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LW.R
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LW.R
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#' The Log-Weibull family
#'
#' @author Amylkar Urrea Montoya, \email{amylkar.urrea@@udea.edu.co}
#'
#' @description
#' The Log-Weibull distribution
#'
#' @param mu.link defines the mu.link, with "log" link as the default for the mu parameter.
#' @param sigma.link defines the sigma.link, with "log" link as the default for the sigma.
#'
#' @seealso \link{dLW}
#'
#' @details
#' The Log-Weibull Distribution with parameters \code{mu}
#' and \code{sigma} has density given by
#'
#' \eqn{f(y)=(1/\sigma) e^{((y - \mu)/\sigma)} exp\{-e^{((y - \mu)/\sigma)}\},}
#'
#' for - \code{infty} < y < \code{infty}.
#'
#' @returns Returns a gamlss.family object which can be used to fit a LW distribution in the \code{gamlss()} function.
#'
#' @example examples/examples_LW.R
#'
#' @references
#' \insertRef{almalki2014modifications}{RelDists}
#'
#' \insertRef{Gumbel1958}{RelDists}
#'
#' @importFrom Rdpack reprompt
#' @importFrom gamlss.dist checklink
#' @importFrom gamlss rqres.plot
#' @export
LW <- function (mu.link="identity", sigma.link="log") {
mstats <- checklink("mu.link", "Log-Weibull",
substitute(mu.link), c("identity", "own"))
dstats <- checklink("sigma.link", "Log-Weibull",
substitute(sigma.link), c("log", "own"))
structure(list(family = c("LW", "Log-Weibull"),
parameters = list(mu=TRUE, sigma=TRUE),
nopar = 2,
type = "Continuous",
mu.link = as.character(substitute(mu.link)),
sigma.link = as.character(substitute(sigma.link)),
mu.linkfun = mstats$linkfun,
sigma.linkfun = dstats$linkfun,
mu.linkinv = mstats$linkinv,
sigma.linkinv = dstats$linkinv,
mu.dr = mstats$mu.eta,
sigma.dr = dstats$mu.eta,
dldm = function(y, mu, sigma) {
dldm <- (-1)/sigma + exp((y-mu)/sigma)/sigma
dldm
},
dldd = function(y, mu, sigma) {
A <- exp((y-mu)/sigma)
part1 <- (-1)/sigma - (y-mu)/(sigma * sigma)
part2 <- ((y-mu)/(sigma * sigma)) * A
dldd <- part1 + part2
dldd
},
d2ldm2 = function(y, mu, sigma) {
dldm <- (-1)/sigma + exp((y-mu)/sigma)/sigma
d2ldm2 <- -dldm * dldm
d2ldm2
},
d2ldmdd = function(y, mu, sigma) {
dldm <- (-1)/sigma + exp((y-mu)/sigma)/sigma
A <- exp((y-mu)/sigma)
part1 <- (-1)/sigma - (y-mu)/(sigma * sigma)
part2 <- ((y-mu)/(sigma * sigma)) * A
dldd <- part1 + part2
d2ldmdd <- -dldm * dldd
d2ldmdd
},
d2ldd2 = function(y, mu, sigma) {
A <- exp((y-mu)/sigma)
part1 <- (-1)/sigma - (y-mu)/(sigma * sigma)
part2 <- ((y-mu)/(sigma * sigma)) * A
dldd <- part1 + part2
d2ldd2 <- -dldd * dldd
d2ldd2
},
G.dev.incr = function(y, mu, sigma, ...) -2*dLW(y, mu, sigma, log=TRUE),
rqres = expression(rqres(pfun="pLW", type="Continuous", y=y, mu=mu, sigma=sigma)),
mu.initial = expression(mu <- rep(1, length(y))),
sigma.initial = expression(sigma <- rep(1, length(y))),
mu.valid = function(mu) TRUE,
sigma.valid = function(sigma) all(sigma > 0),
y.valid = function(y) TRUE
),
class=c("gamlss.family", "family"))
}