混合阿基米德copula函数的选择python代码

以下是一个简单的 Python 代码示例，用于选择混合阿基米德 Copula 函数：

import numpy as np
from scipy.stats import levy_stable, kendalltau

def mix_archimedean_copula(u, alpha, lambdas):
    """
    u: array_like
        n x d matrix of uniform random variables in [0, 1].
    alpha: float
        Archimedean copula parameter.
    lambdas: list of floats
        List of mixing parameters, summing up to 1.
    """
    assert len(lambdas) >= 2, "At least two copulas required."
    assert np.isclose(np.sum(lambdas), 1), "Mixing parameters must sum up to 1."

    n, d = u.shape
    cdfs = []
    for i in range(len(lambdas)):
        cdf_i = levy_stable.cdf(levy_stable.ppf(u, alpha, -lambdas[i], scale=1/np.sqrt(alpha)), alpha, 0, scale=1)
        cdfs.append(cdf_i)
    cdfs = np.stack(cdfs, axis=2)

    return np.sum(lambdas * np.prod(cdfs, axis=2), axis=1)

# Example usage
n = 1000
d = 3
alpha = 1.5
lambdas = [0.5, 0.5]
u = np.random.uniform(size=(n, d))
u_correlated = np.apply_along_axis(lambda x: np.random.permutation(x), 0, u)
copula = mix_archimedean_copula(u_correlated, alpha, lambdas)
tau, _ = kendalltau(u_correlated, axis=0)
print(f"Kendall's tau: {tau}")
print(f"Copula correlation: {np.corrcoef(copula, rowvar=False)}")

该代码通过 Scipy 库中的 `levy_stable` 函数计算阿基米德 Copula 的 CDF，然后将它们加权求和以得到混合 Archimedean Copula 的 CDF。该函数还计算了 Kendall's tau 和 Copula 相关性，以帮助评估模型的性能。