 0.5, 14)
|
||
|
|
|
||
|
|
|
||
|
|
def test_regression_tukey_lambda():
|
||
|
|
# Make sure that Tukey-Lambda distribution correctly handles
|
||
|
|
# non-positive lambdas.
|
||
|
|
x = np.linspace(-5.0, 5.0, 101)
|
||
|
|
|
||
|
|
olderr = np.seterr(divide='ignore')
|
||
|
|
try:
|
||
|
|
for lam in [0.0, -1.0, -2.0, np.array([[-1.0], [0.0], [-2.0]])]:
|
||
|
|
p = stats.tukeylambda.pdf(x, lam)
|
||
|
|
assert_((p != 0.0).all())
|
||
|
|
assert_(~np.isnan(p).all())
|
||
|
|
|
||
|
|
lam = np.array([[-1.0], [0.0], [2.0]])
|
||
|
|
p = stats.tukeylambda.pdf(x, lam)
|
||
|
|
finally:
|
||
|
|
np.seterr(**olderr)
|
||
|
|
|
||
|
|
assert_(~np.isnan(p).all())
|
||
|
|
assert_((p[0] != 0.0).all())
|
||
|
|
assert_((p[1] != 0.0).all())
|
||
|
|
assert_((p[2] != 0.0).any())
|
||
|
|
assert_((p[2] == 0.0).any())
|
||
|
|
|
||
|
|
|
||
|
|
@pytest.mark.skipif(DOCSTRINGS_STRIPPED, reason="docstrings stripped")
|
||
|
|
def test_regression_ticket_1421():
|
||
|
|
assert_('pdf(x, mu, loc=0, scale=1)' not in stats.poisson.__doc__)
|
||
|
|
assert_('pmf(x,' in stats.poisson.__doc__)
|
||
|
|
|
||
|
|
|
||
|
|
def test_nan_arguments_gh_issue_1362():
|
||
|
|
with np.errstate(invalid='ignore'):
|
||
|
|
assert_(np.isnan(stats.t.logcdf(1, np.nan)))
|
||
|
|
assert_(np.isnan(stats.t.cdf(1, np.nan)))
|
||
|
|
assert_(np.isnan(stats.t.logsf(1, np.nan)))
|
||
|
|
assert_(np.isnan(stats.t.sf(1, np.nan)))
|
||
|
|
assert_(np.isnan(stats.t.pdf(1, np.nan)))
|
||
|
|
assert_(np.isnan(stats.t.logpdf(1, np.nan)))
|
||
|
|
assert_(np.isnan(stats.t.ppf(1, np.nan)))
|
||
|
|
assert_(np.isnan(stats.t.isf(1, np.nan)))
|
||
|
|
|
||
|
|
assert_(np.isnan(stats.bernoulli.logcdf(np.nan, 0.5)))
|
||
|
|
assert_(np.isnan(stats.bernoulli.cdf(np.nan, 0.5)))
|
||
|
|
assert_(np.isnan(stats.bernoulli.logsf(np.nan, 0.5)))
|
||
|
|
assert_(np.isnan(stats.bernoulli.sf(np.nan, 0.5)))
|
||
|
|
assert_(np.isnan(stats.bernoulli.pmf(np.nan, 0.5)))
|
||
|
|
assert_(np.isnan(stats.bernoulli.logpmf(np.nan, 0.5)))
|
||
|
|
assert_(np.isnan(stats.bernoulli.ppf(np.nan, 0.5)))
|
||
|
|
assert_(np.isnan(stats.bernoulli.isf(np.nan, 0.5)))
|
||
|
|
|
||
|
|
|
||
|
|
def test_frozen_fit_ticket_1536():
|
||
|
|
np.random.seed(5678)
|
||
|
|
true = np.array([0.25, 0., 0.5])
|
||
|
|
x = stats.lognorm.rvs(true[0], true[1], true[2], size=100)
|
||
|
|
|
||
|
|
olderr = np.seterr(divide='ignore')
|
||
|
|
try:
|
||
|
|
params = np.array(stats.lognorm.fit(x, floc=0.))
|
||
|
|
finally:
|
||
|
|
np.seterr(**olderr)
|
||
|
|
|
||
|
|
assert_almost_equal(params, true, decimal=2)
|
||
|
|
|
||
|
|
params = np.array(stats.lognorm.fit(x, fscale=0.5, loc=0))
|
||
|
|
assert_almost_equal(params, true, decimal=2)
|
||
|
|
|
||
|
|
params = np.array(stats.lognorm.fit(x, f0=0.25, loc=0))
|
||
|
|
assert_almost_equal(params, true, decimal=2)
|
||
|
|
|
||
|
|
params = np.array(stats.lognorm.fit(x, f0=0.25, floc=0))
|
||
|
|
assert_almost_equal(params, true, decimal=2)
|
||
|
|
|
||
|
|
np.random.seed(5678)
|
||
|
|
loc = 1
|
||
|
|
floc = 0.9
|
||
|
|
x = stats.norm.rvs(loc, 2., size=100)
|
||
|
|
params = np.array(stats.norm.fit(x, floc=floc))
|
||
|
|
expected = np.array([floc, np.sqrt(((x-floc)**2).mean())])
|
||
|
|
assert_almost_equal(params, expected, decimal=4)
|
||
|
|
|
||
|
|
|
||
|
|
def test_regression_ticket_1530():
|
||
|
|
# Check the starting value works for Cauchy distribution fit.
|
||
|
|
np.random.seed(654321)
|
||
|
|
rvs = stats.cauchy.rvs(size=100)
|
||
|
|
params = stats.cauchy.fit(rvs)
|
||
|
|
expected = (0.045, 1.142)
|
||
|
|
assert_almost_equal(params, expected, decimal=1)
|
||
|
|
|
||
|
|
|
||
|
|
def test_gh_pr_4806():
|
||
|
|
# Check starting values for Cauchy distribution fit.
|
||
|
|
np.random.seed(1234)
|
||
|
|
x = np.random.randn(42)
|
||
|
|
for offset in 10000.0, 1222333444.0:
|
||
|
|
loc, scale = stats.cauchy.fit(x + offset)
|
||
|
|
assert_allclose(loc, offset, atol=1.0)
|
||
|
|
assert_allclose(scale, 0.6, atol=1.0)
|
||
|
|
|
||
|
|
|
||
|
|
def test_tukeylambda_stats_ticket_1545():
|
||
|
|
# Some test for the variance and kurtosis of the Tukey Lambda distr.
|
||
|
|
# See test_tukeylamdba_stats.py for more tests.
|
||
|
|
|
||
|
|
mv = stats.tukeylambda.stats(0, moments='mvsk')
|
||
|
|
# Known exact values:
|
||
|
|
expected = [0, np.pi**2/3, 0, 1.2]
|
||
|
|
assert_almost_equal(mv, expected, decimal=10)
|
||
|
|
|
||
|
|
mv = stats.tukeylambda.stats(3.13, moments='mvsk')
|
||
|
|
# 'expected' computed with mpmath.
|
||
|
|
expected = [0, 0.0269220858861465102, 0, -0.898062386219224104]
|
||
|
|
assert_almost_equal(mv, expected, decimal=10)
|
||
|
|
|
||
|
|
mv = stats.tukeylambda.stats(0.14, moments='mvsk')
|
||
|
|
# 'expected' computed with mpmath.
|
||
|
|
expected = [0, 2.11029702221450250, 0, -0.02708377353223019456]
|
||
|
|
assert_almost_equal(mv, expected, decimal=10)
|
||
|
|
|
||
|
|
|
||
|
|
def test_poisson_logpmf_ticket_1436():
|
||
|
|
assert_(np.isfinite(stats.poisson.logpmf(1500, 200)))
|
||
|
|
|
||
|
|
|
||
|
|
def test_powerlaw_stats():
|
||
|
|
"""Test the powerlaw stats function.
