# scipy stats.cauchy() | Python

scipy.stats.cauchy() is an cauchy continuous random variable that is defined with a standard format and some shape parameters to complete its specification.

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 : cauchy continuous random variable

Code #1 : Creating cauchy continuous random variable

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

Output :

```RV :
<scipy.stats._distn_infrastructure.rv_frozen object at 0x000002948548C6D8>
```

Code #2 : cauchy random variates and probability distribution function.

 `import` `numpy as np ` `quantile ``=` `np.arange (``0.01``, ``1``, ``0.1``) ` ` `  `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 :

```Random Variates :
[ 2.73388202  4.88389383 -4.89271415  4.63864536 -0.36933865  1.51521875
1.43853452 -0.69619917 -0.68358229  4.13179831]

Probability Distribution :
[0.31827806 0.31450438 0.30486533 0.29040223 0.27250226 0.25260685
0.23198738 0.21162814 0.19220451 0.17412061]```

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``, ``1.0``, ``100``) ` ` `  `# Varying positional arguments ` `y1 ``=` `cauchy.pdf(x, ``2.75``, ``2.75``) ` `y2 ``=` `cauchy.pdf(x, ``3.25``, ``3.25``) ` `plt.plot(x, y1, ``"*"``, x, y2, ``"r--"``) `

Output :

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