def test_cdf():
'''
Tests the cumulative distribution function.
'''
samples = np.array([np.linspace(0, 1, 5), np.linspace(0.2, 0.8, 5)]).T
# Independence copula
independence_copula = IndependenceCopula()
# Comparison values
r_cdf = np.array([0.0, 0.0875, 0.25, 0.4875, 0.8])
p_cdf = independence_copula.cdf(samples)
assert_allclose(p_cdf, r_cdf)
# Gaussian copula family
gaussian_copula = GaussianCopula(0.5)
# Comparison values
r_cdf = np.array([0.0, 0.1520333540, 0.3333333333, 0.5520333540, 0.8])
p_cdf = gaussian_copula.cdf(samples)
assert_allclose(p_cdf, r_cdf)
# Clayton copula family
clayton_copula = ClaytonCopula(5)
# Comparison values
r_cdf = np.array([0.0, 0.2416570262, 0.4366484171, 0.6100768349, 0.8])
p_cdf = clayton_copula.cdf(samples)
assert_allclose(p_cdf, r_cdf)
# Frank copula family
frank_copula = FrankCopula(5)
# Comparison values
r_cdf = np.array([0.0, 0.1800378858, 0.3771485107, 0.5800378858, 0.8])
p_cdf = frank_copula.cdf(samples)
assert_allclose(p_cdf, r_cdf)
def test_pdf():
'''
Tests the probability density function.
'''
samples = np.array([np.linspace(0, 1, 5), np.linspace(0.2, 0.8, 5)]).T
# Independence copula
independence_copula = IndependenceCopula()
# Comparison values
r_pdf = np.array([0.0, 1.0, 1.0, 1.0, 0.0])
p_pdf = independence_copula.pdf(samples)
assert_allclose(p_pdf, r_pdf)
# Gaussian copula family
gaussian_copula = GaussianCopula(0.5)
# Comparison values
r_pdf = np.array([0.0, 1.2417679440, 1.1547005384, 1.2417679440, 0.0])
p_pdf = gaussian_copula.pdf(samples)
assert_allclose(p_pdf, r_pdf)
# Clayton copula family
clayton_copula = ClaytonCopula(5)
# Comparison values
r_pdf = np.array([0.0, 2.1943031503, 2.7037217178, 1.9477508961, 0.0])
p_pdf = clayton_copula.pdf(samples)
assert_allclose(p_pdf, r_pdf)
# Frank copula family
frank_copula = FrankCopula(5)
# Comparison values
r_pdf = np.array([0.0, 1.5167615765, 1.4735637246, 1.5167615765, 0.0])
p_pdf = frank_copula.pdf(samples)
assert_allclose(p_pdf, r_pdf)
def test_rotation_270_deg():
'''
Tests the 270° copula rotation.
'''
samples = np.array([np.linspace(0, 1, 5), np.linspace(0.2, 0.8, 5)]).T
# Clayton copula family rotated 270°
copula = ClaytonCopula(5, rotation='270°')
# Comparison values
r_logpdf = np.array(
[-np.inf, -1.7680858282, 0.9946292379, -2.5713221880, -np.inf])
r_pdf = np.array([0.0, 0.1706593477, 2.7037217178, 0.0764344179, 0.0])
r_logcdf = np.array([
-38.123095, -6.7509119186, -2.7590553856, -0.9153652928, -0.2231435513
])
r_cdf = np.array([0.0, 0.0011698124, 0.0633515829, 0.400370347, 0.8])
r_ccdf = np.array([0.0, 0.0198871044, 0.5564206557, 0.996791538, 1.0])
r_ppcf = np.array([0.0, 0.547275029, 0.4788690972, 0.4493004266, 1.0])
p_logpdf = copula.logpdf(samples)
p_pdf = copula.pdf(samples)
p_logcdf = copula.logcdf(samples)
p_cdf = copula.cdf(samples)
p_ccdf = copula.ccdf(samples)
p_ppcf = copula.ppcf(samples)
assert_allclose(p_logpdf, r_logpdf)
assert_allclose(p_pdf, r_pdf)
assert_allclose(p_logcdf, r_logcdf)
assert_allclose(p_cdf, r_cdf, atol=1e-10)
assert_allclose(p_ccdf, r_ccdf, atol=1e-10)
assert_allclose(p_ppcf, r_ppcf, atol=1e-10)
def test_rotation_180_deg():
'''
Tests the 180° copula rotation.
