I am trying to fit a three parameter inverse gamma distribution to my data in either R or Python. I would like to do this using maximum likelihood estimation (MLE).
The pdf of the three parameter inverse gamma is given by:
Where Γ is the gamma function, ρ is the shape, α is the scale and s is the location parameter
I haven't spotted an R package that can perform MLE to this distribution directly (if you know of one, please let me know!). So I think this leaves either:
- (A) working out the log-likelihood function of the formula
- (B) transforming the data to a gamma distribution. However, this distribution only has two parameters so I'm not clear on how I would calculate the third parameter (I'm not a very mathematical person!).
Any help on a method to use MLE to fit an inverse gamma distribution to my data would be much appreciated! Many thanks in advance.