scipy stats.kurtosistest() function | Python

scipy.stats.kurtosistest(array, axis=0) function test whether the given data set has normal kurtosis (Fisher or Pearson) or not.

What is Kurtosis ?
It is the fourth central moment divided by the square of the variance. It is a measure of the “tailedness” i.e. descriptor of shape of probability distribution of a real-valued random variable. In simple terms, one can say it is a measure of how heavy tail is compared to a normal distribution.

Its formula –

Parameters :
array : Input array or object having the elements.
axis : Axis along which the kurtosistest is to be computed. By default axis = 0.

Returns : Z-score (Statistics value) and P-value for the normally distributed data set.

Code #1:

# Graph using numpy.linspace()
# finding kurtosis

from scipy.stats import kurtosistest
import numpy as np
import pylab as p

x1 = np.linspace( -5, 5, 1000 )
y1 = 1./(np.sqrt(2.*np.pi)) * np.exp( -.5*(x1)**2  )

p.plot(x1, y1, '*')


print( '\nKurtosis for normal distribution :\n', kurtosistest(y1))

Output :

Kurtosis for normal distribution :
 KurtosistestResult(statistic=-2.2557936070461615, pvalue=0.024083559905734513)