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Python – Levy_stable Distribution in Statistics
  • Last Updated : 10 Jan, 2020

scipy.stats.levy_stable() is a Levy-stable 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-stable continuous random variable

Code #1 : Creating Levy-stable Levy continuous random variable



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

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Output :

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D6803648


Code #2 : Levy-stable continuous variates and probability distribution

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import numpy as np 
quantile = np.arange (0.03, 2, 0.21
  
# Random Variates 
R = levy_stable.rvs(1.8, -0.5, size = 10
print ("Random Variates : \n", R) 
  
# PDF 
R = levy_stable.pdf(a, b, quantile) 
print ("\nProbability Distribution : \n", R) 

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Output :

Random Variates : 
 [ 1.20654126 -0.56381774 -1.31527459 -0.90027222  0.52535969  0.03076316
 -4.69310302  0.61194358  1.31207992 -0.84552083]

Probability Distribution : 
 [nan nan nan nan nan nan nan nan nan nan]

Code #3 : Graphical Representation.

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import numpy as np 
import matplotlib.pyplot as plt 
     
distribution = np.linspace(levy_stable.ppf(0.01, 1.8, -0.5), 
                           levy_stable.ppf(0.99, 1.8, -0.5), 100
print("Distribution : \n", distribution)  

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Output :

Distribution : 
 [-4.92358285 -4.8368521  -4.75012136 -4.66339061 -4.57665986 -4.48992912
 -4.40319837 -4.31646762 -4.22973687 -4.14300613 -4.05627538 -3.96954463
 -3.88281389 -3.79608314 -3.70935239 -3.62262164 -3.5358909  -3.44916015
 -3.3624294  -3.27569866 -3.18896791 -3.10223716 -3.01550641 -2.92877567
 -2.84204492 -2.75531417 -2.66858343 -2.58185268 -2.49512193 -2.40839118
 -2.32166044 -2.23492969 -2.14819894 -2.06146819 -1.97473745 -1.8880067
 -1.80127595 -1.71454521 -1.62781446 -1.54108371 -1.45435296 -1.36762222
 -1.28089147 -1.19416072 -1.10742998 -1.02069923 -0.93396848 -0.84723773
 -0.76050699 -0.67377624 -0.58704549 -0.50031475 -0.413584   -0.32685325
 -0.2401225  -0.15339176 -0.06666101  0.02006974  0.10680048  0.19353123
  0.28026198  0.36699273  0.45372347  0.54045422  0.62718497  0.71391571
  0.80064646  0.88737721  0.97410796  1.0608387   1.14756945  1.2343002
  1.32103094  1.40776169  1.49449244  1.58122319  1.66795393  1.75468468
  1.84141543  1.92814618  2.01487692  2.10160767  2.18833842  2.27506916
  2.36179991  2.44853066  2.53526141  2.62199215  2.7087229   2.79545365
  2.88218439  2.96891514  3.05564589  3.14237664  3.22910738  3.31583813
  3.40256888  3.48929962  3.57603037  3.66276112]

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