def test_pdf_bivariate():
# the dim > 2 case is tested when we fitted the copula. Test the bivariate case here
cop = ClaytonCopula(-0.3075057, 2)
u = np.array([
[0.199296, 0.645346],
[0.135279, 0.30006]
])
assert_array_almost_equal(cop.pdf(u), [1.152112, 1.018026])
def test_clayton_random_generates_correctly(copula):
n = 10
assert copula.random(n).shape == (n, copula.dim)
expected = (n, 2)
cop = ClaytonCopula(0)
assert cop.random(n).shape == expected
cop.params = 1.5
assert cop.random(n).shape == expected
def allclayton(x, y, thetaInit=1.4):
sample = len(x)
# Convert to normall #
result = allnorm(x, y)
u = result["u"]
v = result["v"]
sigma = result["sigma"]
hes_norm = result["hes_norm"]
# x - mean, y - mean #
xbar = x - sigma[2]
ybar = y - sigma[3]
# Calculate theta #
data = []
for i in range(len(u)):
data.append([u[i][0], v[i][0]])
data = np.array(data)
cop = ClaytonCopula(theta=thetaInit)
cop.fit(data)
theta = cop.params
# Save frequent calculations #
v_pow_minus_theta = v ** (-theta)
u_pow_minus_theta = u ** (-theta)
minus_sample = -sample
# Find logLikelihood of theta #
cop1 = (sample * np.log(1 + theta)) - ((theta + 1) * np.sum(np.log(u * v))) - ((np.sum(np.log((u ** (-theta)) + (v ** (-theta)) -1))) * (2 + (1/theta))) - (0.5 * sample * np.log(2 * pi * (sigma[0] ** 2))) - (0.5 * np.sum(xbar ** 2) / (sigma[0] ** 2)) - (0.5 * sample * np.log(2 * pi * (sigma[1] ** 2))) - (0.5 * np.sum(ybar ** 2) / (sigma[1] ** 2))
# Calculate hessian of log-copula's density #
hes_cop = (minus_sample / ((theta + 1)**2)) -2 * (theta ** (-3) * np.sum(np.log(u_pow_minus_theta + v_pow_minus_theta - 1))) - 2*(theta ** (-2)) * np.sum(np.divide(np.multiply(np.log(u), u_pow_minus_theta) + np.multiply(np.log(v), v_pow_minus_theta),u_pow_minus_theta + v_pow_minus_theta - 1)) - (2 + (1/theta))*np.sum(np.divide(np.multiply(np.multiply(np.log(u) ** 2, u ** (-theta)) + np.multiply(np.log(v) ** 2, v_pow_minus_theta), u_pow_minus_theta + v_pow_minus_theta - 1) - ((np.multiply((u_pow_minus_theta), np.log(u)) + np.multiply((v_pow_minus_theta), np.log(v)))** 2), (((u ** (-theta)) + (v ** (-theta)) - 1) ** 2)))
s = minus_sample / hes_cop
hes_prior_cop = -1 / (s ** 2)
# Opou loc valame scale apo ton deutero log kai meta.
log_prior = np.log(norm.pdf(theta, loc=0, scale=s)) + np.log(expon.pdf(sigma[0], scale=1)) + np.log(expon.pdf(sigma[1], scale=1))
BF = 1
# Vgazoume to inv kai vazoume -1/
BFu = cop1 + log_prior + 0.5 * np.log(-1/(det(hes_norm) * (hes_cop - hes_prior_cop)))
hes = det(hes_norm) * (hes_cop - hes_prior_cop)
if theta < 10**(-5):
theta = 0
cop1 = 0
BFu = cop1 + log_prior + 0.5 * np.log(-det(np.matmul(hes_norm, hes_cop - hes_prior_cop)))
result = {"theta": theta, "cop1": cop1, "hes": hes, "hes_prior_cor": hes_prior_cop, "BF": BF, "BFu": BFu}
return result
def fitted_clayton(residual_data):
cop = ClaytonCopula(dim=residual_data.shape[1])
cop.fit(residual_data)
return cop
def test_param_set_raises_error(dim, theta, err):
cop = ClaytonCopula(dim=dim)
with pytest.raises(ValueError, match=err):
cop.params = theta
def test_itau_fit(residual_data: np.ndarray):
cop = ClaytonCopula(dim=residual_data.shape[1])
cop.fit(residual_data, method='itau')
assert_almost_equal(cop.params, 0.7848391, 4)
def copula(residual_data: np.ndarray):
dim = residual_data.shape[1]
cop = ClaytonCopula(dim=dim)
cop.params = 0.3075057
return cop