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# scipy stats.foldcauchy() | Python

• Last Updated : 27 Mar, 2019

scipy.stats.foldcauchy() is an folded 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
-> a : shape parameters
-> 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 : folded Cauchy continuous random variable

Code #1 : Creating folded Cauchy continuous random variable

 `from` `scipy.stats ``import` `foldcauchy`` ` `numargs ``=` `foldcauchy.numargs``[a] ``=` `[``0.7``, ] ``*` `numargs``rv ``=` `foldcauchy(a)`` ` `print` `(``"RV : \n"``, rv) `

Output :

```RV :
<scipy.stats._distn_infrastructure.rv_frozen object at 0x0000018D55D8E160>
```

Code #2 : Folded Cauchy random variates and probability distribution function.

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

Output :

```Random Variates :
[1.7445128  2.82630984 0.81871044 5.19668279 7.81537565 1.67855736
3.35417067 0.13838753 1.29145462 1.90601065]

Probability Distribution :
[0.42727064 0.42832192 0.43080143 0.43385803 0.43622229 0.43639823
0.43294602 0.42480391 0.41154712 0.3934792 ]
```

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.         0.06122449 0.12244898 0.18367347 0.24489796 0.30612245
0.36734694 0.42857143 0.48979592 0.55102041 0.6122449  0.67346939
0.73469388 0.79591837 0.85714286 0.91836735 0.97959184 1.04081633
1.10204082 1.16326531 1.2244898  1.28571429 1.34693878 1.40816327
1.46938776 1.53061224 1.59183673 1.65306122 1.71428571 1.7755102
1.83673469 1.89795918 1.95918367 2.02040816 2.08163265 2.14285714
2.20408163 2.26530612 2.32653061 2.3877551  2.44897959 2.51020408
2.57142857 2.63265306 2.69387755 2.75510204 2.81632653 2.87755102
2.93877551 3.        ]```

Code #4 : Varying Positional Arguments

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

Output :

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