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_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_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_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)