估计给定分位数的逆伽马分布的参数

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