Python - Power-Function Distribution in Statistics

Last Updated : 10 Jan, 2020

scipy.stats.powerlaw() is a power-function continuous random variable. It is inherited from the of generic methods as an instance of the rv_continuous class. It completes the methods with details specific for this particular distribution. Parameters :

q : lower and upper tail probability x : quantiles loc : [optional]location parameter. Default = 0 scale : [optional]scale parameter. Default = 1 size : [tuple of ints, optional] shape or random variates. moments : [optional] composed of letters [‘mvsk’]; ‘m’ = mean, ‘v’ = variance, ‘s’ = Fisher’s skew and ‘k’ = Fisher’s kurtosis. (default = ‘mv’). Results : power-function continuous random variable

Code #1 : Creating power-function continuous random variable

Python3 1==

# importing library

from scipy.stats import powerlaw
  
numargs = powerlaw.numargs 
a, b = 4.32, 3.18
rv = powerlaw(a, b) 
  
print ("RV : \n", rv)

Output :

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D8295B48

Code #2 : power-function continuous variates and probability distribution

Python3 1==

import numpy as np 
quantile = np.arange (0.01, 1, 0.1) 

# Random Variates 
R = powerlaw.rvs(a, b) 
print ("Random Variates : \n", R) 

# PDF 
R = powerlaw.pdf(a, b, quantile) 
print ("\nProbability Distribution : \n", R)

Output :

Random Variates : 
 3.860143037448123

Probability Distribution : 
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]

Code #3 : Graphical Representation.

Python3 1==

import numpy as np 
import matplotlib.pyplot as plt 
   
distribution = np.linspace(0, np.minimum(rv.dist.b, 3)) 
print("Distribution : \n", distribution) 
   
plot = plt.plot(distribution, rv.pdf(distribution))

Output :

Distribution : 
 [0.         0.02040816 0.04081633 0.06122449 0.08163265 0.10204082
 0.12244898 0.14285714 0.16326531 0.18367347 0.20408163 0.2244898
 0.24489796 0.26530612 0.28571429 0.30612245 0.32653061 0.34693878
 0.36734694 0.3877551  0.40816327 0.42857143 0.44897959 0.46938776
 0.48979592 0.51020408 0.53061224 0.55102041 0.57142857 0.59183673
 0.6122449  0.63265306 0.65306122 0.67346939 0.69387755 0.71428571
 0.73469388 0.75510204 0.7755102  0.79591837 0.81632653 0.83673469
 0.85714286 0.87755102 0.89795918 0.91836735 0.93877551 0.95918367
 0.97959184 1.        ]

Code #4 : Varying Positional Arguments

Python3 1==

import matplotlib.pyplot as plt 
import numpy as np 
   
x = np.linspace(0, 5, 100) 
   
# Varying positional arguments 
y1 = powerlaw .pdf(x, 1, 3, 5) 
y2 = powerlaw .pdf(x, 1, 4, 4) 
plt.plot(x, y1, "*", x, y2, "r--")