Python - Inverse Gaussian Distribution in Statistics

Last Updated : 10 Jan, 2020

scipy.stats.invgauss() is an inverted gauss 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 :

a : shape parameter c : special case of gengauss. Default equals to c = -1

Code #1 : Creating Inverse Gaussian continuous random variable

Python3 1==

# importing library
from scipy.stats import invgauss   
   
numargs = invgauss.numargs 
[a, b] = [0.7, 0.4] * numargs 
rv = invgauss (a, b) 
   
print ("RV : \n", rv)

Output :

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x1a220d7bd0

Code #2 : Inverse Gaussian continuous variates and probability distribution

Python3 1==

import numpy as np 
quantile = np.arange (0.01, 1) 
    
# Random Variates 
R = invgauss.ppf(0.01, a) 
print ("Random Variates : \n", R) 
   
# PDF 
R = invgauss.pdf(invgauss.ppf(0.01, a), a) 
print ("\nProbability Distribution : \n", R)

Output :

Random Variates : 
 0.25801533159920903

Probability Distribution : 
 0.15984442779701688

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.         0.06122449 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

Python3 1==

import matplotlib.pyplot as plt 
import numpy as np 
   
x = np.linspace(0, 5, 100) 
   
# Varying positional arguments 
y1 = invgauss .pdf(x, 1, 3) 
y2 = invgauss .pdf(x, 1, 4) 
plt.plot(x, y1, "*", x, y2, "r--")