小马哥课堂-统计学-t分布(2)

t分布，随着自由度的增加，而逐渐接近于正态分布

 1 #!/usr/bin/env python3
 2 #-*- coding:utf-8 -*-
 3 #############################################
 4 #File Name: t.py
 5 #Brief:
 6 #Author: frank
 7 #Email: [email protected]
 8 #Created Time:2018-08-17 23:07:24
 9 #Blog: http://www.cnblogs.com/black-mamba
10 #Github: https://github.com/xiaomagejunfu0903/statistic_notes
11 #############################################
12 
13 from scipy.stats import t
14 from scipy.stats import norm
15 import matplotlib.pyplot as plt
16 import numpy as np
17 
18 df = 2
19 rv_t = t(df)
20 x = np.linspace(-4,4, 100)
21 plt.plot(x,rv_t.pdf(x),'y-',label='df=2')
22 
23 x2 = np.linspace(-4,4, 100)
24 plt.plot(x2,t.pdf(x2,5),'g--',label='df=5')
25 
26 x3 = np.linspace(-4,4, 100)
27 plt.plot(x3,t.pdf(x3,10),'b--',label='df=10')
28 
29 x4 = np.linspace(-4,4, 100)
30 plt.plot(x4,t.pdf(x4,120),'r--',label='df=120')
31 
32 x5 = np.linspace(-4,4, 100)
33 plt.plot(x5,norm.pdf(x5),'m--',label='std norm',alpha=0.5)
34 
35 plt.legend()
36 
37 plt.show()

 

从上图可以看出，当df=120时，t曲线几乎与正态分布曲线重合。