Python – kappa3 Distribution in Statistics

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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

# 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

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.

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 = kappa3.pdf(x, 1, 3)  
y2 = kappa3.pdf(x, 1, 4)  
plt.plot(x, y1, "*", x, y2, "r--")  