The skewness is a parameter to measure the symmetry of a data set and the kurtosis to measure how heavy its tails are compared to a normal distribution, see for example here.
scipy.stats provides an easy way to calculate these two quantities, see scipy.stats.kurtosis and scipy.stats.skew.
In my understanding, the skewness and kurtosis of a normal distribution should both be 0 using the functions just mentioned. That is, however, not the case with my code:
import numpy as np
from scipy.stats import kurtosis
from scipy.stats import skew
x = np.linspace( -5, 5, 1000 )
y = 1./(np.sqrt(2.*np.pi)) * np.exp( -.5*(x)**2 ) # normal distribution
print( 'excess kurtosis of normal distribution (should be 0): {}'.format( kurtosis(y) ))
print( 'skewness of normal distribution (should be 0): {}'.format( skew(y) ))
The output is:
excess kurtosis of normal distribution (should be 0): -0.307393087742
skewness of normal distribution (should be 0): 1.11082371392
What am I doing wrong ?
The versions I am using are
python: 2.7.6
scipy : 0.17.1
numpy : 1.12.1