Python - Skew-Normal Distribution in Statistics

scipy.stats.skewnorm() is a skew-normal continuous random variable. It is inherited from the of generic methods as an instance of the rv_continuous class. It completes the methods with details specific for this particular 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 : skew-normal continuous random variable

Code #1 : Creating skew-normal continuous random variable

Python3 1==

# importing library

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

Output :

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D843A9C8

Code #2 : skew-normal continuous variates and probability distribution

Python3 1==

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

# Random Variates 
R = skewnorm.rvs(a, b) 
print ("Random Variates : \n", R) 

# PDF 
R = skewnorm.pdf(a, b, quantile) 
print ("\nProbability Distribution : \n", R)

Output :

Random Variates : 
 4.2082825614230845

Probability Distribution : 
 [7.38229165e-05 1.13031801e-04 1.71343310e-04 2.57152477e-04
 3.82094976e-04 5.62094062e-04 8.18660285e-04 1.18047149e-03
 1.68525001e-03 2.38193677e-03]

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.         0.04081633 0.08163265 0.12244898 0.16326531 0.20408163
 0.24489796 0.28571429 0.32653061 0.36734694 0.40816327 0.44897959
 0.48979592 0.53061224 0.57142857 0.6122449  0.65306122 0.69387755
 0.73469388 0.7755102  0.81632653 0.85714286 0.89795918 0.93877551
 0.97959184 1.02040816 1.06122449 1.10204082 1.14285714 1.18367347
 1.2244898  1.26530612 1.30612245 1.34693878 1.3877551  1.42857143
 1.46938776 1.51020408 1.55102041 1.59183673 1.63265306 1.67346939
 1.71428571 1.75510204 1.79591837 1.83673469 1.87755102 1.91836735
 1.95918367 2.        ]

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 = skewnorm .pdf(x, 1, 3, 5) 
y2 = skewnorm .pdf(x, 1, 4, 4) 
plt.plot(x, y1, "*", x, y2, "r--")

Output :

Python - Skew-Normal Distribution in Statistics

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