'''
samples = np.array([np.linspace(0, 1, 5), np.linspace(0.2, 0.8, 5)]).T
# Clayton copula family rotated 180°
copula = ClaytonCopula(5, rotation='180°')
# Comparison values
r_logpdf = np.array(
[-np.inf, 0.6666753203, 0.9946292379, 0.7858645247, -np.inf])
r_pdf = np.array([0.0, 1.9477508961, 2.7037217178, 2.1943031503, 0.0])
r_logcdf = np.array(
[-np.inf, -1.5602819348, -0.8286269453, -0.4437013452, -0.2231435513])
r_cdf = np.array([0.0, 0.2100768349, 0.4366484171, 0.6416570262, 0.8])
r_ccdf = np.array([0.0, 0.3163606244, 0.5564206557, 0.8916601339, 1.0])
r_ppcf = np.array([0.0, 0.2140692068, 0.4788690972, 0.7005153398, 1.0])
p_logpdf = copula.logpdf(samples)
p_pdf = copula.pdf(samples)
p_logcdf = copula.logcdf(samples)
p_cdf = copula.cdf(samples)
p_ccdf = copula.ccdf(samples)
p_ppcf = copula.ppcf(samples)
assert_allclose(p_logpdf, r_logpdf)
assert_allclose(p_pdf, r_pdf)
assert_allclose(p_logcdf, r_logcdf)
assert_allclose(p_cdf, r_cdf)
assert_allclose(p_ccdf, r_ccdf)
assert_allclose(p_ppcf, r_ppcf)
def test_rotation_90_deg():
'''
Tests the 90° copula rotation.
'''
samples = np.array([np.linspace(0, 1, 5), np.linspace(0.2, 0.8, 5)]).T
# Clayton copula family rotated 90°
copula = ClaytonCopula(5, rotation='90°')
# Comparison values
r_logpdf = np.array(
[-np.inf, -2.571322188, 0.9946292379, -1.7680858282, -np.inf])
r_pdf = np.array([0.0, 0.0764344179, 2.7037217178, 0.1706593477, 0.0])
r_logcdf = np.array(
[-np.inf, -7.9010702481, -2.7590553856, -0.9133704691, -0.2231435513])
r_cdf = np.array([0.0, 0.000370347, 0.0633515829, 0.4011698124, 0.8])
r_ccdf = np.array([0.0, 0.003208462, 0.4435793443, 0.9801128956, 1.0])
r_ppcf = np.array([0.0, 0.5506995734, 0.5211309028, 0.452724971, 1.0])
p_logpdf = copula.logpdf(samples)
p_pdf = copula.pdf(samples)
p_logcdf = copula.logcdf(samples)
p_cdf = copula.cdf(samples)
p_ccdf = copula.ccdf(samples)
p_ppcf = copula.ppcf(samples)
assert_allclose(p_logpdf, r_logpdf)
assert_allclose(p_pdf, r_pdf)
assert_allclose(p_logcdf, r_logcdf)
assert_allclose(p_cdf, r_cdf)
assert_allclose(p_ccdf, r_ccdf)
assert_allclose(p_ppcf, r_ppcf)
def test_ppcf():
'''
Tests the conditional cumulative distribution function.
