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EEG.R
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EEG.R
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#' The Extended Exponential Geometric family
#'
#' @author Johan David Marin Benjumea, \email{johand.marin@@udea.edu.co}
#'
#' @description
#' The Extended Exponential Geometric family
#'
#' @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{dEEG}
#'
#' @details
#' The Extended Exponential Geometric distribution with parameters \code{mu}
#' and \code{sigma} has density given by
#'
#' \eqn{f(x)= \mu \sigma \exp(-\mu x)(1 - (1 - \sigma)\exp(-\mu x))^{-2},}
#'
#' for \eqn{x > 0}, \eqn{\mu > 0} and \eqn{\sigma > 0}.
#'
#' @returns Returns a gamlss.family object which can be used to fit a EEG distribution in the \code{gamlss()} function.
#'
#' @example examples/examples_EEG.R
#'
#' @references
#' \insertRef{almalki2014modifications}{RelDists}
#'
#' \insertRef{adamidis2005extension}{RelDists}
#'
#' @importFrom gamlss.dist checklink
#' @importFrom gamlss rqres.plot
#' @export
EEG <- function (mu.link="log", sigma.link="log"){
mstats <- checklink("mu.link", "Extended Exponential Geometric",
substitute(mu.link), c("log", "own"))
dstats <- checklink("sigma.link", "Extended Exponential Geometric",
substitute(sigma.link), c("log", "own"))
structure(list(family=c("EEG", "Extended Exponential Geometric"),
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) {
exp1 <- (1-sigma)*exp(-mu*y)
exp2 <- 1/1-exp1
dldm <- 1/mu - y - 2*y*exp1*exp2
dldm
},
dldd = function(y, mu, sigma) {
exp1 <- (1-sigma)*exp(-mu*y)
exp2 <- 1/1-exp1
dldd <- 1/sigma - 2*exp(-mu*y)*exp2
dldd
},
d2ldm2 = function(y, mu, sigma) {
exp1 <- (1-sigma)*exp(-mu*y)
exp2 <- 1/1-exp1
dldm <- 1/mu - y - 2*y*exp1*exp2
d2ldm2 <- -dldm * dldm
d2ldm2
},
d2ldmdd = function(y, mu, sigma) {
exp1 <- (1-sigma)*exp(-mu*y)
exp2 <- 1/1-exp1
dldm <- 1/mu - y - 2*y*exp1*exp2
dldd <- 1/sigma - 2*exp(-mu*y)*exp2
d2ldmdd <- -dldm * dldd
d2ldmdd
},
d2ldd2 = function(y, mu, sigma) {
exp1 <- (1-sigma)*exp(-mu*y)
exp2 <- 1/1-exp1
dldd <- 1/sigma - 2*exp(-mu*y)*exp2
d2ldd2 <- -dldd * dldd
d2ldd2
},
G.dev.incr = function(y, mu, sigma, ...) -2*dEEG(y, mu, sigma, log=TRUE),
rqres = expression(rqres(pfun="pEEG", 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) all(mu > 0),
sigma.valid = function(sigma) all(sigma > 0),
y.valid = function(y) all(y > 0)
),
class=c("gamlss.family", "family"))
}