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Python – Johnson SU Distribution in Statistics

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  • Last Updated : 10 Jan, 2020

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--"

Output :


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