Weibull: (Weighted) MLE of Weibull Distribution

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

Description

Two-parameter Weibull distribution is characterized by the following probability density function,

f(x;λ, k)= \frac{k}{λ} ≤ft( \frac{x}{λ} \right)^{k-1} \exp( -(x/λ)^k )

where the domain is x \in [0,∞) with scale λ > 0 and shape k > 0 parameter.

Usage

Weibull(x, weight = NULL)

Arguments

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.

Value

a named list containing (weighted) MLE of

lambda

scale parameter λ.

k

shape parameter k.

Author(s)

Kisung You

Examples

#  generate data from half-normal
x = abs(stats::rnorm(100))

#  fit unweighted
Weibull(x)

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

# generate data and fit unweighted MLE
x    = abs(stats::rnorm(ndata))
xmle = Weibull(x)

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

  MLE = Weibull(x, weight=ww)
  vec.lbd[i] = MLE$lambda
  vec.k[i]   = MLE$k
  if ((i%%10) == 0){
    print(paste0(" iteration ",i,"/",niter," complete.."))
  }
}

# visualize distributions of weighted estimates and MLE
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,2))
hist(vec.lbd, main="scale 'lambda'")
abline(v=xmle$lambda, lwd=3, col="red")
hist(vec.k,   main="shape 'k'")
abline(v=xmle$k, lwd=3, col="blue")
par(opar)

## End(Not run) 

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