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#############################################################################
## Copyright (c) 2010-2022 Rune Haubo Bojesen Christensen
##
## This file is part of the ordinal package for R (*ordinal*)
##
## *ordinal* is free software: you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 2 of the License, or
## (at your option) any later version.
##
## *ordinal* is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## A copy of the GNU General Public License is available at
## <https://www.r-project.org/Licenses/> and/or
## <http://www.gnu.org/licenses/>.
#############################################################################
## This file contains:
## [pdqrg]gumbel functions for the gumbel distribution.
## Here ggumbel is the gradient of the density function, dgumbel.
pgumbel <-
function(q, location = 0, scale = 1, lower.tail = TRUE, max = TRUE)
### CDF for Gumbel max and min distributions
### Currently only unit length location and scale are supported.
{
if(max) ## right skew, loglog link
.C("pgumbel_C",
q = as.double(q),
length(q),
as.double(location)[1],
as.double(scale)[1],
as.integer(lower.tail),
NAOK = TRUE)$q
else ## left skew, cloglog link
.C("pgumbel2_C",
q = as.double(q),
length(q),
as.double(location)[1],
as.double(scale)[1],
as.integer(lower.tail),
NAOK = TRUE)$q
}
pgumbelR <- function(q, location = 0, scale = 1, lower.tail = TRUE)
### R equivalent of pgumbel()
{
q <- (q - location)/scale
p <- exp(-exp(-q))
if (!lower.tail) 1 - p else p
}
pgumbel2R <- function(q, location = 0, scale = 1, lower.tail = TRUE)
{
q <- (-q - location)/scale
p <- exp(-exp(-q))
if (!lower.tail) p else 1 - p
}
dgumbel <-
function(x, location = 0, scale = 1, log = FALSE, max = TRUE)
### PDF for the Gumbel max and mon distributions
{
if(max) ## right skew, loglog link
.C("dgumbel_C",
x = as.double(x),
length(x),
as.double(location)[1],
as.double(scale)[1],
as.integer(log),
NAOK = TRUE)$x
else ## left skew, cloglog link
.C("dgumbel2_C",
x = as.double(x),
length(x),
as.double(location)[1],
as.double(scale)[1],
as.integer(log),
NAOK = TRUE)$x
}
dgumbelR <- function(x, location = 0, scale = 1, log = FALSE)
### dgumbel in R
{
q <- (x - location)/scale
log.d <- -exp(-q) - q - log(scale)
if (!log) exp(log.d) else log.d
}
dgumbel2R <- function(x, location = 0, scale = 1, log = FALSE)
{
q <- (-x - location)/scale
log.d <- -exp(-q) - q - log(scale)
if (!log) exp(log.d) else log.d
}
ggumbel <- function(x, max = TRUE) {
### gradient of dgumbel(x) wrt. x
if(max) ## right skew, loglog link
.C("ggumbel_C",
x = as.double(x),
length(x),
NAOK = TRUE)$x
else ## left skew, cloglog link
.C("ggumbel2_C",
x = as.double(x),
length(x),
NAOK = TRUE)$x
}
ggumbelR <- function(x){
### ggumbel in R
q <- exp(-x)
ifelse(q == Inf, 0, {
eq <- exp(-q)
-eq*q + eq*q*q
})
}
ggumbel2R <- function(x) -ggumbelR(-x)
rgumbel <- function(n, location = 0, scale = 1, max = TRUE) {
if(max)
location - scale * log(-log(runif(n)))
else
location + scale * log(-log(runif(n)))
}
qgumbel <- function(p, location = 0, scale = 1, lower.tail = TRUE, max = TRUE) {
if(!lower.tail) p <- 1 - p
if(max) ## right skew, loglog link
location - scale * log(-log(p))
else ## left skew, cloglog link
location + scale * log(-log(1 - p))
}
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