Python – Normal Inverse Gaussian Distribution in Statistics

scipy.stats.norminvgauss() is a Normal Inverse Gaussian 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 : Normal Inverse Gaussian continuous random variable

Code #1 : Creating Normal Inverse Gaussian continuous random variable

# importing library

from scipy.stats import norminvgauss

numargs = norminvgauss.numargs
a, b = 4.32, 3.18
rv = norminvgauss(a, b)

print ("RV : \n", rv)

Output :

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D7E7F988

Code #2 : Normal Inverse Gaussian continuous variates and probability distribution

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

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

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

Output :

Random Variates : 
 1.3435537740460517

Probability Distribution : 
 [1.47553069e-06 2.26852616e-06 3.47672896e-06 5.31156917e-06
 8.08889275e-06 1.22787583e-05 1.85780134e-05 2.80155365e-05
 4.21040186e-05 6.30575858e-05]
 

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.         0.04081633 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.        ]