# R/distr.R In mlt: Most Likely Transformations

#### Defines functions .distr.MaxExtrVal.MinExtrVal.Logistic.Normal

```.Normal <- function()
list(p = pnorm, d = dnorm, q = qnorm,
dd = function(x) -dnorm(x = x) * x,
ddd = function(x) dnorm(x = x) * (x^2 - 1),
dd2d = function(x) -x,
name = "normal")

.Logistic <- function()
list(p = plogis, d = dlogis, q = qlogis,
dd = function(x) {
ex <- exp(x)
(ex - ex^2) / (1 + ex)^3
},
ddd = function(x) {
ex <- exp(x)
(ex - 4 * ex^2 + ex^3) / (1 + ex)^4
},
dd2d = function(x) {
ex <- exp(x)
(1 - ex) / (1 + ex)
},
name = "logistic")

.MinExtrVal <- function()
list(p = function(x) 1 - exp(-exp(x)),
q = function(p) log(-log1p(- p)),
d = function(x, log = FALSE) {
ret <- x - exp(x)
if (!log) return(exp(ret))
ret
},
dd = function(x) {
ex <- exp(x)
(ex - ex^2) / exp(ex)
},
ddd = function(x) {
ex <- exp(x)
(ex - 3*ex^2 + ex^3) / exp(ex)
},
dd2d = function(x)
1 - exp(x),
name = "minimum extreme value")

.MaxExtrVal <- function()
list(p = function(x) exp(-exp(-x)),
q = function(p) -log(-log(p)),
d = function(x, log = FALSE) {
ret <- - x - exp(-x)
if (!log) return(exp(ret))
ret
},
dd = function(x) {
ex <- exp(-x)
exp(-ex - x) * (ex - 1)
},
ddd = function(x) {
ex <- exp(-x)
exp(-x - ex) * (ex - 1)^2 - exp(-ex - 2 * x)
},
dd2d = function(x)
exp(-x) - 1,
name = "maximum extreme value")

.distr <- function(which = c("Normal", "Logistic",
"MinExtrVal", "MaxExtrVal")) {
which <- match.arg(which)
do.call(paste(".", which, sep = ""), list())
}
```

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mlt documentation built on Oct. 6, 2019, 5:05 p.m.