Open In App
Related Articles

Inverse Gamma Distribution in Python

Improve
Improve
Improve
Like Article
Like
Save Article
Save
Report issue
Report
Inverse Gamma distribution is a continuous probability distribution with two parameters on the positive real line. It is the reciprocate distribution of a variable distributed according to the gamma distribution. It is very useful in Bayesian statistics as the marginal distribution for the unknown variance of a normal distribution. It is used for considering the alternate parameter for the normal distribution in terms of the precision which is actually the reciprocal of the variance.

scipy.stats.invgamma() :

It is an inverted gamma continuous random variable. It is an instance of the rv_continuous class. It inherits from the collection of generic methods and combines them with the complete specification of distribution. Code #1 : Creating inverted gamma continuous random variable
from scipy.stats import invgamma  
    
numargs = invgamma.numargs
[a] = [0.3] * numargs
rv = invgamma (a)
    
print ("RV : \n", rv) 

                    
Output :
RV : scipy.stats._distn_infrastructure.rv_frozen object at 0x00000230B0B28748
  Code #2 : Inverse Gamma continuous variates and probability distribution
import numpy as np
quantile = np.arange (0.01, 1, 0.1)
     
# Random Variates
R = invgamma.rvs(a, scale = 2,  size = 10)
print ("Random Variates : \n", R)
    
# PDF
R = invgamma .pdf(a, quantile, loc = 0, scale = 1)
print ("\nProbability Distribution : \n", R)

                    
Output :
Random Variates : 
 [4.18816252e+00 2.02807957e+03 8.37914946e+01 1.94368997e+00
 3.78345091e+00 1.00496176e+06 3.42396458e+03 3.45520522e+00
 2.81037118e+00 1.72359706e+03]

Probability Distribution : 
 [0.0012104  0.0157619  0.03512042 0.05975504 0.09007126 0.12639944
 0.16898506 0.21798098 0.27344182 0.33532072]
  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 = invgamma .pdf(x, 1, 3)
y2 = invgamma .pdf(x, 1, 4)
plt.plot(x, y1, "*", x, y2, "r--")

                    
Output :

Last Updated : 02 Aug, 2019
Like Article
Save Article
Previous
Next
Share your thoughts in the comments
Similar Reads