Python - kappa3 Distribution in Statistics

Last Updated : 10 Jan, 2020

scipy.stats.kappa3() is an Kappa 3 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 : kappa3 continuous random variable

Code #1 : Creating kappa3 continuous random variable

Python3 1==

# importing library

from scipy.stats import kappa3  
  
numargs = kappa3.numargs 
a, b = 4.32, 3.18
rv = kappa3(a, b) 
  
print ("RV : \n", rv)

Output :

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D51A5F48

Code #2 : Johnson SU continuous variates and probability distribution

Python3 1==

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

# Random Variates 
R = kappa3.rvs(a, b, scale = 2, size = 10) 
print ("Random Variates : \n", R)

Output :

Random Variates : 
 [5.52352397 4.77488722 5.6151088  5.46494471 3.7711133  4.89730708
 3.21392979 8.8291956  3.47994212 3.28716187]

Code #3 : Graphical Representation.

Python3 1==

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

Python3 1==

import matplotlib.pyplot as plt 
import numpy as np 
   
x = np.linspace(0, 5, 100) 
   
# Varying positional arguments 
y1 = kappa3.pdf(x, 1, 3) 
y2 = kappa3.pdf(x, 1, 4) 
plt.plot(x, y1, "*", x, y2, "r--")