# Python – Zipf Discrete Distribution in Statistics

• Last Updated : 10 Jan, 2020

scipy.stats.zipf() is a zipf discrete random variable. It is inherited from the of generic methods as an instance of the rv_discrete class. It completes the methods with details specific for this particular distribution.

Parameters :

x : quantiles
loc : [optional]location parameter. Default = 0
scale : [optional]scale parameter. Default = 1
moments : [optional] composed of letters [‘mvsk’]; ‘m’ = mean, ‘v’ = variance, ‘s’ = Fisher’s skew and ‘k’ = Fisher’s kurtosis. (default = ‘mv’).

Results : zipf discrete random variable

Code #1 : Creating zipf discrete random variable

 `# importing library`` ` `from` `scipy.stats ``import` `zipf ``   ` `numargs ``=` `zipf .numargs ``a, b ``=` `0.2``, ``0.8``rv ``=` `zipf (a, b) ``   ` `print` `(``"RV : \n"``, rv)  `

Output :

```RV :
scipy.stats._distn_infrastructure.rv_frozen object at 0x0000016A4D865848
```

Code #2 : zipf discrete variates and probability distribution

 `import` `numpy as np ``quantile ``=` `np.arange (``0.01``, ``1``, ``0.1``) `` ` `# Random Variates ``R ``=` `zipf .pmf(a, b) ``print` `(``"Random Variates : \n"``, R) `` ` `# PDF ``x ``=` `np.linspace(zipf.ppf(``0.01``, a, b),``                ``zipf.ppf(``0.99``, a, b), ``10``)``R ``=` `zipf.ppf(x, ``1``, ``3``)``print` `(``"\nProbability Distribution : \n"``, R) `

Output :

```Random Variates :
nan

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(``0``, np.minimum(rv.dist.b, ``2``)) ``print``(``"Distribution : \n"``, distribution) `

Output :

```Distribution :
[0.         0.04081633 0.08163265 0.12244898 0.16326531 0.20408163
0.24489796 0.28571429 0.32653061 0.36734694 0.40816327 0.44897959
0.48979592 0.53061224 0.57142857 0.6122449  0.65306122 0.69387755
0.73469388 0.7755102  0.81632653 0.85714286 0.89795918 0.93877551
0.97959184 1.02040816 1.06122449 1.10204082 1.14285714 1.18367347
1.2244898  1.26530612 1.30612245 1.34693878 1.3877551  1.42857143
1.46938776 1.51020408 1.55102041 1.59183673 1.63265306 1.67346939
1.71428571 1.75510204 1.79591837 1.83673469 1.87755102 1.91836735
1.95918367 2.        ]
```

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