scipy.stats.kurtosis(array, axis=0, fisher=True, bias=True) function calculates the kurtosis (Fisher or Pearson) of a data set. It is the 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 kurtosis value is to be measured. By default axis = 0.
fisher : Bool; Fisher’s definition is used (normal 0.0) if True; else Pearson’s definition is used (normal 3.0) if set to False.
bias : Bool; calculations are corrected for statistical bias, if set to False.Returns : Kurtosis value of the normal distribution for the data set.
Code #1:
# Graph using numpy.linspace() # finding kurtosis from scipy.stats import kurtosis 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 :', kurtosis(y1)) print( '\nKurtosis for normal distribution :', kurtosis(y1, fisher = False)) print( '\nKurtosis for normal distribution :', kurtosis(y1, fisher = True)) |
Output :
Kurtosis for normal distribution : -0.3073930877422071 Kurtosis for normal distribution : 2.692606912257793 Kurtosis for normal distribution : -0.3073930877422071
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