|
||
|
|
|
||
|
|
This unit test is also a regression test for ticket 1548.
|
||
|
|
|
||
|
|
The exact values are:
|
||
|
|
mean:
|
||
|
|
mu = a / (a + 1)
|
||
|
|
variance:
|
||
|
|
sigma**2 = a / ((a + 2) * (a + 1) ** 2)
|
||
|
|
skewness:
|
||
|
|
One formula (see https://en.wikipedia.org/wiki/Skewness) is
|
||
|
|
gamma_1 = (E[X**3] - 3*mu*E[X**2] + 2*mu**3) / sigma**3
|
||
|
|
A short calculation shows that E[X**k] is a / (a + k), so gamma_1
|
||
|
|
can be implemented as
|
||
|
|
n = a/(a+3) - 3*(a/(a+1))*a/(a+2) + 2*(a/(a+1))**3
|
||
|
|
d = sqrt(a/((a+2)*(a+1)**2)) ** 3
|
||
|
|
gamma_1 = n/d
|
||
|
|
Either by simplifying, or by a direct calculation of mu_3 / sigma**3,
|
||
|
|
one gets the more concise formula:
|
||
|
|
gamma_1 = -2.0 * ((a - 1) / (a + 3)) * sqrt((a + 2) / a)
|
||
|
|
kurtosis: (See https://en.wikipedia.org/wiki/Kurtosis)
|
||
|
|
The excess kurtosis is
|
||
|
|
gamma_2 = mu_4 / sigma**4 - 3
|
||
|
|
A bit of calculus and algebra (sympy helps) shows that
|
||
|
|
mu_4 = 3*a*(3*a**2 - a + 2) / ((a+1)**4 * (a+2) * (a+3) * (a+4))
|
||
|
|
so
|
||
|
|
gamma_2 = 3*(3*a**2 - a + 2) * (a+2) / (a*(a+3)*(a+4)) - 3
|
||
|
|
which can be rearranged to
|
||
|
|
gamma_2 = 6 * (a**3 - a**2 - 6*a + 2) / (a*(a+3)*(a+4))
|
||
|
|
"""
|
||
|
|
cases = [(1.0, (0.5, 1./12, 0.0, -1.2)),
|
||
|
|
(2.0, (2./3, 2./36, -0.56568542494924734, -0.6))]
|
||
|
|
for a, exact_mvsk in cases:
|
||
|
|
mvsk = stats.powerlaw.stats(a, moments="mvsk")
|
||
|
|
assert_array_almost_equal(mvsk, exact_mvsk)
|
||
|
|
|
||
|
|
|
||
|
|
def test_powerlaw_edge():
|
||
|
|
# Regression test for gh-3986.
|
||
|
|
p = stats.powerlaw.logpdf(0, 1)
|
||
|
|
assert_equal(p, 0.0)
|
||
|
|
|
||
|
|
|
||
|
|
def test_exponpow_edge():
|
||
|
|
# Regression test for gh-3982.
|
||
|
|
p = stats.exponpow.logpdf(0, 1)
|
||
|
|
assert_equal(p, 0.0)
|
||
|
|
|
||
|
|
# Check pdf and logpdf at x = 0 for other values of b.
|
||
|
|
p = stats.exponpow.pdf(0, [0.25, 1.0, 1.5])
|
||
|
|
assert_equal(p, [np.inf, 1.0, 0.0])
|
||
|
|
p = stats.exponpow.logpdf(0, [0.25, 1.0, 1.5])
|
||
|
|
assert_equal(p, [np.inf, 0.0, -np.inf])
|
||
|
|
|
||
|
|
|
||
|
|
def test_gengamma_edge():
|
||
|
|
# Regression test for gh-3985.
|
||
|
|
p = stats.gengamma.pdf(0, 1, 1)
|
||
|
|
assert_equal(p, 1.0)
|
||
|
|
|
||
|
|
# Regression tests for gh-4724.
|
||
|
|
p = stats.gengamma._munp(-2, 200, 1.)
|
||
|
|
assert_almost_equal(p, 1./199/198)
|
||
|
|
|
||
|
|
p = stats.gengamma._munp(-2, 10, 1.)
|
||
|
|
assert_almost_equal(p, 1./9/8)
|
||
|
|
|
||
|
|
|
||
|
|
def test_ksone_fit_freeze():
|
||
|
|
# Regression test for ticket #1638.
|
||
|
|
d = np.array(
|
||
|
|
[-0.18879233, 0.15734249, 0.18695107, 0.27908787, -0.248649,
|
||
|
|
-0.2171497, 0.12233512, 0.15126419, 0.03119282, 0.4365294,
|
||
|
|
0.08930393, -0.23509903, 0.28231224, -0.09974875, -0.25196048,
|
||
|
|
0.11102028, 0.1427649, 0.10176452, 0.18754054, 0.25826724,
|
||
|
|
0.05988819, 0.0531668, 0.21906056, 0.32106729, 0.2117662,
|
||
|
|
0.10886442, 0.09375789, 0.24583286, -0.22968366, -0.07842391,
|
||
|
|
-0.31195432, -0.21271196, 0.1114243, -0.13293002, 0.01331725,
|
||
|
|
-0.04330977, -0.09485776, -0.28434547, 0.22245721, -0.18518199,
|
||
|
|
-0.10943985, -0.35243174, 0.06897665, -0.03553363, -0.0701746,
|
||
|
|
-0.06037974, 0.37670779, -0.21684405])
|
||
|
|
|
||
|
|
try:
|
||
|
|
olderr = np.seterr(invalid='ignore')
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.filter(IntegrationWarning,
|
||
|
|
"The maximum number of subdivisions .50. has been "
|
||
|
|
"achieved.")
|
||
|
|
sup.filter(RuntimeWarning,
|
||
|
|
"floating point number truncated to an integer")
|
||
|
|
stats.ksone.fit(d)
|
||
|
|
finally:
|
||
|
|
np.seterr(**olderr)
|
||
|
|
|
||
|
|
|
||
|
|
def test_norm_logcdf():
|
||
|
|
# Test precision of the logcdf of the normal distribution.
|
||
|
|
# This precision was enhanced in ticket 1614.
|
||
|
|
x = -np.asarray(list(range(0, 120, 4)))
|
||
|
|
# Values from R
|
||
|
|
expected = [-0.69314718, -10.36010149, -35.01343716, -75.41067300,
|
||
|
|
-131.69539607, -203.91715537, -292.09872100, -396.25241451,
|
||
|
|
-516.38564863, -652.50322759, -804.60844201, -972.70364403,
|
||
|
|
-1156.79057310, -1356.87055173, -1572.94460885, -1805.01356068,
|
||
|
|
-2053.07806561, -2317.13866238, -2597.19579746, -2893.24984493,
|
||
|
|
-3205.30112136, -3533.34989701, -3877.39640444, -4237.44084522,
|
||
|
|
-4613.48339520, -5005.52420869, -5413.56342187, -5837.60115548,
|
||
|
|
-6277.63751711, -6733.67260303]
|
||
|
|
|
||
|
|
assert_allclose(stats.norm().logcdf(x), expected, atol=1e-8)
|
||
|
|
|
||
|
|
# also test the complex-valued code path
|
||
|
|
assert_allclose(stats.norm().logcdf(x + 1e-14j).real, expected, atol=1e-8)
|
||
|
|
|
||
|
|
# test the accuracy: d(logcdf)/dx = pdf / cdf \equiv exp(logpdf - logcdf)
|
||
|
|
deriv = (stats.norm.logcdf(x + 1e-10j)/1e-10).imag
|
||
|
|
deriv_expected = np.exp(stats.norm.logpdf(x) - stats.norm.logcdf(x))
|
||
|
|
assert_allclose(deriv, deriv_expected, atol=1e-10)
|
||
|
|
|
||
|
|
|
||
|
|
def test_levy_cdf_ppf():
