# 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]```

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