You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
87 lines
3.2 KiB
Python
87 lines
3.2 KiB
Python
import numpy as np
|
|
from numpy.testing import assert_allclose, assert_equal
|
|
|
|
from scipy.stats._tukeylambda_stats import (tukeylambda_variance,
|
|
tukeylambda_kurtosis)
|
|
|
|
|
|
def test_tukeylambda_stats_known_exact():
|
|
"""Compare results with some known exact formulas."""
|
|
# Some exact values of the Tukey Lambda variance and kurtosis:
|
|
# lambda var kurtosis
|
|
# 0 pi**2/3 6/5 (logistic distribution)
|
|
# 0.5 4 - pi (5/3 - pi/2)/(pi/4 - 1)**2 - 3
|
|
# 1 1/3 -6/5 (uniform distribution on (-1,1))
|
|
# 2 1/12 -6/5 (uniform distribution on (-1/2, 1/2))
|
|
|
|
# lambda = 0
|
|
var = tukeylambda_variance(0)
|
|
assert_allclose(var, np.pi**2 / 3, atol=1e-12)
|
|
kurt = tukeylambda_kurtosis(0)
|
|
assert_allclose(kurt, 1.2, atol=1e-10)
|
|
|
|
# lambda = 0.5
|
|
var = tukeylambda_variance(0.5)
|
|
assert_allclose(var, 4 - np.pi, atol=1e-12)
|
|
kurt = tukeylambda_kurtosis(0.5)
|
|
desired = (5./3 - np.pi/2) / (np.pi/4 - 1)**2 - 3
|
|
assert_allclose(kurt, desired, atol=1e-10)
|
|
|
|
# lambda = 1
|
|
var = tukeylambda_variance(1)
|
|
assert_allclose(var, 1.0 / 3, atol=1e-12)
|
|
kurt = tukeylambda_kurtosis(1)
|
|
assert_allclose(kurt, -1.2, atol=1e-10)
|
|
|
|
# lambda = 2
|
|
var = tukeylambda_variance(2)
|
|
assert_allclose(var, 1.0 / 12, atol=1e-12)
|
|
kurt = tukeylambda_kurtosis(2)
|
|
assert_allclose(kurt, -1.2, atol=1e-10)
|
|
|
|
|
|
def test_tukeylambda_stats_mpmath():
|
|
"""Compare results with some values that were computed using mpmath."""
|
|
a10 = dict(atol=1e-10, rtol=0)
|
|
a12 = dict(atol=1e-12, rtol=0)
|
|
data = [
|
|
# lambda variance kurtosis
|
|
[-0.1, 4.78050217874253547, 3.78559520346454510],
|
|
[-0.0649, 4.16428023599895777, 2.52019675947435718],
|
|
[-0.05, 3.93672267890775277, 2.13129793057777277],
|
|
[-0.001, 3.30128380390964882, 1.21452460083542988],
|
|
[0.001, 3.27850775649572176, 1.18560634779287585],
|
|
[0.03125, 2.95927803254615800, 0.804487555161819980],
|
|
[0.05, 2.78281053405464501, 0.611604043886644327],
|
|
[0.0649, 2.65282386754100551, 0.476834119532774540],
|
|
[1.2, 0.242153920578588346, -1.23428047169049726],
|
|
[10.0, 0.00095237579757703597, 2.37810697355144933],
|
|
[20.0, 0.00012195121951131043, 7.37654321002709531],
|
|
]
|
|
|
|
for lam, var_expected, kurt_expected in data:
|
|
var = tukeylambda_variance(lam)
|
|
assert_allclose(var, var_expected, **a12)
|
|
kurt = tukeylambda_kurtosis(lam)
|
|
assert_allclose(kurt, kurt_expected, **a10)
|
|
|
|
# Test with vector arguments (most of the other tests are for single
|
|
# values).
|
|
lam, var_expected, kurt_expected = zip(*data)
|
|
var = tukeylambda_variance(lam)
|
|
assert_allclose(var, var_expected, **a12)
|
|
kurt = tukeylambda_kurtosis(lam)
|
|
assert_allclose(kurt, kurt_expected, **a10)
|
|
|
|
|
|
def test_tukeylambda_stats_invalid():
|
|
"""Test values of lambda outside the domains of the functions."""
|
|
lam = [-1.0, -0.5]
|
|
var = tukeylambda_variance(lam)
|
|
assert_equal(var, np.array([np.nan, np.inf]))
|
|
|
|
lam = [-1.0, -0.25]
|
|
kurt = tukeylambda_kurtosis(lam)
|
|
assert_equal(kurt, np.array([np.nan, np.inf]))
|
|
|