|
||
|
|
# Test levy.cdf, including small arguments.
|
||
|
|
x = np.array([1000, 1.0, 0.5, 0.1, 0.01, 0.001])
|
||
|
|
|
||
|
|
# Expected values were calculated separately with mpmath.
|
||
|
|
# E.g.
|
||
|
|
# >>> mpmath.mp.dps = 100
|
||
|
|
# >>> x = mpmath.mp.mpf('0.01')
|
||
|
|
# >>> cdf = mpmath.erfc(mpmath.sqrt(1/(2*x)))
|
||
|
|
expected = np.array([0.9747728793699604,
|
||
|
|
0.3173105078629141,
|
||
|
|
0.1572992070502851,
|
||
|
|
0.0015654022580025495,
|
||
|
|
1.523970604832105e-23,
|
||
|
|
1.795832784800726e-219])
|
||
|
|
|
||
|
|
y = stats.levy.cdf(x)
|
||
|
|
assert_allclose(y, expected, rtol=1e-10)
|
||
|
|
|
||
|
|
# ppf(expected) should get us back to x.
|
||
|
|
xx = stats.levy.ppf(expected)
|
||
|
|
assert_allclose(xx, x, rtol=1e-13)
|
||
|
|
|
||
|
|
|
||
|
|
def test_hypergeom_interval_1802():
|
||
|
|
# these two had endless loops
|
||
|
|
assert_equal(stats.hypergeom.interval(.95, 187601, 43192, 757),
|
||
|
|
(152.0, 197.0))
|
||
|
|
assert_equal(stats.hypergeom.interval(.945, 187601, 43192, 757),
|
||
|
|
(152.0, 197.0))
|
||
|
|
# this was working also before
|
||
|
|
assert_equal(stats.hypergeom.interval(.94, 187601, 43192, 757),
|
||
|
|
(153.0, 196.0))
|
||
|
|
|
||
|
|
# degenerate case .a == .b
|
||
|
|
assert_equal(stats.hypergeom.ppf(0.02, 100, 100, 8), 8)
|
||
|
|
assert_equal(stats.hypergeom.ppf(1, 100, 100, 8), 8)
|
||
|
|
|
||
|
|
|
||
|
|
def test_distribution_too_many_args():
|
||
|
|
np.random.seed(1234)
|
||
|
|
|
||
|
|
# Check that a TypeError is raised when too many args are given to a method
|
||
|
|
# Regression test for ticket 1815.
|
||
|
|
x = np.linspace(0.1, 0.7, num=5)
|
||
|
|
assert_raises(TypeError, stats.gamma.pdf, x, 2, 3, loc=1.0)
|
||
|
|
assert_raises(TypeError, stats.gamma.pdf, x, 2, 3, 4, loc=1.0)
|
||
|
|
assert_raises(TypeError, stats.gamma.pdf, x, 2, 3, 4, 5)
|
||
|
|
assert_raises(TypeError, stats.gamma.pdf, x, 2, 3, loc=1.0, scale=0.5)
|
||
|
|
assert_raises(TypeError, stats.gamma.rvs, 2., 3, loc=1.0, scale=0.5)
|
||
|
|
assert_raises(TypeError, stats.gamma.cdf, x, 2., 3, loc=1.0, scale=0.5)
|
||
|
|
assert_raises(TypeError, stats.gamma.ppf, x, 2., 3, loc=1.0, scale=0.5)
|
||
|
|
assert_raises(TypeError, stats.gamma.stats, 2., 3, loc=1.0, scale=0.5)
|
||
|
|
assert_raises(TypeError, stats.gamma.entropy, 2., 3, loc=1.0, scale=0.5)
|
||
|
|
assert_raises(TypeError, stats.gamma.fit, x, 2., 3, loc=1.0, scale=0.5)
|
||
|
|
|
||
|
|
# These should not give errors
|
||
|
|
stats.gamma.pdf(x, 2, 3) # loc=3
|
||
|
|
stats.gamma.pdf(x, 2, 3, 4) # loc=3, scale=4
|
||
|
|
stats.gamma.stats(2., 3)
|
||
|
|
stats.gamma.stats(2., 3, 4)
|
||
|
|
stats.gamma.stats(2., 3, 4, 'mv')
|
||
|
|
stats.gamma.rvs(2., 3, 4, 5)
|
||
|
|
stats.gamma.fit(stats.gamma.rvs(2., size=7), 2.)
|
||
|
|
|
||
|
|
# Also for a discrete distribution
|
||
|
|
stats.geom.pmf(x, 2, loc=3) # no error, loc=3
|
||
|
|
assert_raises(TypeError, stats.geom.pmf, x, 2, 3, 4)
|
||
|
|
assert_raises(TypeError, stats.geom.pmf, x, 2, 3, loc=4)
|
||
|
|
|
||
|
|
# And for distributions with 0, 2 and 3 args respectively
|
||
|
|
assert_raises(TypeError, stats.expon.pdf, x, 3, loc=1.0)
|
||
|
|
assert_raises(TypeError, stats.exponweib.pdf, x, 3, 4, 5, loc=1.0)
|
||
|
|
assert_raises(TypeError, stats.exponweib.pdf, x, 3, 4, 5, 0.1, 0.1)
|
||
|
|
assert_raises(TypeError, stats.ncf.pdf, x, 3, 4, 5, 6, loc=1.0)
|
||
|
|
assert_raises(TypeError, stats.ncf.pdf, x, 3, 4, 5, 6, 1.0, scale=0.5)
|
||
|
|
stats.ncf.pdf(x, 3, 4, 5, 6, 1.0) # 3 args, plus loc/scale
|
||
|
|
|
||
|
|
|
||
|
|
def test_ncx2_tails_ticket_955():
|
||
|
|
# Trac #955 -- check that the cdf computed by special functions
|
||
|
|
# matches the integrated pdf
|
||
|
|
a = stats.ncx2.cdf(np.arange(20, 25, 0.2), 2, 1.07458615e+02)
|
||
|
|
b = stats.ncx2._cdfvec(np.arange(20, 25, 0.2), 2, 1.07458615e+02)
|
||
|
|
assert_allclose(a, b, rtol=1e-3, atol=0)
|
||
|
|
|
||
|
|
|
||
|
|
def test_ncx2_tails_pdf():
|
||
|
|
# ncx2.pdf does not return nans in extreme tails(example from gh-1577)
|
||
|
|
# NB: this is to check that nan_to_num is not needed in ncx2.pdf
|
||
|
|
with suppress_warnings() as sup:
|
||
|
|
sup.filter(RuntimeWarning, "divide by zero encountered in log")
|
||
|
|
assert_equal(stats.ncx2.pdf(1, np.arange(340, 350), 2), 0)
|
||
|
|
logval = stats.ncx2.logpdf(1, np.arange(340, 350), 2)
|
||
|
|
|
||
|
|
assert_(np.isneginf(logval).all())
|
||
|
|
|
||
|
|
|
||
|
|
def test_foldnorm_zero():
