Lomax: (Weighted) MLE of Lomax Distribution

Description Usage Arguments Value Author(s) Examples

View source: R/Lomax.R

Description

Lomax distribution, also called Pareto Type 2 distribution, is characterized by the following probability density function,

f(x;α,λ) = \frac{α}{λ} ≤ft[ 1 + \frac{x}{λ} \right]^{-(α+1)}

where the domain is x \in [0,∞) with two parameters α > 0 for shape and λ > 0 for scale.

Usage

1
Lomax(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

alpha

shape parameter α.

lambda

scale parameter λ.

Author(s)

Kisung You

Examples

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
#  generate data from exponential distribution
x = abs(stats::rexp(100))

#  fit unweighted
Lomax(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))
xmle = Lomax(x)

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

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

## End(Not run) 

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