ShiftedGompertz: (Weighted) MLE of Shifted Gompertz Distribution

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

Description

Shifted Gompertz distribution is characterized by the following probability density function,

f(x;b,η) = b \exp(-bx) \exp(-η \exp(-bx)) ≤ft( 1 + η(1-\exp(-bx)) \right)

where the domain is x \in [0,∞) with two parameters b ≥q 0 for scale and η ≥q 0 for shape.

Usage

ShiftedGompertz(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

b

scale parameter b.

eta

shape parameter η.

Author(s)

Kisung You

Examples

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

#  fit unweighted
ShiftedGompertz(x)

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

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

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

  MLE = ShiftedGompertz(x, weight=ww)
  vec.b[i]   = MLE$b
  vec.eta[i] = MLE$eta
  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.b, main="scale 'b'")
abline(v=xmle$b, lwd=3, col="red")
hist(vec.eta,  main="shape 'eta'")
abline(v=xmle$eta,  lwd=3, col="blue")
par(opar)

## End(Not run) 

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