'''
samples = np.array([np.linspace(0, 1, 5), np.linspace(0.2, 0.8, 5)]).T
# Independence copula
independence_copula = IndependenceCopula()
# Comparison values
r_ppcf = np.array([0.0, 0.25, 0.5, 0.75, 1.0])
p_ppcf = independence_copula.ppcf(samples)
assert_allclose(p_ppcf, r_ppcf)
# Test other axis
r_ppcf = np.array([0.2, 0.35, 0.5, 0.65, 0.8])
p_ppcf = independence_copula.ppcf(samples, axis=0)
assert_allclose(p_ppcf, r_ppcf)
# Gaussian copula family
gaussian_copula = GaussianCopula(0.5)
# Comparison values
r_ppcf = np.array([0.0, 0.218642669, 0.5, 0.781357331, 1.0])
p_ppcf = gaussian_copula.ppcf(samples)
assert_allclose(p_ppcf, r_ppcf)
# Test other axis
r_ppcf = np.array([0.0, 0.2511286797, 0.5, 0.7488713203, 1.0])
p_ppcf = gaussian_copula.ppcf(samples, axis=0)
assert_allclose(p_ppcf, r_ppcf)
# Clayton copula family
clayton_copula = ClaytonCopula(5)
# Comparison values
r_ppcf = np.array([0.0, 0.2994846602, 0.5211309028, 0.7859307932, 1.0])
p_ppcf = clayton_copula.ppcf(samples)
assert_allclose(p_ppcf, r_ppcf)
# Test other axis
r_ppcf = np.array(
[0.0, 0.2337467913, 0.5211309028, 0.8127416749, 0.9634924840])
p_ppcf = clayton_copula.ppcf(samples, axis=0)
assert_allclose(p_ppcf, r_ppcf)
# Frank copula family
frank_copula = FrankCopula(5)
# Comparison values
r_ppcf = np.array([0.0, 0.21162507, 0.5, 0.78837493, 1.0])
p_ppcf = frank_copula.ppcf(samples)
assert_allclose(p_ppcf, r_ppcf)
# Test other axis
r_ppcf = np.array([0.0442921, 0.20900068, 0.5, 0.79099932, 0.9557079])
p_ppcf = frank_copula.ppcf(samples, axis=0)
assert_allclose(p_ppcf, r_ppcf)
def test_ccdf():
'''
Tests the conditional cumulative distribution function.
'''
samples = np.array([np.linspace(0, 1, 5), np.linspace(0.2, 0.8, 5)]).T
# Independence copula
independence_copula = IndependenceCopula()
# Comparison values
r_ccdf = np.array([0.0, 0.25, 0.5, 0.75, 1.0])
p_ccdf = independence_copula.ccdf(samples)
assert_allclose(p_ccdf, r_ccdf)
# Test other axis
r_ccdf = np.array([0.2, 0.35, 0.5, 0.65, 0.8])
p_ccdf = independence_copula.ccdf(samples, axis=0)
assert_allclose(p_ccdf, r_ccdf)
# Gaussian copula family
gaussian_copula = GaussianCopula(0.5)
# Comparison values
r_ccdf = np.array([0.0, 0.2889793807, 0.5, 0.7110206193, 1.0])
p_ccdf = gaussian_copula.ccdf(samples)
assert_allclose(p_ccdf, r_ccdf)
# Test other axis
r_ccdf = np.array([1.0, 0.4778649221, 0.5, 0.5221350779, 0.0])
p_ccdf = gaussian_copula.ccdf(samples, axis=0)
assert_allclose(p_ccdf, r_ccdf)
# Clayton copula family
clayton_copula = ClaytonCopula(5)
# Comparison values
r_ccdf = np.array([0.0, 0.1083398661, 0.4435793443, 0.6836393756, 1.0])
p_ccdf = clayton_copula.ccdf(samples)
assert_allclose(p_ccdf, r_ccdf)
# Test other axis
r_ccdf = np.array([0.0, 0.815748922, 0.4435793443, 0.2896940854, 0.262144])
p_ccdf = clayton_copula.ccdf(samples, axis=0)
assert_allclose(p_ccdf, r_ccdf)
# Frank copula family
frank_copula = FrankCopula(5)
# Comparison values
r_ccdf = np.array([0.0, 0.3070854, 0.5, 0.6929146, 1.0])
p_ccdf = frank_copula.ccdf(samples)
assert_allclose(p_ccdf, r_ccdf)
# Test other axis
r_ccdf = np.array([0.63640865, 0.58629237, 0.5, 0.41370763, 0.36359135])
p_ccdf = frank_copula.ccdf(samples, axis=0)
assert_allclose(p_ccdf, r_ccdf)
def test_logcdf():
'''
Tests the log of the cumulative distribution function.
