09.编程理解无偏性与相合性

编程理解无偏性与相合性

无偏性

from statistics import mean
from statistics import variance
import random
import matplotlib.pyplot as plt


def variance_bias(data):
    """方差"""
    n = len(data)
    if n <= 1:
        return None

    mean_value = mean(data)
    return sum((e - mean_value) ** 2 for e in data) / n


def sample(num_of_samples, sample_sz, var):
    data = []
    for _ in range(num_of_samples):
        data.append(var([random.uniform(0.0, 1.0) for _ in range(sample_sz)]))
    return data


if __name__ == "__main__":

    data1 = sample(1000, 40, variance_bias)
    plt.hist(data1, bins="auto", rwidth=0.8)
    plt.axvline(x=mean(data1), c='black')
    plt.axvline(x=1/12, c='red')
    print("bias :", mean(data1), 1/12)
    plt.show()

    data2 = sample(1000, 40, variance)
    plt.hist(data2, bins="auto", rwidth=0.8)
    plt.axvline(x=mean(data2), c='black')
    plt.axvline(x=1/12, c='red')
    print("unbias :", mean(data2), 1/12)
    plt.show()

 

 相合性

import random
from statistics import mean, variance
import matplotlib.pyplot as plt

if __name__ == "__main__":

    sample_means = []
    sample_vars = []
    indices = []

    for sz in range(20, 10001, 50):
        indices.append(sz)
        sample = [random.gauss(0.0, 1.0) for _ in range(sz)]
        sample_means.append(mean(sample))
        sample_vars.append(variance(sample))

    plt.plot(indices, sample_means)
    plt.plot(indices, sample_vars)
    plt.show()