Levy: (Weighted) MLE of Lévy Distribution

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

Description

Lévy distribution is characterized by the following probability density function,

f(x;μ,c) = √{\frac{c}{2π}} \frac{e^{-\frac{c}{2(x-μ)}}}{(x-μ)^{3/2}}

where the domain is x \in [μ,∞) with two parameters μ for location and c for scale.

Usage

Levy(x, weight = NULL)

Arguments

x	a length-n vector of values in [μ,∞). Due to its dependence on parameter μ, actual input can be any real-valued vector.
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

mu

location parameter μ.

c

scale parameter c.

Author(s)

Kisung You

Examples

#  generate data from exponential distribution and shift
x = abs(stats::rexp(100)) + 2

#  fit unweighted
Levy(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::rexp(ndata)) + 2
xmle = Levy(x)

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

  MLE = Levy(x, weight=ww)
  vec.mu[i] = MLE$mu
  vec.c[i]  = MLE$c
  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.mu, main="location 'mu'")
abline(v=xmle$mu, lwd=3, col="red")
hist(vec.c,  main="scale 'c'")
abline(v=xmle$c,  lwd=3, col="blue")
par(opar)

## End(Not run) 

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