# scipy stats.erlang() | Python

scipy.stats.erlang() : is an Erlang continuous random variable that is defined with a standard format and some shape parameters to complete its specification. it is a special case of the Gamma 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 : erlang continuous random variable

Code #1 : Creating erlang continuous random variable

 `from` `scipy.stats ``import` `erlang  ` ` `  `numargs ``=` `erlang.numargs ` `[a] ``=` `[``0.6``, ] ``*` `numargs ` `rv ``=` `erlang(a) ` ` `  `print` `(``"RV : \n"``, rv)  `

Output :

```RV :
<scipy.stats._distn_infrastructure.rv_frozen object at 0x0000018D544FBC88>
```

Code #2 : erlang random variates and probability distribution.

 `import` `numpy as np ` `quantile ``=` `np.arange (``0.01``, ``1``, ``0.1``) ` `  `  `# Random Variates ` `R ``=` `erlang.rvs(a, scale ``=` `2``,  size ``=` `10``) ` `print` `(``"Random Variates : \n"``, R) ` ` `  `# PDF ` `R ``=` `erlang.pdf(a, quantile, loc ``=` `0``, scale ``=` `1``) ` `print` `(``"\nProbability Distribution : \n"``, R) `

Output :

```Random Variates :
[5.65708510e+00 5.16045580e+00 1.02056956e-01 3.64349340e-01
5.65593073e+00 2.27100280e+00 9.77623414e-04 2.01994399e-01
8.84331471e-01 2.20817630e+00]

Probability Distribution :
[0.01, 0.11, 0.21, 0.31, 0.41, 0.51, 0.61, 0.71, 0.81, 0.91]
```

Code #3 : Graphical Representation.

 `import` `numpy as np ` `import` `matplotlib.pyplot as plt ` ` `  `distribution ``=` `np.linspace(``0``, np.minimum(rv.dist.b, ``5``)) ` `print``(``"Distribution : \n"``, distribution) ` ` `  `plot ``=` `plt.plot(distribution, rv.pdf(distribution)) `

Output :

```Distribution :
Distribution :
[0.         0.10204082 0.20408163 0.30612245 0.40816327 0.51020408
0.6122449  0.71428571 0.81632653 0.91836735 1.02040816 1.12244898
1.2244898  1.32653061 1.42857143 1.53061224 1.63265306 1.73469388
1.83673469 1.93877551 2.04081633 2.14285714 2.24489796 2.34693878
2.44897959 2.55102041 2.65306122 2.75510204 2.85714286 2.95918367
3.06122449 3.16326531 3.26530612 3.36734694 3.46938776 3.57142857
3.67346939 3.7755102  3.87755102 3.97959184 4.08163265 4.18367347
4.28571429 4.3877551  4.48979592 4.59183673 4.69387755 4.79591837
4.89795918 5.        ]```

Code #4 : Varying Positional Arguments

 `import` `matplotlib.pyplot as plt ` `import` `numpy as np ` ` `  `x ``=` `np.linspace(``0``, ``5``, ``100``) ` ` `  `# Varying positional arguments ` `y1 ``=` `erlang.pdf(x, ``2``, ``6``) ` `y2 ``=` `erlang.pdf(x, ``1``, ``4``) ` `plt.plot(x, y1, ``"*"``, x, y2, ``"r--"``) `

Output :

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