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--")

Output :