Python verifies that the Jarque-bera conforms to the normal distribution

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The normal distribution is a normality test of the general distributions. When the sequence obeys a normal distribution, JB statistics:

Gradually obey the distribution. where n is the sample size, the s,k is the skewness and kurtosis of the random variable respectively. The calculation formula is as follows:

Python's sicipy.stats is a function of a call to Skewness and Kurtosis, stats.skew(y) stats.kurtosis(y) where the formula for Kurtosis is

In Excel, the skewness and kurtosis are calculated as follows:

Let's do it all over again. The formula for calculating skewness and skew in Python's scipy library and the establishment of normal distribution test.

Code

Import NumPy as Npimport scipy.stats as Statsdef self_jbtest (y):    # sample size n    n = y.size    y_ = Y-y.mean ()    "" " C4/>M2: Second-order center massive    Skew skewness = three-Step center moment with m2^1.5 ratio    Krut peak = four-order center Mega vs. M2^2    "" "    M2 = Np.mean (y_**2)    skew =  Np.mean (y_**3)/m2**1.5    Krut = Np.mean (y_**4)/m2**2    "" "    calculates the JB statistic and establishes hypothesis test    " ""    JB = N (skew* *2/6 + (krut-3) **2/24)    pvalue = 1-STATS.CHI2.CDF (jb,df=2)    print ("skewness:", Stats.skew (y), skew)    print (" Peak: ", Stats.kurtosis (y) +3,krut)    print (" JB test: ", 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))

Results

=============== restart:c:\users\tinysoft\desktop\jb normality test. py = = ============= skewness: 0.5383125387398069 0.53831253874 Peak: 2.9948926317585918 2.99489263176 JB Test: (0.48297818444514068, 0.78545737133644544) [0.48297818 0.78545737] skewness: -1.0488825341925703-1.04888253419 Peak: 13.40804986639119 13.40804        98664 JB Test: (4697.0050126426095, 0.0) [4697.00501264 0. ]