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dGGD.R
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dGGD.R
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#' The Generalized Gompertz distribution
#'
#' @author Johan David Marin Benjumea, \email{johand.marin@@udea.edu.co}
#'
#' @description
#' Density, distribution function, quantile function,
#' random generation and hazard function for the generalized Gompertz distribution with
#' parameters \code{mu} \code{sigma} and \code{nu}.
#'
#' @param x,q vector of quantiles.
#' @param p vector of probabilities.
#' @param n number of observations.
#' @param mu,nu scale parameter.
#' @param sigma shape parameters.
#' @param log,log.p logical; if TRUE, probabilities p are given as log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].
#'
#' @details
#' The Generalized Gompertz Distribution with parameters \code{mu},
#' \code{sigma} and \code{nu} has density given by
#'
#' \eqn{f(x)= \nu \mu \exp(-\frac{\mu}{\sigma}(\exp(\sigma x - 1))) (1 - \exp(-\frac{\mu}{\sigma}(\exp(\sigma x - 1))))^{(\nu - 1)} ,}
#'
#' for \eqn{x \geq 0}, \eqn{\mu > 0}, \eqn{\sigma \geq 0} and \eqn{\nu > 0}.
#'
#' @return
#' \code{dGGD} gives the density, \code{pGGD} gives the distribution
#' function, \code{qGGD} gives the quantile function, \code{rGGD}
#' generates random deviates and \code{hGGD} gives the hazard function.
#'
#' @example examples/examples_dGGD.R
#'
#' @references
#'\insertRef{el2013generalized}{RelDists}
#'
#' @export
dGGD <- function(x, mu, sigma, nu, log=FALSE){
if (any(x < 0))
stop(paste("x must be positive", "\n", ""))
if (any(mu <= 0))
stop(paste("mu must be positive", "\n", ""))
if (any(sigma < 0))
stop(paste("sigma must be positive", "\n", ""))
if (any(nu <= 0))
stop(paste("nu must be positive", "\n", ""))
loglik <- log(nu) + log(mu) + sigma*x - mu/sigma*(exp(sigma*x) - 1) +
(nu - 1)*log(1 - exp(- mu/sigma*(exp(sigma*x) - 1)))
if (log == FALSE)
density <- exp(loglik)
else
density <- loglik
return(density)
}
#' @export
#' @rdname dGGD
pGGD <- function(q, mu, sigma, nu, lower.tail=TRUE, log.p=FALSE){
if (any(q < 0))
stop(paste("q must be positive", "\n", ""))
if (any(mu <= 0))
stop(paste("mu must be positive", "\n", ""))
if (any(sigma < 0))
stop(paste("sigma must be positive", "\n", ""))
if (any(nu <= 0))
stop(paste("nu must be positive", "\n", ""))
cdf <- (1 - exp((-mu/sigma)*(exp(sigma*q)-1)))^nu
if (lower.tail == TRUE)
cdf <- cdf
else cdf <- 1 - cdf
if (log.p == FALSE)
cdf <- cdf
else cdf <- log(cdf)
cdf
}
#' @export
#' @rdname dGGD
qGGD <- function(p, mu, sigma, nu, lower.tail=TRUE, log.p=FALSE){
if (any(mu <= 0))
stop(paste("mu must be positive", "\n", ""))
if (any(sigma < 0))
stop(paste("sigma must be positive", "\n", ""))
if (any(nu <= 0))
stop(paste("nu must be positive", "\n", ""))
if (log.p == TRUE) p <- exp(p)
else p <- p
if (lower.tail == TRUE) p <- p
else p <- 1 - p
if (any(p < 0) | any(p > 1))
stop(paste("p must be between 0 and 1", "\n", ""))
q <- 1/sigma * log(1 - sigma/mu*log(1 - p^(1/nu)))
q
}
#' @importFrom stats runif
#' @export
#' @rdname dGGD
rGGD <- function(n, mu, sigma, nu){
if(any(n <= 0))
stop(paste("n must be positive","\n",""))
if (any(mu <= 0))
stop(paste("mu must be positive", "\n", ""))
if (any(sigma < 0))
stop(paste("sigma must be positive", "\n", ""))
if (any(nu <= 0))
stop(paste("nu must be positive", "\n", ""))
n <- ceiling(n)
p <- runif(n)
r <- qGGD(p, mu, sigma, nu)
r
}
#' @export
#' @rdname dGGD
hGGD<-function(x, mu, sigma, nu){
if (any(x < 0))
stop(paste("x must be positive", "\n", ""))
if (any(mu <= 0))
stop(paste("mu must be positive", "\n", ""))
if (any(sigma < 0))
stop(paste("sigma must be positive", "\n", ""))
if (any(nu <= 0))
stop(paste("nu must be positive", "\n", ""))
h <- dGGD(x, mu, sigma, nu, log=FALSE) /
pGGD(q=x, mu, sigma, nu, lower.tail=FALSE, log.p=FALSE)
h
}