def test_chi2_moments(self):
# construct the expansion for \chi^2
N, df = 6, 15
cum = [_chi2_cumulant(n+1, df) for n in range(N)]
with warnings.catch_warnings():
warnings.simplefilter("ignore", RuntimeWarning)
ne = ExpandedNormal(cum, name='edgw_chi2')
# compare the moments
assert_allclose([_chi2_moment(n, df) for n in range(N)],
[ne.moment(n) for n in range(N)])
# compare the pdf [fragile!]
# this one is actually not a very good test: there is, strictly
# speaking, no guarantee that the pdfs match point-by-point
# m, s = df, np.sqrt(df)
# x = np.linspace(m - s, m + s, 10)
# assert_allclose(ne.pdf(x), stats.chi2.pdf(x, df),
# atol=1e-4, rtol=1e-5)
# pdf-cdf roundtrip
check_pdf(ne, arg=(), msg='')
# cdf-ppf roundtrip
check_cdf_ppf(ne, arg=(), msg='')
# cdf + sf == 1
check_cdf_sf(ne, arg=(), msg='')
# generate rvs & run a KS test
np.random.seed(765456)
rvs = ne.rvs(size=500)
check_distribution_rvs(ne, args=(), alpha=0.01, rvs=rvs)
def test_chi2_moments(self):
# construct the expansion for \chi^2
N, df = 6, 15
cum = [_chi2_cumulant(n + 1, df) for n in range(N)]
with warnings.catch_warnings():
warnings.simplefilter("ignore", RuntimeWarning)
ne = ExpandedNormal(cum, name='edgw_chi2')
# compare the moments
assert_allclose([_chi2_moment(n, df) for n in range(N)],
[ne.moment(n) for n in range(N)])
# compare the pdf [fragile!]
# this one is actually not a very good test: there is, strictly
# speaking, no guarantee that the pdfs match point-by-point
# m, s = df, np.sqrt(df)
# x = np.linspace(m - s, m + s, 10)
# assert_allclose(ne.pdf(x), stats.chi2.pdf(x, df),
# atol=1e-4, rtol=1e-5)
# pdf-cdf roundtrip
check_pdf(ne, arg=(), msg='')
# cdf-ppf roundtrip
check_cdf_ppf(ne, arg=(), msg='')
# cdf + sf == 1
check_cdf_sf(ne, arg=(), msg='')
# generate rvs & run a KS test
np.random.seed(765456)
rvs = ne.rvs(size=500)
check_distribution_rvs(ne, args=(), alpha=0.01, rvs=rvs)
def test_coefficients(self):
with warnings.catch_warnings():
warnings.simplefilter('ignore', UserWarning)
# 3rd order in n**(1/2)
ne3 = ExpandedNormal([0., 1., 1.])
assert_allclose(ne3._coef, [1., 0., 0., 1./6])
# 4th order in n**(1/2)
ne4 = ExpandedNormal([0., 1., 1., 1.])
assert_allclose(ne4._coef, [1., 0., 0., 1./6, 1./24, 0., 1./72])
# 5th order
ne5 = ExpandedNormal([0., 1., 1., 1., 1.])
assert_allclose(ne5._coef, [1., 0., 0., 1./6, 1./24, 1./120,
1./72, 1./144, 0., 1./1296])
# adding trailing zeroes increases the order
ne33 = ExpandedNormal([0., 1., 1., 0.])
assert_allclose(ne33._coef, [1., 0., 0., 1./6, 0., 0., 1./72])
def test_normal(self):
# with two cumulants, it's just a gaussian
ne2 = ExpandedNormal([3, 4])
x = np.linspace(-2., 2., 100)
assert_allclose(ne2.pdf(x), stats.norm.pdf(x, loc=3, scale=2))
def test_pdf_no_roots(self):
with warnings.catch_warnings():
warnings.simplefilter("error", RuntimeWarning)
ne = ExpandedNormal([0, 1])
ne = ExpandedNormal([0, 1, 0.1, 0.1])
def test_normal(self):
# with two cumulants, it's just a gaussian
ne2 = ExpandedNormal([3, 4])
x = np.linspace(-2., 2., 100)
assert_allclose(ne2.pdf(x), stats.norm.pdf(x, loc=3, scale=2))