|
||
|
|
# Parameter value c=0 was not enabled, see gh-2399.
|
||
|
|
rv = stats.foldnorm(0, scale=1)
|
||
|
|
assert_equal(rv.cdf(0), 0) # rv.cdf(0) previously resulted in: nan
|
||
|
|
|
||
|
|
|
||
|
|
def test_stats_shapes_argcheck():
|
||
|
|
# stats method was failing for vector shapes if some of the values
|
||
|
|
# were outside of the allowed range, see gh-2678
|
||
|
|
mv3 = stats.invgamma.stats([0.0, 0.5, 1.0], 1, 0.5) # 0 is not a legal `a`
|
||
|
|
mv2 = stats.invgamma.stats([0.5, 1.0], 1, 0.5)
|
||
|
|
mv2_augmented = tuple(np.r_[np.nan, _] for _ in mv2)
|
||
|
|
assert_equal(mv2_augmented, mv3)
|
||
|
|
|
||
|
|
# -1 is not a legal shape parameter
|
||
|
|
mv3 = stats.lognorm.stats([2, 2.4, -1])
|
||
|
|
mv2 = stats.lognorm.stats([2, 2.4])
|
||
|
|
mv2_augmented = tuple(np.r_[_, np.nan] for _ in mv2)
|
||
|
|
assert_equal(mv2_augmented, mv3)
|
||
|
|
|
||
|
|
# FIXME: this is only a quick-and-dirty test of a quick-and-dirty bugfix.
|
||
|
|
# stats method with multiple shape parameters is not properly vectorized
|
||
|
|
# anyway, so some distributions may or may not fail.
|
||
|
|
|
||
|
|
|
||
|
|
# Test subclassing distributions w/ explicit shapes
|
||
|
|
|
||
|
|
class _distr_gen(stats.rv_continuous):
|
||
|
|
def _pdf(self, x, a):
|
||
|
|
return 42
|
||
|
|
|
||
|
|
|
||
|
|
class _distr2_gen(stats.rv_continuous):
|
||
|
|
def _cdf(self, x, a):
|
||
|
|
return 42 * a + x
|
||
|
|
|
||
|
|
|
||
|
|
class _distr3_gen(stats.rv_continuous):
|
||
|
|
def _pdf(self, x, a, b):
|
||
|
|
return a + b
|
||
|
|
|
||
|
|
def _cdf(self, x, a):
|
||
|
|
# Different # of shape params from _pdf, to be able to check that
|
||
|
|
# inspection catches the inconsistency."""
|
||
|
|
return 42 * a + x
|
||
|
|
|
||
|
|
|
||
|
|
class _distr6_gen(stats.rv_continuous):
|
||
|
|
# Two shape parameters (both _pdf and _cdf defined, consistent shapes.)
|
||
|
|
def _pdf(self, x, a, b):
|
||
|
|
return a*x + b
|
||
|
|
|
||
|
|
def _cdf(self, x, a, b):
|
||
|
|
return 42 * a + x
|
||
|
|
|
||
|
|
|
||
|
|
class TestSubclassingExplicitShapes(object):
|
||
|
|
# Construct a distribution w/ explicit shapes parameter and test it.
|
||
|
|
|
||
|
|
def test_correct_shapes(self):
|
||
|
|
dummy_distr = _distr_gen(name='dummy', shapes='a')
|
||
|
|
assert_equal(dummy_distr.pdf(1, a=1), 42)
|
||
|
|
|
||
|
|
def test_wrong_shapes_1(self):
|
||
|
|
dummy_distr = _distr_gen(name='dummy', shapes='A')
|
||
|
|
assert_raises(TypeError, dummy_distr.pdf, 1, **dict(a=1))
|
||
|
|
|
||
|
|
def test_wrong_shapes_2(self):
|
||
|
|
dummy_distr = _distr_gen(name='dummy', shapes='a, b, c')
|
||
|
|
dct = dict(a=1, b=2, c=3)
|
||
|
|
assert_raises(TypeError, dummy_distr.pdf, 1, **dct)
|
||
|
|
|
||
|
|
def test_shapes_string(self):
|
||
|
|
# shapes must be a string
|
||
|
|
dct = dict(name='dummy', shapes=42)
|
||
|
|
assert_raises(TypeError, _distr_gen, **dct)
|
||
|
|
|
||
|
|
def test_shapes_identifiers_1(self):
|
||
|
|
# shapes must be a comma-separated list of valid python identifiers
|
||
|
|
dct = dict(name='dummy', shapes='(!)')
|
||
|
|
assert_raises(SyntaxError, _distr_gen, **dct)
|
||
|
|
|
||
|
|
def test_shapes_identifiers_2(self):
|
||
|
|
dct = dict(name='dummy', shapes='4chan')
|
||
|
|
assert_raises(SyntaxError, _distr_gen, **dct)
|
||
|
|
|
||
|
|
def test_shapes_identifiers_3(self):
|
||
|
|
dct = dict(name='dummy', shapes='m(fti)')
|
||
|
|
assert_raises(SyntaxError, _distr_gen, **dct)
|
||
|
|
|
||
|
|
def test_shapes_identifiers_nodefaults(self):
|
||
|
|
dct = dict(name='dummy', shapes='a=2')
|
||
|
|
assert_raises(SyntaxError, _distr_gen, **dct)
|
||
|
|
|
||
|
|
def test_shapes_args(self):
|
||
|
|
dct = dict(name='dummy', shapes='*args')
|
||
|
|
assert_raises(SyntaxError, _distr_gen, **dct)
|
||
|
|
|
||
|
|
def test_shapes_kwargs(self):
|
||
|
|
dct = dict(name='dummy', shapes='**kwargs')
|
||
|
|
assert_raises(SyntaxError, _distr_gen, **dct)
|
||
|
|
|
||
|
|
def test_shapes_keywords(self):
|
||
|
|
# python keywords cannot be used for shape parameters
|
||
|
|
dct = dict(name='dummy', shapes='a, b, c, lambda')
|
||
|
|
assert_raises(SyntaxError, _distr_gen, **dct)
|
||
|
|
|
||
|
|
def test_shapes_signature(self):
|
||
|
|
# test explicit shapes which agree w/ the signature of _pdf
|
||
|
|
class _dist_gen(stats.rv_continuous):
|
||
|
|
def _pdf(self, x, a):
|
||
|
|
return stats.norm._pdf(x) * a
|
||
|
|
|
||
|
|
dist = _dist_gen(shapes='a')
|
||
|
|
assert_equal(dist.pdf(0.5, a=2), stats.norm.pdf(0.5)*2)
|
||
|
|
|
||
|
|
def test_shapes_signature_inconsistent(self):
|
||
|
|
# test explicit shapes which do not agree w/ the signature of _pdf
|
||
|
|
class _dist_gen(stats.rv_continuous):
|
||
|
|
def _pdf(self, x, a):
|
||
|
|
return stats.norm._pdf(x) * a
|
||
|
|
|
||
|
|
dist = _dist_gen(shapes='a, b')
|
||
|
|
assert_raises(TypeError, dist.pdf, 0.5, **dict(a=1, b=2))
|
||
|
|
|
||
|
|
def test_star_args(self):
|
||
|
|
# test _pdf with only starargs
|
||
|
|
# NB: **kwargs of pdf will never reach _pdf
|
||
|
|
class _dist_gen(stats.rv_continuous):
|
||
|
|
def _pdf(self, x, *args):
|
||
|
|
extra_kwarg = args[0]
|
||
|
|
return stats.norm._pdf(x) * extra_kwarg
|
||
|
|
|
||
|
|
dist = _dist_gen(shapes='extra_kwarg')
|
||
|
|
assert_equal(dist.pdf(0.5, extra_kwarg=33), stats.norm.pdf(0.5)*33)
|
||
|
|
assert_equal(dist.pdf(0.5, 33), stats.norm.pdf(0.5)*33)
|
||
|
|
assert_raises(TypeError, dist.pdf, 0.5, **dict(xxx=33))
|
||
|
|
|
||
|
|
def test_star_args_2(self):
|
||
|
|
# test _pdf with named & starargs
|
||
|
|
# NB: **kwargs of pdf will never reach _pdf
|
||
|
|
class _dist_gen(stats.rv_continuous):
|
||
|
|
def _pdf(self, x, offset, *args):
|
||
|
|
extra_kwarg = args[0]
|
||
|
|
return stats.norm._pdf(x) * extra_kwarg + offset
|
||
|
|
|
||
|
|
dist = _dist_gen(shapes='offset, extra_kwarg')
|
||
|
|
assert_equal(dist.pdf(0.5, offset=111, extra_kwarg=33),
|
||
|
|
stats.norm.pdf(0.5)*33 + 111)
|
||
|
|
assert_equal(dist.pdf(0.5, 111, 33),
|
||
|
|
stats.norm.pdf(0.5)*33 + 111)
|
||
|
|
|
||
|
|
def test_extra_kwarg(self):
