Kumaraswamy: (Weighted) MLE of Kumaraswamy Distribution

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

Description

Kumaraswamy distribution is characterized by the following probability density function,

f(x;a,b) = a b x^{a-1} (1-x^a)^{b-1}

where the domain is x \in (0,1) with two shape parameters a,b > 0.

Usage

Kumaraswamy(x, weight = NULL)

Arguments

x	a length-n vector of values in (0,1).
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

nonnegative shape parameter a.

b

nonnegative shape parameter b.

Author(s)

Kisung You

Examples

#  generate data from Unif(0,1)
x = stats::runif(100)

#  fit unweighted
Kumaraswamy(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::runif(ndata)
xmle = Gumbel(x)

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

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

## End(Not run) 

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