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

 #!/usr/bin/env python3
 #-*- coding:utf-8 -*-
 #############################################
 #File Name: t.py
 #Brief:
 #Author: frank
 #Email: frank0903@aliyun.com
 #Created Time:2018-08-17 23:07:24
 #Blog: http://www.cnblogs.com/black-mamba
 #Github: https://github.com/xiaomagejunfu0903/statistic_notes
 #############################################

 from scipy.stats import t
 from scipy.stats import norm
 import matplotlib.pyplot as plt
 import numpy as np

 df = 2
 rv_t = t(df)
 x = np.linspace(-4,4, 100)
 plt.plot(x,rv_t.pdf(x),'y-',label='df=2')

 x2 = np.linspace(-4,4, 100)
 plt.plot(x2,t.pdf(x2,5),'g--',label='df=5')

 x3 = np.linspace(-4,4, 100)
 plt.plot(x3,t.pdf(x3,10),'b--',label='df=10')

 x4 = np.linspace(-4,4, 100)
 plt.plot(x4,t.pdf(x4,120),'r--',label='df=120')

 x5 = np.linspace(-4,4, 100)
 plt.plot(x5,norm.pdf(x5),'m--',label='std norm',alpha=0.5)

 plt.legend()

 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。