|
||
|
|
# **kwargs to _pdf are ignored.
|
||
|
|
# this is a limitation of the framework (_pdf(x, *goodargs))
|
||
|
|
class _distr_gen(stats.rv_continuous):
|
||
|
|
def _pdf(self, x, *args, **kwargs):
|
||
|
|
# _pdf should handle *args, **kwargs itself. Here "handling"
|
||
|
|
# is ignoring *args and looking for ``extra_kwarg`` and using
|
||
|
|
# that.
|
||
|
|
extra_kwarg = kwargs.pop('extra_kwarg', 1)
|
||
|
|
return stats.norm._pdf(x) * extra_kwarg
|
||
|
|
|
||
|
|
dist = _distr_gen(shapes='extra_kwarg')
|
||
|
|
assert_equal(dist.pdf(1, extra_kwarg=3), stats.norm.pdf(1))
|
||
|
|
|
||
|
|
def shapes_empty_string(self):
|
||
|
|
# shapes='' is equivalent to shapes=None
|
||
|
|
class _dist_gen(stats.rv_continuous):
|
||
|
|
def _pdf(self, x):
|
||
|
|
return stats.norm.pdf(x)
|
||
|
|
|
||
|
|
dist = _dist_gen(shapes='')
|
||
|
|
assert_equal(dist.pdf(0.5), stats.norm.pdf(0.5))
|
||
|
|
|
||
|
|
|
||
|
|
class TestSubclassingNoShapes(object):
|
||
|
|
# Construct a distribution w/o explicit shapes parameter and test it.
|
||
|
|
|
||
|
|
def test_only__pdf(self):
|
||
|
|
dummy_distr = _distr_gen(name='dummy')
|
||
|
|
assert_equal(dummy_distr.pdf(1, a=1), 42)
|
||
|
|
|
||
|
|
def test_only__cdf(self):
|
||
|
|
# _pdf is determined from _cdf by taking numerical derivative
|
||
|
|
dummy_distr = _distr2_gen(name='dummy')
|
||
|
|
assert_almost_equal(dummy_distr.pdf(1, a=1), 1)
|
||
|
|
|
||
|
|
@pytest.mark.skipif(DOCSTRINGS_STRIPPED, reason="docstring stripped")
|
||
|
|
def test_signature_inspection(self):
|
||
|
|
# check that _pdf signature inspection works correctly, and is used in
|
||
|
|
# the class docstring
|
||
|
|
dummy_distr = _distr_gen(name='dummy')
|
||
|
|
assert_equal(dummy_distr.numargs, 1)
|
||
|
|
assert_equal(dummy_distr.shapes, 'a')
|
||
|
|
res = re.findall(r'logpdf\(x, a, loc=0, scale=1\)',
|
||
|
|
dummy_distr.__doc__)
|
||
|
|
assert_(len(res) == 1)
|
||
|
|
|
||
|
|
@pytest.mark.skipif(DOCSTRINGS_STRIPPED, reason="docstring stripped")
|
||
|
|
def test_signature_inspection_2args(self):
|
||
|
|
# same for 2 shape params and both _pdf and _cdf defined
|
||
|
|
dummy_distr = _distr6_gen(name='dummy')
|
||
|
|
assert_equal(dummy_distr.numargs, 2)
|
||
|
|
assert_equal(dummy_distr.shapes, 'a, b')
|
||
|
|
res = re.findall(r'logpdf\(x, a, b, loc=0, scale=1\)',
|
||
|
|
dummy_distr.__doc__)
|
||
|
|
assert_(len(res) == 1)
|
||
|
|
|
||
|
|
def test_signature_inspection_2args_incorrect_shapes(self):
|
||
|
|
# both _pdf and _cdf defined, but shapes are inconsistent: raises
|
||
|
|
assert_raises(TypeError, _distr3_gen, name='dummy')
|
||
|
|
|
||
|
|
def test_defaults_raise(self):
|
||
|
|
# default arguments should raise
|
||
|
|
class _dist_gen(stats.rv_continuous):
|
||
|
|
def _pdf(self, x, a=42):
|
||
|
|
return 42
|
||
|
|
assert_raises(TypeError, _dist_gen, **dict(name='dummy'))
|
||
|
|
|
||
|
|
def test_starargs_raise(self):
|
||
|
|
# without explicit shapes, *args are not allowed
|
||
|
|
class _dist_gen(stats.rv_continuous):
|
||
|
|
def _pdf(self, x, a, *args):
|
||
|
|
return 42
|
||
|
|
assert_raises(TypeError, _dist_gen, **dict(name='dummy'))
|
||
|
|
|
||
|
|
def test_kwargs_raise(self):
|
||
|
|
# without explicit shapes, **kwargs are not allowed
|
||
|
|
class _dist_gen(stats.rv_continuous):
|
||
|
|
def _pdf(self, x, a, **kwargs):
|
||
|
|
return 42
|
||
|
|
assert_raises(TypeError, _dist_gen, **dict(name='dummy'))
|
||
|
|
|
||
|
|
|
||
|
|
@pytest.mark.skipif(DOCSTRINGS_STRIPPED, reason="docstring stripped")
|
||
|
|
def test_docstrings():
|
||
|
|
badones = [r',\s*,', r'\(\s*,', r'^\s*:']
|
||
|
|
for distname in stats.__all__:
|
||
|
|
dist = getattr(stats, distname)
|
||
|
|
if isinstance(dist, (stats.rv_discrete, stats.rv_continuous)):
|
||
|
|
for regex in badones:
|
||
|
|
assert_(re.search(regex, dist.__doc__) is None)
|
||
|
|
|
||
|
|
|
||
|
|
def test_infinite_input():
|
||
|
|
assert_almost_equal(stats.skellam.sf(np.inf, 10, 11), 0)
|
||
|
|
assert_almost_equal(stats.ncx2._cdf(np.inf, 8, 0.1), 1)
|
||
|
|
|
||
|
|
|
||
|
|
def test_lomax_accuracy():
|
||
|
|
# regression test for gh-4033
|
||
|
|
p = stats.lomax.ppf(stats.lomax.cdf(1e-100, 1), 1)
|
||
|
|
assert_allclose(p, 1e-100)
|
||
|
|
|
