Hello.

What I had in mind in this (for the bivariate case).

Christophe

library(gumbel)

#simulate random sample
xy <- rgumbel(100, pi)
xy[, 1] <- qnorm(xy[, 1])
xy[, 2] <- qexp(xy[, 2])

#estimate the alpha parameter with canonical maximum likelihood (i.e. assume
ecdf for marginals)
alphahat <- gumbel.CML(xy[, 1], xy[, 2])

eqf <- function(x, marg.number)
    as.numeric( quantile(xy[, marg.number], probs=x) )

#check it looks like the standad normal distribution
plot(eqf(0:100/100, 1), 0:100, type="l")
#check it looks like the standad exponential distribution
plot(eqf(0:100/100, 2), 0:100, type="l")

myrand <- function(n)
{
    myunif <- rgumbel(n, alphahat)
    myunif[, 1] <- eqf(myunif[, 1], 1)
    myunif[, 2] <- eqf(myunif[, 2], 2)
    myunif
}

par(mfrow=c(1, 2))

plot(xy[,1], xy[,2], main="original sample", xlab="x", ylab="y")

asample <- myrand(100)

plot(asample[,1], asample[,2], main="sample from the fitted parameter",
xlab="x", ylab="y")


2011/1/24 salmajj <salmajj@softhome.net>

>
> Hi Christophe,
> thanks a lot for your response,
> Actually i do not well understand this point "apply eqf on each marginal" !
> please could you give me more insight?
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-- 
Christophe DUTANG
Ph. D. student at ISFA, Lyon, France

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