87 lines
3.2 KiB
Python
87 lines
3.2 KiB
Python
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import numpy as np
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from numpy.testing import assert_allclose, assert_equal
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from scipy.stats._tukeylambda_stats import (tukeylambda_variance,
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tukeylambda_kurtosis)
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def test_tukeylambda_stats_known_exact():
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"""Compare results with some known exact formulas."""
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# Some exact values of the Tukey Lambda variance and kurtosis:
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# lambda var kurtosis
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# 0 pi**2/3 6/5 (logistic distribution)
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# 0.5 4 - pi (5/3 - pi/2)/(pi/4 - 1)**2 - 3
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# 1 1/3 -6/5 (uniform distribution on (-1,1))
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# 2 1/12 -6/5 (uniform distribution on (-1/2, 1/2))
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# lambda = 0
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var = tukeylambda_variance(0)
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assert_allclose(var, np.pi**2 / 3, atol=1e-12)
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kurt = tukeylambda_kurtosis(0)
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assert_allclose(kurt, 1.2, atol=1e-10)
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# lambda = 0.5
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var = tukeylambda_variance(0.5)
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assert_allclose(var, 4 - np.pi, atol=1e-12)
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kurt = tukeylambda_kurtosis(0.5)
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desired = (5./3 - np.pi/2) / (np.pi/4 - 1)**2 - 3
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assert_allclose(kurt, desired, atol=1e-10)
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# lambda = 1
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var = tukeylambda_variance(1)
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assert_allclose(var, 1.0 / 3, atol=1e-12)
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kurt = tukeylambda_kurtosis(1)
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assert_allclose(kurt, -1.2, atol=1e-10)
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# lambda = 2
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var = tukeylambda_variance(2)
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assert_allclose(var, 1.0 / 12, atol=1e-12)
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kurt = tukeylambda_kurtosis(2)
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assert_allclose(kurt, -1.2, atol=1e-10)
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def test_tukeylambda_stats_mpmath():
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"""Compare results with some values that were computed using mpmath."""
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a10 = dict(atol=1e-10, rtol=0)
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a12 = dict(atol=1e-12, rtol=0)
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data = [
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# lambda variance kurtosis
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[-0.1, 4.78050217874253547, 3.78559520346454510],
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[-0.0649, 4.16428023599895777, 2.52019675947435718],
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[-0.05, 3.93672267890775277, 2.13129793057777277],
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[-0.001, 3.30128380390964882, 1.21452460083542988],
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[0.001, 3.27850775649572176, 1.18560634779287585],
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[0.03125, 2.95927803254615800, 0.804487555161819980],
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[0.05, 2.78281053405464501, 0.611604043886644327],
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[0.0649, 2.65282386754100551, 0.476834119532774540],
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[1.2, 0.242153920578588346, -1.23428047169049726],
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[10.0, 0.00095237579757703597, 2.37810697355144933],
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[20.0, 0.00012195121951131043, 7.37654321002709531],
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]
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for lam, var_expected, kurt_expected in data:
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var = tukeylambda_variance(lam)
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assert_allclose(var, var_expected, **a12)
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kurt = tukeylambda_kurtosis(lam)
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assert_allclose(kurt, kurt_expected, **a10)
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# Test with vector arguments (most of the other tests are for single
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# values).
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lam, var_expected, kurt_expected = zip(*data)
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var = tukeylambda_variance(lam)
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assert_allclose(var, var_expected, **a12)
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kurt = tukeylambda_kurtosis(lam)
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assert_allclose(kurt, kurt_expected, **a10)
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def test_tukeylambda_stats_invalid():
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"""Test values of lambda outside the domains of the functions."""
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lam = [-1.0, -0.5]
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var = tukeylambda_variance(lam)
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assert_equal(var, np.array([np.nan, np.inf]))
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lam = [-1.0, -0.25]
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kurt = tukeylambda_kurtosis(lam)
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assert_equal(kurt, np.array([np.nan, np.inf]))
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