InvGamma: (Weighted) MLE of Inverse Gamma Distribution
In kyoustat/T4mle: What the Package Does Using Title Case

Description Usage Arguments Value Author(s) Examples

Inverse Gamma distribution is characterized by the following probability density function,

f(x;α,β) = \frac{β^α}{Γ(α)} x^{-α-1} \exp≤ft( -\frac{β}{x}\right)

where the domain is x \in (0,∞) with two parameters α > 0 for shape and β > 0 for scale.

1	InvGamma(x, weight = NULL)

`x`	a length-n vector of values in (0,∞).
`weight`	a length-n weight vector. If set as `NULL`, it gives an equal weight, leading to standard MLE.

a named list containing (weighted) MLE of

alpha: shape parameter α.
beta: scale parameter β.

Kisung You

#  generate data from exponential distribution
x = stats::rexp(100)

#  fit unweighted
InvGamma(x)

## Not run: 
# put random weights to see effect of weights
niter = 500
ndata = 200

# generate data as above and fit unweighted MLE
x    = stats::rexp(ndata)
xmle = InvGamma(x)

# iterate
vec.alpha = rep(0,niter)
vec.beta  = rep(0,niter)
for (i in 1:niter){
  # random weight
  ww = abs(stats::rnorm(ndata))

  MLE = InvGamma(x, weight=ww)
  vec.alpha[i] = MLE$alpha
  vec.beta[i]  = MLE$beta
  if ((i%%10) == 0){
    print(paste0(" iteration ",i,"/",niter," complete.."))
  }
}

# distribution of weighted estimates + standard MLE
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,2))
hist(vec.alpha, main="shape 'alpha'")
abline(v=xmle$alpha, lwd=3, col="red")
hist(vec.beta,  main="scale 'beta'")
abline(v=xmle$beta, lwd=3, col="blue")
par(opar)

## End(Not run)