jarque bera测试结果

Question

I dont understand the results of a Jarque Bera test.

from statsmodels.stats.stattools import jarque_bera    
np.random.seed(123)
jarque_bera(np.random.normal(-5, 1, 1000))

Results:

(0.1675179797931011,
 0.9196528750223983,
 -0.029040113501245704,
 2.9745614712223074)

3rd value looks like P-value. The others I thought are Kurtosis and Skew and the 4th I dont know.

So I tested my theory but it was wrong as per the code below:

import scipy.stats as stats

print(stats.skew(np.random.normal(-5, 1, 1000)))
print(stats.kurtosis(np.random.normal(-5, 1, 1000)))

-0.19743173433793879
-0.11038007419823126

Answer 1

You need n > 2000 for the Jarque Bera test to be valid

The output gives you; the test stat, the p value, skew, kurtosis in that order. Not sure why this is not in the docs though?

Also the implemented Jarque Bera test uses Pearson's definition of kurtosis not Fisher's , so...

from statsmodels.stats.stattools import jarque_bera  
import scipy.stats as stats
import numpy as np

np.random.seed(123)
samples = np.random.normal(-5, 1, 3000)

print(jarque_bera(samples))
print(stats.skew(samples))
print(stats.kurtosis(samples, fisher=False))

Output..

(3.9600892567754835, 0.13806307564092868, -0.08899286958111645, 3.0013381737844793)
-0.08899286958111645
3.0013381737844793