# Python – Power-Function Distribution in Statistics

Last Updated : 10 Jan, 2020

scipy.stats.powerlaw() is a power-function 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 [â€˜mvskâ€™]; â€˜mâ€™ = mean, â€˜vâ€™ = variance, â€˜sâ€™ = Fisherâ€™s skew and â€˜kâ€™ = Fisherâ€™s kurtosis. (default = â€˜mvâ€™).

Results : power-function continuous random variable

Code #1 : Creating power-function continuous random variable

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

Output :

```RV :
scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D8295B48
```

Code #2 : power-function continuous variates and probability distribution

 `import` `numpy as np  ` `quantile ``=` `np.arange (``0.01``, ``1``, ``0.1``)  ` ` `  `# Random Variates  ` `R ``=` `powerlaw.rvs(a, b)  ` `print` `(``"Random Variates : \n"``, R)  ` ` `  `# PDF  ` `R ``=` `powerlaw.pdf(a, b, quantile)  ` `print` `(``"\nProbability Distribution : \n"``, R)  `

Output :

```Random Variates :
3.860143037448123

Probability Distribution :
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]

```

Code #3 : Graphical Representation.

 `import` `numpy as np  ` `import` `matplotlib.pyplot as plt  ` `    `  `distribution ``=` `np.linspace(``0``, np.minimum(rv.dist.b, ``3``))  ` `print``(``"Distribution : \n"``, distribution)  ` `    `  `plot ``=` `plt.plot(distribution, rv.pdf(distribution))  `

Output :

```Distribution :
[0.         0.02040816 0.04081633 0.06122449 0.08163265 0.10204082
0.12244898 0.14285714 0.16326531 0.18367347 0.20408163 0.2244898
0.24489796 0.26530612 0.28571429 0.30612245 0.32653061 0.34693878
0.36734694 0.3877551  0.40816327 0.42857143 0.44897959 0.46938776
0.48979592 0.51020408 0.53061224 0.55102041 0.57142857 0.59183673
0.6122449  0.63265306 0.65306122 0.67346939 0.69387755 0.71428571
0.73469388 0.75510204 0.7755102  0.79591837 0.81632653 0.83673469
0.85714286 0.87755102 0.89795918 0.91836735 0.93877551 0.95918367
0.97959184 1.        ]
```

Code #4 : Varying Positional Arguments

 `import` `matplotlib.pyplot as plt  ` `import` `numpy as np  ` `    `  `x ``=` `np.linspace(``0``, ``5``, ``100``)  ` `    `  `# Varying positional arguments  ` `y1 ``=` `powerlaw .pdf(x, ``1``, ``3``, ``5``)  ` `y2 ``=` `powerlaw .pdf(x, ``1``, ``4``, ``4``)  ` `plt.plot(x, y1, ``"*"``, x, y2, ``"r--"``)  `

Output :