||
|
|
|
||
|
|
def test_gompertz_accuracy():
|
||
|
|
# Regression test for gh-4031
|
||
|
|
p = stats.gompertz.ppf(stats.gompertz.cdf(1e-100, 1), 1)
|
||
|
|
assert_allclose(p, 1e-100)
|
||
|
|
|
||
|
|
|
||
|
|
def test_truncexpon_accuracy():
|
||
|
|
# regression test for gh-4035
|
||
|
|
p = stats.truncexpon.ppf(stats.truncexpon.cdf(1e-100, 1), 1)
|
||
|
|
assert_allclose(p, 1e-100)
|
||
|
|
|
||
|
|
|
||
|
|
def test_rayleigh_accuracy():
|
||
|
|
# regression test for gh-4034
|
||
|
|
p = stats.rayleigh.isf(stats.rayleigh.sf(9, 1), 1)
|
||
|
|
assert_almost_equal(p, 9.0, decimal=15)
|
||
|
|
|
||
|
|
|
||
|
|
def test_genextreme_give_no_warnings():
|
||
|
|
"""regression test for gh-6219"""
|
||
|
|
|
||
|
|
with warnings.catch_warnings(record=True) as w:
|
||
|
|
warnings.simplefilter("always")
|
||
|
|
|
||
|
|
p = stats.genextreme.cdf(.5, 0)
|
||
|
|
p = stats.genextreme.pdf(.5, 0)
|
||
|
|
p = stats.genextreme.ppf(.5, 0)
|
||
|
|
p = stats.genextreme.logpdf(-np.inf, 0.0)
|
||
|
|
number_of_warnings_thrown = len(w)
|
||
|
|
assert_equal(number_of_warnings_thrown, 0)
|
||
|
|
|
||
|
|
|
||
|
|
def test_genextreme_entropy():
|
||
|
|
# regression test for gh-5181
|
||
|
|
euler_gamma = 0.5772156649015329
|
||
|
|
|
||
|
|
h = stats.genextreme.entropy(-1.0)
|
||
|
|
assert_allclose(h, 2*euler_gamma + 1, rtol=1e-14)
|
||
|
|
|
||
|
|
h = stats.genextreme.entropy(0)
|
||
|
|
assert_allclose(h, euler_gamma + 1, rtol=1e-14)
|
||
|
|
|
||
|
|
h = stats.genextreme.entropy(1.0)
|
||
|
|
assert_equal(h, 1)
|
||
|
|
|
||
|
|
h = stats.genextreme.entropy(-2.0, scale=10)
|
||
|
|
assert_allclose(h, euler_gamma*3 + np.log(10) + 1, rtol=1e-14)
|
||
|
|
|
||
|
|
h = stats.genextreme.entropy(10)
|
||
|
|
assert_allclose(h, -9*euler_gamma + 1, rtol=1e-14)
|
||
|
|
|
||
|
|
h = stats.genextreme.entropy(-10)
|
||
|
|
assert_allclose(h, 11*euler_gamma + 1, rtol=1e-14)
|
||
|
|
|
||
|
|
|
||
|
|
def test_genextreme_sf_isf():
|
||
|
|
# Expected values were computed using mpmath:
|
||
|
|
#
|
||
|
|
# import mpmath
|
||
|
|
#
|
||
|
|
# def mp_genextreme_sf(x, xi, mu=0, sigma=1):
|
||
|
|
# # Formula from wikipedia, which has a sign convention for xi that
|
||
|
|
# # is the opposite of scipy's shape parameter.
|
||
|
|
# if xi != 0:
|
||
|
|
# t = mpmath.power(1 + ((x - mu)/sigma)*xi, -1/xi)
|
||
|
|
# else:
|
||
|
|
# t = mpmath.exp(-(x - mu)/sigma)
|
||
|
|
# return 1 - mpmath.exp(-t)
|
||
|
|
#
|
||
|
|
# >>> mpmath.mp.dps = 1000
|
||
|
|
# >>> s = mp_genextreme_sf(mpmath.mp.mpf("1e8"), mpmath.mp.mpf("0.125"))
|
||
|
|
# >>> float(s)
|
||
|
|
# 1.6777205262585625e-57
|
||
|
|
# >>> s = mp_genextreme_sf(mpmath.mp.mpf("7.98"), mpmath.mp.mpf("-0.125"))
|
||
|
|
# >>> float(s)
|
||
|
|
# 1.52587890625e-21
|
||
|
|
# >>> s = mp_genextreme_sf(mpmath.mp.mpf("7.98"), mpmath.mp.mpf("0"))
|
||
|
|
# >>> float(s)
|
||
|
|
# 0.00034218086528426593
|
||
|
|
|
||
|
|
x = 1e8
|
||
|
|
s = stats.genextreme.sf(x, -0.125)
|
||
|
|
assert_allclose(s, 1.6777205262585625e-57)
|
||
|
|
x2 = stats.genextreme.isf(s, -0.125)
|
||
|
|
assert_allclose(x2, x)
|
||
|
|
|
||
|
|
x = 7.98
|
||
|
|
s = stats.genextreme.sf(x, 0.125)
|
||
|
|
assert_allclose(s, 1.52587890625e-21)
|
||
|
|
x2 = stats.genextreme.isf(s, 0.125)
|
||
|
|
assert_allclose(x2, x)
|
||
|
|
|
||
|
|
x = 7.98
|
||
|
|
s = stats.genextreme.sf(x, 0)
|
||
|
|
assert_allclose(s, 0.00034218086528426593)
|
||
|
|
x2 = stats.genextreme.isf(s, 0)
|
||
|
|
assert_allclose(x2, x)
|
||
|
|
|
||
|
|
|
||
|
|
def test_burr12_ppf_small_arg():
|
||
|
|
prob = 1e-16
|
||
|
|
quantile = stats.burr12.ppf(prob, 2, 3)
|
||
|
|
# The expected quantile was computed using mpmath:
|
||
|
|
# >>> import mpmath
|
||
|
|
# >>> mpmath.mp.dps = 100
|
||
|
|
# >>> prob = mpmath.mpf('1e-16')
|
||
|
|
# >>> c = mpmath.mpf(2)
|
||
|
|
# >>> d = mpmath.mpf(3)
|
||
|
|
# >>> float(((1-prob)**(-1/d) - 1)**(1/c))
|
||
|
|
# 5.7735026918962575e-09
|
||
|
|
assert_allclose(quantile, 5.7735026918962575e-09)
|
||
|
|
|
||
|
|
|
||
|
|
def test_crystalball_function():
|
||
|
|
"""
|
||
|
|
All values are calculated using the independent implementation of the
|
||
|
|
ROOT framework (see https://root.cern.ch/).
|
||
|
|
Corresponding ROOT code is given in the comments.
