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Python – Levy Distribution in Statistics

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scipy.stats.levy() is a levy 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 : levy continuous random variable
Code #1 : Creating levy continuous random variable
# importing library
  
from scipy.stats import levy  
    
numargs = levy.numargs 
a, b = 4.32, 3.18
rv = levy(a, b) 
    
print ("RV : \n", rv)  

                    
Output :
RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D661FF48
Code #2 : levy continuous variates and probability distribution
import numpy as np 
quantile = np.arange (0.01, 1, 0.1
  
# Random Variates 
R = levy.rvs(a, b) 
print ("Random Variates : \n", R) 
  
# PDF 
R = levy.pdf(a, b, quantile) 
print ("\nProbability Distribution : \n", R) 

                    
Output :
Random Variates : 
 10.146582883442196

Probability Distribution : 
 [0.03263232 0.10358487 0.13698141 0.15928865 0.17532664 0.18715139
 0.19589569 0.2022745  0.20677902 0.20976675]
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.         0.06122449 0.12244898 0.18367347 0.24489796 0.30612245
 0.36734694 0.42857143 0.48979592 0.55102041 0.6122449  0.67346939
 0.73469388 0.79591837 0.85714286 0.91836735 0.97959184 1.04081633
 1.10204082 1.16326531 1.2244898  1.28571429 1.34693878 1.40816327
 1.46938776 1.53061224 1.59183673 1.65306122 1.71428571 1.7755102
 1.83673469 1.89795918 1.95918367 2.02040816 2.08163265 2.14285714
 2.20408163 2.26530612 2.32653061 2.3877551  2.44897959 2.51020408
 2.57142857 2.63265306 2.69387755 2.75510204 2.81632653 2.87755102
 2.93877551 3.        ]
 
Code #4 : Varying Positional Arguments
import matplotlib.pyplot as plt 
import numpy as np 
     
x = np.linspace(0, 5, 100
     
# Varying positional arguments 
y1 = levy .pdf(x, 1, 3
y2 = levy .pdf(x, 1, 4
plt.plot(x, y1, "*", x, y2, "r--"

                    
Output :

Last Updated : 10 Jan, 2020
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