Python tests whether Jarque-Bera conforms to normal distribution

零到壹度
Release: 2018-04-09 16:19:06
Original
11977 people have browsed it


The content of this article is to test whether Jarque-Bera conforms to the normal distribution in python. It has a certain reference value. Friends in need can refer to it

Normal distribution is a normality test of a population distribution. When the sequence obeys the normal distribution, the JB statistic:

Python tests whether Jarque-Bera conforms to normal distribution

##gradually obeys distributed. Where n is the sample size, S and K are the skewness and kurtosis of the random variable respectively. Calculated as follows:


Python tests whether Jarque-Bera conforms to normal distribution

#The functions called for skewness and kurtosis in python's sicipy.stats are

stats.skew(y)
, stats.kurtosis(y), where the formula of kurtosis is In excel, the calculation formulas for skewness and kurtosis are as follows :

Python tests whether Jarque-Bera conforms to normal distribution


# Next, implement the formulas for calculating skewness and skew in Python's scipy library and establish a normal distribution test.

Code

import numpy as npimport scipy.stats as statsdef self_JBtest(y):
    # 样本规模n
    n = y.size
    y_ = y - y.mean()    """
    M2:二阶中心钜
    skew 偏度 = 三阶中心矩 与 M2^1.5的比
    krut 峰值 = 四阶中心钜 与 M2^2 的比
    """
    M2 = np.mean(y_**2)
    skew =  np.mean(y_**3)/M2**1.5
    krut = np.mean(y_**4)/M2**2

    """
    计算JB统计量,以及建立假设检验
    """
    JB = n*(skew**2/6 + (krut-3 )**2/24)
    pvalue = 1 - stats.chi2.cdf(JB,df=2)
    print("偏度:",stats.skew(y),skew)
    print("峰值:",stats.kurtosis(y)+3,krut)
    print("JB检验:",stats.jarque_bera(y))    return np.array([JB,pvalue])

y1 = stats.norm.rvs(size=10)

y2 = stats.t.rvs(size=1000,df=4)

print(self_JBtest(y1))

print(self_JBtest(y2))
Copy after login
Result

=============== RESTART: C:\Users\tinysoft\Desktop\JB正态性检验.py =============== 

  偏度: 0.5383125387398069 0.53831253874 

  峰值: 2.9948926317585918 2.99489263176 

  JB检验: (0.48297818444514068, 0.78545737133644544) 

  [ 0.48297818  0.78545737] 

  偏度: -1.0488825341925703 -1.04888253419 

  峰值: 13.40804986639119 13.4080498664 

  JB检验: (4697.0050126426095, 0.0) 

  [ 4697.00501264     0.        ]
Copy after login
Python tests whether Jarque-Bera conforms to normal distribution

The above is the detailed content of Python tests whether Jarque-Bera conforms to normal distribution. For more information, please follow other related articles on the PHP Chinese website!

Related labels:
source:php.cn
Statement of this Website
The content of this article is voluntarily contributed by netizens, and the copyright belongs to the original author. This site does not assume corresponding legal responsibility. If you find any content suspected of plagiarism or infringement, please contact admin@php.cn
Popular Tutorials
More>
Latest Downloads
More>
Web Effects
Website Source Code
Website Materials
Front End Template