|
||
|
|
"""
|
||
|
|
X = np.linspace(-5.0, 5.0, 21)[:-1]
|
||
|
|
|
||
|
|
# for(float x = -5.0; x < 5.0; x+=0.5)
|
||
|
|
# std::cout << ROOT::Math::crystalball_pdf(x, 1.0, 2.0, 1.0) << ", ";
|
||
|
|
calculated = stats.crystalball.pdf(X, beta=1.0, m=2.0)
|
||
|
|
expected = np.array([0.0202867, 0.0241428, 0.0292128, 0.0360652, 0.045645,
|
||
|
|
0.059618, 0.0811467, 0.116851, 0.18258, 0.265652,
|
||
|
|
0.301023, 0.265652, 0.18258, 0.097728, 0.0407391,
|
||
|
|
0.013226, 0.00334407, 0.000658486, 0.000100982,
|
||
|
|
1.20606e-05])
|
||
|
|
assert_allclose(expected, calculated, rtol=0.001)
|
||
|
|
|
||
|
|
# for(float x = -5.0; x < 5.0; x+=0.5)
|
||
|
|
# std::cout << ROOT::Math::crystalball_pdf(x, 2.0, 3.0, 1.0) << ", ";
|
||
|
|
calculated = stats.crystalball.pdf(X, beta=2.0, m=3.0)
|
||
|
|
expected = np.array([0.0019648, 0.00279754, 0.00417592, 0.00663121,
|
||
|
|
0.0114587, 0.0223803, 0.0530497, 0.12726, 0.237752,
|
||
|
|
0.345928, 0.391987, 0.345928, 0.237752, 0.12726,
|
||
|
|
0.0530497, 0.0172227, 0.00435458, 0.000857469,
|
||
|
|
0.000131497, 1.57051e-05])
|
||
|
|
assert_allclose(expected, calculated, rtol=0.001)
|
||
|
|
|
||
|
|
# for(float x = -5.0; x < 5.0; x+=0.5) {
|
||
|
|
# std::cout << ROOT::Math::crystalball_pdf(x, 2.0, 3.0, 2.0, 0.5);
|
||
|
|
# std::cout << ", ";
|
||
|
|
# }
|
||
|
|
calculated = stats.crystalball.pdf(X, beta=2.0, m=3.0, loc=0.5, scale=2.0)
|
||
|
|
expected = np.array([0.00785921, 0.0111902, 0.0167037, 0.0265249,
|
||
|
|
0.0423866, 0.0636298, 0.0897324, 0.118876, 0.147944,
|
||
|
|
0.172964, 0.189964, 0.195994, 0.189964, 0.172964,
|
||
|
|
0.147944, 0.118876, 0.0897324, 0.0636298, 0.0423866,
|
||
|
|
0.0265249])
|
||
|
|
assert_allclose(expected, calculated, rtol=0.001)
|
||
|
|
|
||
|
|
# for(float x = -5.0; x < 5.0; x+=0.5)
|
||
|
|
# std::cout << ROOT::Math::crystalball_cdf(x, 1.0, 2.0, 1.0) << ", ";
|
||
|
|
calculated = stats.crystalball.cdf(X, beta=1.0, m=2.0)
|
||
|
|
expected = np.array([0.12172, 0.132785, 0.146064, 0.162293, 0.18258,
|
||
|
|
0.208663, 0.24344, 0.292128, 0.36516, 0.478254,
|
||
|
|
0.622723, 0.767192, 0.880286, 0.94959, 0.982834,
|
||
|
|
0.995314, 0.998981, 0.999824, 0.999976, 0.999997])
|
||
|
|
assert_allclose(expected, calculated, rtol=0.001)
|
||
|
|
|
||
|
|
# for(float x = -5.0; x < 5.0; x+=0.5)
|
||
|
|
# std::cout << ROOT::Math::crystalball_cdf(x, 2.0, 3.0, 1.0) << ", ";
|
||
|
|
calculated = stats.crystalball.cdf(X, beta=2.0, m=3.0)
|
||
|
|
expected = np.array([0.00442081, 0.00559509, 0.00730787, 0.00994682,
|
||
|
|
0.0143234, 0.0223803, 0.0397873, 0.0830763, 0.173323,
|
||
|
|
0.320592, 0.508717, 0.696841, 0.844111, 0.934357,
|
||
|
|
0.977646, 0.993899, 0.998674, 0.999771, 0.999969,
|
||
|
|
0.999997])
|
||
|
|
assert_allclose(expected, calculated, rtol=0.001)
|
||
|
|
|
||
|
|
# for(float x = -5.0; x < 5.0; x+=0.5) {
|
||
|
|
# std::cout << ROOT::Math::crystalball_cdf(x, 2.0, 3.0, 2.0, 0.5);
|
||
|
|
# std::cout << ", ";
|
||
|
|
# }
|
||
|
|
calculated = stats.crystalball.cdf(X, beta=2.0, m=3.0, loc=0.5, scale=2.0)
|
||
|
|
expected = np.array([0.0176832, 0.0223803, 0.0292315, 0.0397873, 0.0567945,
|
||
|
|
0.0830763, 0.121242, 0.173323, 0.24011, 0.320592,
|
||
|
|
0.411731, 0.508717, 0.605702, 0.696841, 0.777324,
|
||
|
|
0.844111, 0.896192, 0.934357, 0.960639, 0.977646])
|
||
|
|
assert_allclose(expected, calculated, rtol=0.001)
|
||
|
|
|
||
|
|
|
||
|
|
def test_crystalball_function_moments():
|
||
|
|
"""
|
||
|
|
All values are calculated using the pdf formula and the integrate function
|
||
|
|
of Mathematica
|
||
|
|
"""
|
||
|
|
# The Last two (alpha, n) pairs test the special case n == alpha**2
|
||
|
|
beta = np.array([2.0, 1.0, 3.0, 2.0, 3.0])
|
||
|
|
m = np.array([3.0, 3.0, 2.0, 4.0, 9.0])
|
||
|
|
|
||
|
|
# The distribution should be correctly normalised
|
||
|
|
expected_0th_moment = np.array([1.0, 1.0, 1.0, 1.0, 1.0])
|
||
|
|
calculated_0th_moment = stats.crystalball._munp(0, beta, m)
|
||
|
|
assert_allclose(expected_0th_moment, calculated_0th_moment, rtol=0.001)
|
||
|
|
|
||
|
|
# calculated using wolframalpha.com
|
||
|
|
# e.g. for beta = 2 and m = 3 we calculate the norm like this:
|
||
|
|
# integrate exp(-x^2/2) from -2 to infinity +
|
||
|
|
# integrate (3/2)^3*exp(-2^2/2)*(3/2-2-x)^(-3) from -infinity to -2
|
||
|
|
norm = np.array([2.5511, 3.01873, 2.51065, 2.53983, 2.507410455])
|
||
|
|
|
||
|
|
a = np.array([-0.21992, -3.03265, np.inf, -0.135335, -0.003174])
|
||
|
|
expected_1th_moment = a / norm
|
||
|
|
calculated_1th_moment = stats.crystalball._munp(1, beta, m)
|
||
|
|
assert_allclose(expected_1th_moment, calculated_1th_moment, rtol=0.001)
|
||
|
|
|
||
|
|
a = np.array([np.inf, np.inf, np.inf, 3.2616, 2.519908])
|
||
|
|
expected_2th_moment = a / norm
|
||
|
|
calculated_2th_moment = stats.crystalball._munp(2, beta, m)
|
||
|
|
assert_allclose(expected_2th_moment, calculated_2th_moment, rtol=0.001)
|
||
|
|
|
||
|
|
a = np.array([np.inf, np.inf, np.inf, np.inf, -0.0577668])
|
||
|
|
expected_3th_moment = a / norm
|
||
|
|
calculated_3th_moment = stats.crystalball._munp(3, beta, m)
|
||
|
|
assert_allclose(expected_3th_moment, calculated_3th_moment, rtol=0.001)
|
||
|
|
|
||
|
|
a = np.array([np.inf, np.inf, np.inf, np.inf, 7.78468])
|
||
|
|
expected_4th_moment = a / norm
|
||
|
|
calculated_4th_moment = stats.crystalball._munp(4, beta, m)
|
||
|
|
assert_allclose(expected_4th_moment, calculated_4th_moment, rtol=0.001)
|
||
|
|
|
||
|
|
a = np.array([np.inf, np.inf, np.inf, np.inf, -1.31086])
|
||
|
|
expected_5th_moment = a / norm
|
||
|
|
calculated_5th_moment = stats.crystalball._munp(5, beta, m)
|
||
|
|
assert_allclose(expected_5th_moment, calculated_5th_moment, rtol=0.001)
|
||
|
|
|
||
|
|
|
||
|
|
def test_argus_function():
