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Python – Power-Function Distribution in Statistics

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  • 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




# 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




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.




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




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--"

Output :


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