Python – Levy_stable Distribution in Statistics

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

# 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)

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]