'''
samples = np.array([np.linspace(0, 1, 5), np.linspace(0.2, 0.8, 5)]).T
# Independence copula
independence_copula = IndependenceCopula()
# Comparison values
r_logcdf = np.array(
[-np.inf, -2.4361164856, -1.3862943611, -0.7184649885, -0.2231435513])
p_logcdf = independence_copula.logcdf(samples)
assert_allclose(p_logcdf, r_logcdf)
# Gaussian copula family
gaussian_copula = GaussianCopula(0.5)
# Comparison values
r_logcdf = np.array(
[-np.inf, -1.8836553477, -1.0986122887, -0.5941468105, -0.2231435513])
p_logcdf = gaussian_copula.logcdf(samples)
assert_allclose(p_logcdf, r_logcdf)
# Clayton copula family
clayton_copula = ClaytonCopula(5)
# Comparison values
r_logcdf = np.array(
[-np.inf, -1.4202358053, -0.8286269453, -0.4941703709, -0.2231435513])
p_logcdf = clayton_copula.logcdf(samples)
assert_allclose(p_logcdf, r_logcdf)
# Frank copula family
frank_copula = FrankCopula(5)
# Comparison values
r_logcdf = np.array(
[-np.inf, -1.7145879734, -0.9751162414, -0.5446618572, -0.2231435513])
p_logcdf = frank_copula.logcdf(samples)
assert_allclose(p_logcdf, r_logcdf)
def test_logpdf():
'''
Tests the log of the probability density function.
'''
samples = np.array([np.linspace(0, 1, 5), np.linspace(0.2, 0.8, 5)]).T
# Independence copula
independence_copula = IndependenceCopula()
# Comparison values
r_logpdf = np.array([-np.inf, 0.0, 0.0, 0.0, -np.inf])
p_logpdf = independence_copula.logpdf(samples)
assert_allclose(p_logpdf, r_logpdf)
# Gaussian copula family
gaussian_copula = GaussianCopula(0.5)
# Comparison values
r_logpdf = np.array(
[-np.inf, 0.2165361255, 0.1438410362, 0.2165361255, -np.inf])
p_logpdf = gaussian_copula.logpdf(samples)
assert_allclose(p_logpdf, r_logpdf)
# Clayton copula family
clayton_copula = ClaytonCopula(5)
# Comparison values
r_logpdf = np.array(
[-np.inf, 0.7858645247, 0.9946292379, 0.6666753203, -np.inf])
p_logpdf = clayton_copula.logpdf(samples)
assert_allclose(p_logpdf, r_logpdf)
# Frank copula family
frank_copula = FrankCopula(5)
# Comparison values
r_logpdf = np.array(
[-np.inf, 0.4165775202, 0.3876837693, 0.4165775202, -np.inf])
p_logpdf = frank_copula.logpdf(samples)
assert_allclose(p_logpdf, r_logpdf)
def setUp(self):
'''
Saves the current random state for later recovery, sets the random seed
to get reproducible results and manually constructs a mixed vine.
'''
# Save random state for later recovery
self.random_state = np.random.get_state()
# Set fixed random seed
np.random.seed(0)
# Manually construct mixed vine
self.dim = 3 # Dimension
self.vine = MixedVine(self.dim)
# Specify marginals
self.vine.set_marginal(0, norm(0, 1))
self.vine.set_marginal(1, poisson(5))
self.vine.set_marginal(2, gamma(2, 0, 4))
# Specify pair copulas
self.vine.set_copula(1, 0, GaussianCopula(0.5))
self.vine.set_copula(1, 1, FrankCopula(4))
self.vine.set_copula(2, 0, ClaytonCopula(5))
