02.中心极限定理验证

"""
中心极限定理指的是给定一个任意分布的总体。
我每次从这些总体中随机抽取 n 个抽样，一共抽 m 次。 
然后把这 m 组抽样分别求出平均值/和。 这些平均值/和的分布接近正态分布。
"""

import numpy as np
import matplotlib.pyplot as plt

# 1 给定任意分布的总体
population = np.random.randint(0, 100, 100000)

# 2 随机抽取m个样本，抽取n次
def sample_choice(population, sample_num, sample_size):
    samples = []
    for i in range(sample_num):
        sample = []
        for j in range(sample_size):
            unit = np.random.choice(population)
            sample.append(unit)
        samples.append(sample)

    return samples

# 3 计算样本均值
def samples_mean(samples):
    sample_mean = []
    for i in range(len(samples)):
        sample_mean.append(np.mean(samples[i]))
    
    return sample_mean

# 4 中心定理结果
def central_limit_theorem():
    # 1.任意分布总体
    population = np.random.randint(0, 100, 100000)
    # 2.抽样
    samples = sample_choice(population, 1000, 50)
    # 3.求样本均值
    sample_mean = samples_mean(samples)

    plt.hist(sample_mean, bins=30)
    plt.show()


if __name__ == "__main__":
    central_limit_theorem()