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# 2005-09-26, Alberto Viglione
#
# Algorithm based on Hosking and Wallis...
f.gumb <- function(x,xi,alfa) {
f <- alfa^(-1) * exp(-(x - xi)/alfa)*exp(-exp(-(x - xi)/alfa))
return(f)
}
F.gumb <- function(x,xi,alfa) {
F <- exp(-exp(-(x - xi)/alfa))
return(F)
}
invF.gumb <- function(F,xi,alfa) {
# if ((F < 0) || (F > 1)) {
# stop("F must be between 0 and 1")
# }
x <- xi - alfa*log(-log(F))
return(x)
}
Lmom.gumb <- function(xi,alfa) {
gamma <- 0.5772 # Euler's constant
lambda1 <- xi + alfa*gamma
lambda2 <- alfa*log(2)
tau3 <- rep(log(9/8)/log(2), length(xi))
tau4 <- rep((16*log(2) - 10*log(3))/log(2), length(xi))
output <- list(lambda1=lambda1, lambda2=lambda2, tau3=tau3, tau4=tau4)
return(output)
}
par.gumb <- function(lambda1,lambda2) {
gamma <- 0.5772 # Euler's constant
alfa <- lambda2/log(2)
xi <- lambda1 - alfa*gamma
output <- list(xi=xi, alfa=alfa)
return(output)
}
rand.gumb <- function(numerosita,xi,alfa) {
F <- runif(numerosita, min=0.0000000001, max=0.9999999999)
x <- invF.gumb(F,xi,alfa)
return(x)
}
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