I have this code to calculate kurtosis (http://mathworld.wolfram.com/Kurtosis.html) using my own code and I compare it to scipy.stats.kurtosis
a = array([ 1. , 2. , 2.5, 400. , 6. , 0. ])
#kurtosis (gives: 4.19886)
print (sum((a - np.mean(a)) ** 4)/len(a)) / np.std(a)**4
# scipy kurtosis (gives: 5.996677)
print scipy.stats.kurtosis(a,bias=False)
why is scipy giving a different result? I followed the definition in mathworld.
If you read the documentation of scipy's kurtosis function, scipy is calculting Excess Kurtosis by default (with the minus 3):
scipy.stats.kurtosis(a, axis=0, fisher=True, bias=True)
Computes the kurtosis (Fisher or Pearson) of a dataset.
Kurtosis is the fourth central moment divided by the square of the variance. If Fisher’s definition is used, then 3.0 is subtracted from the result to give 0.0 for a normal distribution.
If bias is False then the kurtosis is calculated using k statistics to eliminate bias coming from biased moment estimators
Setting fisher to False will give you what you expected:
In [1]: a = np.array([ 1. , 2. , 2.5, 400. , 6. , 0. ])
In [2]: scipy.stats.kurtosis(a, fisher=False)
Out[2]: 4.198860780044809