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Python – kappa4 Distribution in Statistics
• Last Updated : 10 Jan, 2020

scipy.stats.kappa4() is an Kappa 4 continuous random variable that is defined with a standard format and some shape parameters to complete its specification. The probability density is defined in the standard form and the loc and scale parameters are used to shift and/or scale the 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 : kappa4 continuous random variable

Code #1 : Creating kappa4 continuous random variable

 `# importing library`` ` `from` `scipy.stats ``import` `kappa4  ``   ` `numargs ``=` `kappa4.numargs ``a, b ``=` `4.32``, ``3.18``rv ``=` `kappa4(a, b) ``   ` `print` `(``"RV : \n"``, rv)  `

Output :

```RV :
scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D50D62C8
```

Code #2 : Johnson SU continuous variates and probability distribution

 `import` `numpy as np ``quantile ``=` `np.arange (``0.01``, ``1``, ``0.1``) `` ` `# Random Variates ``R ``=` `kappa4.rvs(a, b, scale ``=` `2``, size ``=` `10``) ``print` `(``"Random Variates : \n"``, R) `

Output :

```Random Variates :
[0.62293659 0.62825781 0.62377628 0.62308697 0.62665555 0.62802109
0.62872844 0.62728058 0.62679381 0.62297679]

```

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 ``=` `kappa4 .pdf(x, ``1``, ``3``) ``y2 ``=` `kappa4 .pdf(x, ``1``, ``4``) ``plt.plot(x, y1, ``"*"``, x, y2, ``"r--"``) `

Output :

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