Python – Inverse Gaussian Distribution in Statistics

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

# 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

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.

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

Output :