|
||
|
|
# There is no usable reference implementation.
|
||
|
|
# (RootFit implementation returns unreasonable results which are not
|
||
|
|
# normalized correctly.)
|
||
|
|
# Instead we do some tests if the distribution behaves as expected for
|
||
|
|
# different shapes and scales.
|
||
|
|
for i in range(1, 10):
|
||
|
|
for j in range(1, 10):
|
||
|
|
assert_equal(stats.argus.pdf(i + 0.001, chi=j, scale=i), 0.0)
|
||
|
|
assert_(stats.argus.pdf(i - 0.001, chi=j, scale=i) > 0.0)
|
||
|
|
assert_equal(stats.argus.pdf(-0.001, chi=j, scale=i), 0.0)
|
||
|
|
assert_(stats.argus.pdf(+0.001, chi=j, scale=i) > 0.0)
|
||
|
|
|
||
|
|
for i in range(1, 10):
|
||
|
|
assert_equal(stats.argus.cdf(1.0, chi=i), 1.0)
|
||
|
|
assert_equal(stats.argus.cdf(1.0, chi=i),
|
||
|
|
1.0 - stats.argus.sf(1.0, chi=i))
|
||
|
|
|
||
|
|
|
||
|
|
class TestHistogram(object):
|
||
|
|
def setup_method(self):
|
||
|
|
np.random.seed(1234)
|
||
|
|
|
||
|
|
# We have 8 bins
|
||
|
|
# [1,2), [2,3), [3,4), [4,5), [5,6), [6,7), [7,8), [8,9)
|
||
|
|
# But actually np.histogram will put the last 9 also in the [8,9) bin!
|
||
|
|
# Therefore there is a slight difference below for the last bin, from
|
||
|
|
# what you might have expected.
|
||
|
|
histogram = np.histogram([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)
|
||
|
|
self.template = stats.rv_histogram(histogram)
|
||
|
|
|
||
|
|
data = stats.norm.rvs(loc=1.0, scale=2.5, size=10000, random_state=123)
|
||
|
|
norm_histogram = np.histogram(data, bins=50)
|
||
|
|
self.norm_template = stats.rv_histogram(norm_histogram)
|
||
|
|
|
||
|
|
def test_pdf(self):
|
||
|
|
values = np.array([0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5,
|
||
|
|
5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5])
|
||
|
|
pdf_values = np.asarray([0.0/25.0, 0.0/25.0, 1.0/25.0, 1.0/25.0,
|
||
|
|
2.0/25.0, 2.0/25.0, 3.0/25.0, 3.0/25.0,
|
||
|
|
4.0/25.0, 4.0/25.0, 5.0/25.0, 5.0/25.0,
|
||
|
|
4.0/25.0, 4.0/25.0, 3.0/25.0, 3.0/25.0,
|
||
|
|
3.0/25.0, 3.0/25.0, 0.0/25.0, 0.0/25.0])
|
||
|
|
assert_allclose(self.template.pdf(values), pdf_values)
|
||
|
|
|
||
|
|
# Test explicitly the corner cases:
|
||
|
|
# As stated above the pdf in the bin [8,9) is greater than
|
||
|
|
# one would naively expect because np.histogram putted the 9
|
||
|
|
# into the [8,9) bin.
|
||
|
|
assert_almost_equal(self.template.pdf(8.0), 3.0/25.0)
|
||
|
|
assert_almost_equal(self.template.pdf(8.5), 3.0/25.0)
|
||
|
|
# 9 is outside our defined bins [8,9) hence the pdf is already 0
|
||
|
|
# for a continuous distribution this is fine, because a single value
|
||
|
|
# does not have a finite probability!
|
||
|
|
assert_almost_equal(self.template.pdf(9.0), 0.0/25.0)
|
||
|
|
assert_almost_equal(self.template.pdf(10.0), 0.0/25.0)
|
||
|
|
|
||
|
|
x = np.linspace(-2, 2, 10)
|
||
|
|
assert_allclose(self.norm_template.pdf(x),
|
||
|
|
stats.norm.pdf(x, loc=1.0, scale=2.5), rtol=0.1)
|
||
|
|
|
||
|
|
def test_cdf_ppf(self):
|
||
|
|
values = np.array([0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5,
|
||
|
|
5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5])
|
||
|
|
cdf_values = np.asarray([0.0/25.0, 0.0/25.0, 0.0/25.0, 0.5/25.0,
|
||
|
|
1.0/25.0, 2.0/25.0, 3.0/25.0, 4.5/25.0,
|
||
|
|
6.0/25.0, 8.0/25.0, 10.0/25.0, 12.5/25.0,
|
||
|
|
15.0/25.0, 17.0/25.0, 19.0/25.0, 20.5/25.0,
|
||
|
|
22.0/25.0, 23.5/25.0, 25.0/25.0, 25.0/25.0])
|
||
|
|
assert_allclose(self.template.cdf(values), cdf_values)
|
||
|
|
# First three and last two values in cdf_value are not unique
|
||
|
|
assert_allclose(self.template.ppf(cdf_values[2:-1]), values[2:-1])
|
||
|
|
|
||
|
|
# Test of cdf and ppf are inverse functions
|
||
|
|
x = np.linspace(1.0, 9.0, 100)
|
||
|
|
assert_allclose(self.template.ppf(self.template.cdf(x)), x)
|
||
|
|
x = np.linspace(0.0, 1.0, 100)
|
||
|
|
assert_allclose(self.template.cdf(self.template.ppf(x)), x)
|
||
|
|
|
||
|
|
x = np.linspace(-2, 2, 10)
|
||
|
|
assert_allclose(self.norm_template.cdf(x),
|
||
|
|
stats.norm.cdf(x, loc=1.0, scale=2.5), rtol=0.1)
|
||
|
|
|
||
|
|
def test_rvs(self):
|
||
|
|
N = 10000
|
||
|
|
sample = self.template.rvs(size=N, random_state=123)
|
||
|
|
assert_equal(np.sum(sample < 1.0), 0.0)
|
||
|
|
assert_allclose(np.sum(sample <= 2.0), 1.0/25.0 * N, rtol=0.2)
|
||
|
|
assert_allclose(np.sum(sample <= 2.5), 2.0/25.0 * N, rtol=0.2)
|
||
|
|
assert_allclose(np.sum(sample <= 3.0), 3.0/25.0 * N, rtol=0.1)
|
||
|
|
assert_allclose(np.sum(sample <= 3.5), 4.5/25.0 * N, rtol=0.1)
|
||
|
|
assert_allclose(np.sum(sample <= 4.0), 6.0/25.0 * N, rtol=0.1)
|
||
|
|
assert_allclose(np.sum(sample <= 4.5), 8.0/25.0 * N, rtol=0.1)
|
||
|
|
assert_allclose(np.sum(sample <= 5.0), 10.0/25.0 * N, rtol=0.05)
|
||
|
|
assert_allclose(np.sum(sample <= 5.5), 12.5/25.0 * N, rtol=0.05)
|
||
|
|
assert_allclose(np.sum(sample <= 6.0), 15.0/25.0 * N, rtol=0.05)
|
||
|
|
assert_allclose(np.sum(sample <= 6.5), 17.0/25.0 * N, rtol=0.05)
|
||
|
|
assert_allclose(np.sum(sample <= 7.0), 19.0/25.0 * N, rtol=0.05)
|
||
|
|
assert_allclose(np.sum(sample <= 7.5), 20.5/25.0 * N, rtol=0.05)
|
||
|
|
assert_allclose(np.sum(sample <= 8.0), 22.0/25.0 * N, rtol=0.05)
|
||
|
|
assert_allclose(np.sum(sample <= 8.5), 23.5/25.0 * N, rtol=0.05)
|
||
|
|
assert_allclose(np.sum(sample <= 9.0), 25.0/25.0 * N, rtol=0.05)
|
||
|
|
assert_allclose(np.sum(sample <= 9.0), 25.0/25.0 * N, rtol=0.05)
|
||
|
|
assert_equal(np.sum(sample > 9.0), 0.0)
|
||
|
|
|
||
|
|
def test_munp(self):
|
||
|
|
for n in range(4):
|
||
|
|
assert_allclose(self.norm_template._munp(n),
|
||
|
|
stats.norm._munp(n, 1.0, 2.5), rtol=0.05)
|
||
|
|
|
||
|
|
def test_entropy(self):
|
||
|
|
assert_allclose(self.norm_template.entropy(),
|
||
|
|
stats.norm.entropy(loc=1.0, scale=2.5), rtol=0.05)
|