GenGamma: (Weighted) MLE of Generalized Gamma Distribution

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

Description

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

f(x;a,d,p) = \frac{p/ a^d }{Γ(d/p)} x^{d-1} \exp≤ft( -(x/a)^p \right)

where the domain is x \in (0,∞) with three parameters a > 0 for scale and d, p > 0.

Usage

GenGamma(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

a

scale parameter a.

b

parameter b.

p

parameter p.

Author(s)

Kisung You

Examples

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

#  fit unweighted
GenGamma(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 = GenGamma(x)

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

  MLE = GenGamma(x, weight=ww)
  vec.a[i] = MLE$a
  vec.d[i] = MLE$d
  vec.p[i] = MLE$p
  if ((i%%10) == 0){
    print(paste0(" iteration ",i,"/",niter," complete.."))
  }
}

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

## End(Not run) 

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