Python - Levy_stable Distribution in Statistics - GeeksforGeeks

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 probabilityx : quantilesloc : [optional]location parameter. Default = 0scale : [optional]scale parameter. Default = 1size : [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
# importing library  from scipy.stats import levy_stable      numargs = levy_stable.numargs a, b = 4.32, 3.18rv = levy_stable(a, b)     print ("RV : \n", rv)  
Output :
RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D6803648

Code #2 : Levy-stable continuous variates and probability distribution
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) 
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.
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)  
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]
Python scipy-stats-functions
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