混合copula函数的选择python代码

以下是使用Python中的SciPy库来选择混合Copula函数的示例代码：

import numpy as np
import matplotlib.pyplot as plt
from scipy import optimize, stats
from scipy.stats import norm, uniform, pearsonr
from scipy.optimize import minimize

# Generate correlated random variables
np.random.seed(123)
size = 500
rho = 0.5
cov = np.array([[1, rho], [rho, 1]])
x, y = stats.multivariate_normal.rvs(cov=cov, size=size).T

# Define the likelihood function for the copula
def copula_likelihood(params, data):
    """Return the negative log-likelihood for a Gaussian Copula."""
    rho, alpha = params
    copula = stats.gaussian_kde(data.T)
    log_likelihood = np.sum(np.log(copula(np.column_stack((norm.ppf(stats.uniform.rvs(size=len(data))), alpha * norm.ppf(stats.uniform.rvs(size=len(data))))))))
    return -log_likelihood

# Define the optimization function to find the maximum likelihood estimate
def optimize_copula(data):
    """Find the maximum likelihood estimate for a Gaussian Copula."""
    initial_guess = [0, 0.5]
    bounds = ((-1, 1), (0, 1))
    result = minimize(copula_likelihood, initial_guess, args=data, bounds=bounds)
    return result.x

# Find the maximum likelihood estimate for the copula
params = optimize_copula(np.column_stack((x, y)))

# Plot the original data and the fitted copula
plt.figure(figsize=(8, 8))
plt.scatter(x, y, marker='.')
u, v = np.meshgrid(np.linspace(0, 1, num=100), np.linspace(0, 1, num=100))
z = stats.gaussian_kde(np.column_stack((norm.ppf(u.reshape(-1)), params[1] * norm.ppf(v.reshape(-1))))).evaluate(np.column_stack((u.reshape(-1), v.reshape(-1))))
plt.contour(u, v, z.reshape(100, 100), levels=[0.01, 0.05, 0.1, 0.2, 0.3, 0.4])
plt.xlim(-4, 4)
plt.ylim(-4, 4)
plt.xlabel('X')
plt.ylabel('Y')
plt.title('Gaussian Copula')
plt.show()

这段代码生成了一个大小为500的双变量数据集，然后使用SciPy库中的最小化函数来查找最大似然估计，以获得混合Copula函数的参数。最后，它绘制了原始数据和拟合Copula函数的等高线图。