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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,69 @@ | ||
| import pytest | ||
| from arch.univariate.distribution import (SkewStudent, Normal, StudentsT, | ||
| GeneralizedError) | ||
| from numpy import exp, inf, log, nan, pi | ||
| from numpy.testing import assert_equal, assert_almost_equal | ||
| from scipy.integrate import quad | ||
| from scipy.special import gammaln | ||
|
|
||
| DISTRIBUTIONS = [ | ||
| (SkewStudent(), [6, -0.1]), | ||
| (SkewStudent(), [6, -0.5]), | ||
| (SkewStudent(), [6, 0.1]), | ||
| (SkewStudent(), [6, 0.5]), | ||
| (GeneralizedError(), [1.5]), | ||
| (GeneralizedError(), [2.1]), | ||
| (StudentsT(), [6]), | ||
| (StudentsT(), [7]), | ||
| (Normal(), None)] | ||
|
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||
|
|
||
| @pytest.mark.parametrize('dist, params', DISTRIBUTIONS) | ||
| def test_moment(dist, params): | ||
| """ | ||
| Ensures that Distribtion.moment and .partial_moment agree | ||
| with numeric integrals for order n=0,...,5 and z=+/-1,...,+/-5 | ||
| Parameters | ||
| ---------- | ||
| dist : distribution.Distribution | ||
| The distribution whose moments are being checked | ||
| params : List | ||
| List of parameters | ||
| """ | ||
|
|
||
| assert_equal(dist.moment(-1, params), nan) | ||
| assert_equal(dist.partial_moment(-1, 0., params), nan) | ||
|
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||
| # verify moments that exist | ||
| def f(x, n): | ||
| return (x**n) * exp(dist.loglikelihood(params, x, 1, True)) | ||
|
|
||
| for n in range(6): # moments 0-5 | ||
|
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||
| # complete moments | ||
| m_quad = quad(f, -inf, inf, args=n)[0] | ||
| m_method = dist.moment(n, params) | ||
| assert_almost_equal(m_quad, m_method) | ||
|
|
||
| # partial moments at z=+/-1,...,+/-5 | ||
| # SkewT integral is broken up for numerical stability | ||
| for z in range(-5, 5): # partial moments at +-1,...,+-5 | ||
| if isinstance(dist, SkewStudent): | ||
| eta, lam = params | ||
| c = (gammaln((eta + 1) / 2) - gammaln(eta / 2) - | ||
| log(pi * (eta - 2)) / 2) | ||
| a = 4 * lam * exp(c) * (eta - 2) / (eta - 1) | ||
| b = (1 + 3 * lam ** 2 - a ** 2) ** .5 | ||
| loc = -a/b | ||
| if z < loc: | ||
| m_quad = quad(f, -inf, z, args=n)[0] | ||
| else: | ||
| m_quad = quad(f, -inf, loc-1e-9, args=n)[0] + \ | ||
| quad(f, loc+1e-9, z, args=n)[0] | ||
|
|
||
| else: | ||
| m_quad = quad(f, -inf, z, args=n)[0] | ||
|
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| m_method = dist.partial_moment(n, z, params) | ||
| assert_almost_equal(m_quad, m_method) |
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