Estimate the parameters of an inverse gamma distribution given quantiles

Question

I'm trying to estimate the parameters of an inverse Gamma distribution given its 0.025 and 0.975 quantiles.

Currently, I've found rriskDistributions::get.gamma.par which gives me the estimation of parameters given quantiles of a Gamma distribution. However, I cannot figure out the relationship between the quantiles of Gammas and inverse Gammas.

How should I continue, or is there a package that can do this for me?

Answer 1

You can write your own objective function that computes the squared deviation between the computed quantiles for a particular set of inverse-gamma parameters and the target quantiles:

library(invgamma)
objfun <- function(p,target) {
    qq <- qinvgamma(c(0.025,0.975),shape=p[1],rate=p[2])
    sum((qq-target)^2)
}

Then use optim() to minimize:

## example
tt <- qinvgamma(c(0.025,0.975), shape=2,rate=2)
optim(par=c(1,4),  ## starting values; must be sensible
      fn=objfun,
      target=tt)
$par
[1] 1.980279 1.948050

$value
[1] 9.0741e-05

$counts
function gradient 
      61       NA 

$convergence
[1] 0

$message
NULL