# Python – Johnson SU Distribution in Statistics

scipy.stats.johnsonsu() is a Johnson SU 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 : Johnson SU continuous random variable

Code #1 : Creating Johnson SU continuous random variable

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

Output :

```RV :
scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D4E91708
```

Code #2 : Johnson SU continuous variates and probability distribution

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

Output :

```Random Variates :
[-6.33841843 -5.35469028 -5.36145351 -4.4504208  -1.91574847 -5.01633416
-5.37699657 -4.15794134 -4.90450547 -2.93846617]

Probability Distribution :
[5.34745702e-06 2.86846536e-05 2.54767528e-05 1.66921608e-05
9.34800722e-06 4.69729578e-06 2.16525150e-06 9.26607636e-07
3.70800055e-07 1.39402846e-07]
```

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 ``=` `johnsonsu .pdf(x, ``1``, ``3``)  ` `y2 ``=` `johnsonsu .pdf(x, ``1``, ``4``)  ` `plt.plot(x, y1, ``"*"``, x, y2, ``"r--"``)  `

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