Gumbel: (Weighted) MLE of Gumbel Distribution

In kyoustat/T4mle: What the Package Does Using Title Case

Description

Gumbel distribution is characterized by the following probability density function,

f(x;μ,β) = \frac{1}{β} \exp(-(z+e^{-z}))

with z=(x-μ)/β. The domain is real number \mathbf{R} with location μ \in \mathbf{R} and scale β > 0 parameters.

Usage

Gumbel(x, weight = NULL)

Arguments

x	a length-n vector of nonnegative real numbers.
weight	a length-n weight vector. If set as NULL, it gives an equal weight, leading to standard MLE.

Value

a named list containing (weighted) MLE of

mu

location parameter μ.

beta

scale parameter β.

Author(s)

Kisung You

Examples

#  generate data from standard normal
x = stats::rnorm(100)

#  fit unweighted
Gumbel(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::rnorm(ndata)
xmle = Gumbel(x)

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

  MLE = Gumbel(x, weight=ww)
  vec.mu[i]   = MLE$mu
  vec.beta[i] = MLE$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.mu, main="location 'mu'")
abline(v=xmle$mu, lwd=3, col="red")
hist(vec.beta, main="scale 'beta'")
abline(v=xmle$beta, lwd=3, col="blue")
par(opar)

## End(Not run) 

kyoustat/T4mle documentation built on March 26, 2020, 12:09 a.m.