Description Usage Arguments Value Author(s) Examples
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.
1 |
x |
a length-n vector of values in (0,∞). |
weight |
a length-n weight vector. If set as |
a named list containing (weighted) MLE of
shape parameter α.
scale parameter λ.
Kisung You
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)
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