Rayleigh: (Weighted) MLE of Rayleigh Distribution

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

Description

Rayleigh distribution is characterized by the following probability density function,

f(x;σ) = \frac{x}{σ^2} \exp( -x^2 / (2σ^2))

where the domain is nonnegative real number x \in [0,∞) with scale parameter σ > 0.

Usage

Rayleigh(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

sigma

scale parameter σ.

Author(s)

Kisung You

Examples

#  generate data from exponential distribution with lambda=1
x = stats::rexp(100, rate=1)

#  fit unweighted
Rayleigh(x)

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

# generate data and fit unweighted MLE
x    = stats::rexp(ndata, rate=1)
xmle = Rayleigh(x)

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

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

# distribution of weighted estimates + standard MLE
opar <- par(no.readonly=TRUE)
hist(vec.sigma, main="scale 'sigma'")
abline(v=xmle$sigma, lwd=3, col="red")
par(opar)

## End(Not run) 

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