Law of large numbers(大数定理)
the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law,the average of the results obtained from a large number of trials should be close to the expected value,and will tend to become closer as more trials are performed.
当试验次数足够大时,样本均值趋向于总体均值。
实例
以掷骰子为例，已知总体均值为3.5，随着实验次数的增加，样本均值将发生怎样的变化呢？
#!/usr/bin/env python3 #-*- coding:utf-8 -*- ############################################# #File Name: lln.py #Brief: 以掷骰子为例，演示随着试验次数的增加，样本均值趋于总体均值 #Author: frank #Email: [email protected] #Created Time:2018-08-07 22:29:00 #Blog: http://www.cnblogs.com/black-mamba #Github: https://github.com/suonikeyinsuxiao ############################################# import numpy as np import matplotlib.pyplot as plt #总实验次数 total_num = 1000 #骰子的6面 num_sides = 6 plt.figure(1) #设置x轴的范围 xmin,xmax = plt.xlim(0,total_num) print("xmin:{},xmax:{}".format(xmin,xmax)) #设置y轴的范围 ymin,ymax = plt.ylim(1,6) print("ymin:{},ymax:{}".format(ymin,ymax)) #设置坐标轴的名称 plt.xlabel(‘number of trials‘) plt.ylabel(‘average‘) #画均值线 plt.plot((0,total_num),(3.5,3.5),c=‘b‘) l = [] n_s = range(1,total_num) #number of trials:n,mean of sample:average for n in n_s: average = np.mean(np.random.randint(1,7,n)) l.append(average) #print("n:{},average:{}".format(n,average)) #plt.scatter(n,average,c=‘r‘,s=1,alpha=0.5) plt.plot(n_s,l,alpha=0.5,c=‘red‘) plt.figure(2) #设置x轴的范围 ymin,ymax = plt.ylim(0,total_num) print("ymin:{},ymax)) #设置y轴的范围 xmin,xmax = plt.xlim(1,6) print("xmin:{},xmax)) #设置坐标轴的名称 plt.xlabel(‘number of trials‘) plt.ylabel(‘average‘) plt.plot((3.5,(0,c=‘b‘) #plt.plot(l,n_s,c=‘red‘) for n in n_s: average = np.mean(np.random.randint(1,average)) plt.scatter(average,n,alpha=0.5) plt.show()
