我从三个具有设定权重的分布中进行采样，并交叉检查采样是否按预期工作。（每个分布的权重 * 平均值）是相同的，它是，标准差也是相同的。然而，我似乎不能得到标准差匹配？我不知道为什么，因为我认为采样是按预期工作，但需要帮助弄清楚为什么std_generated和expected_std是不同的

import numpy as np
from scipy.stats import expon
np.random.seed(42)  # Set a specific seed value

# Assuming disbn_1, disbn_2, and disbn_3 are your frozen distribution objects
# and w_1, w_2, w_3 are the corresponding probabilities

# Set up your distribution objects
par_1 = 2.0  # Adjust this parameter according to your specific distribution
disbn_1 = expon(scale=par_1)
disbn_2 = expon(scale=1.0)  # Adjust parameters as needed
disbn_3 = expon(scale=0.5)  # Adjust parameters as needed

# Set up probabilities
w_1, w_2, w_3 = 0.4, 0.3, 0.3
weights = np.array([w_1, w_2, w_3])

# Number of samples you want to generate
num_samples = 5000000  # Increase the number of samples

# Sample from the distributions with specified probabilities
selected_distributions = [disbn_1, disbn_2, disbn_3]
random_indices = np.random.choice(len(weights), size=num_samples, p=weights)

# Use np.choose to select samples based on random indices
selected_samples = np.choose(random_indices, [dist.rvs(size=num_samples) for dist in selected_distributions])

# Calculate summary statistics
mean_generated = np.mean(selected_samples)
std_generated = np.std(selected_samples,ddof=0) 

# Calculate expected mean and std based on the specified distribution and probabilities
expected_mean = np.sum(weights * np.array([dist.mean() for dist in selected_distributions]))
expected_std = np.sqrt(np.sum(weights * np.array([dist.var() for dist in selected_distributions])))

# Display results
print(f"Mean of generated samples: {mean_generated:.6f}")
print(f"Expected mean based on distribution: {expected_mean:.6f}")
print()
print(f"Standard deviation of generated samples: {std_generated:.6f}")
print(f"Expected standard deviation based on distribution: {expected_std:.6f}")

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