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dMOEW.R
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dMOEW.R
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#' The Marshall-Olkin Extended Weibull distribution
#'
#' @author Amylkar Urrea Montoya, \email{amylkar.urrea@@udea.edu.co}
#'
#' @description
#' Density, distribution function, quantile function,
#' random generation and hazard function for the Marshall-Olkin Extended Weibull 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 parameter.
#' @param sigma parameter.
#' @param nu parameter.
#' @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 Marshall-Olkin Extended Weibull distribution \code{mu},
#' \code{sigma} and \code{nu} has density given by
#'
#' \eqn{f(x) = \frac{\mu \sigma \nu (\nu x)^{\sigma - 1} exp\{{-(\nu x )^{\sigma}}\}}{\{1-(1-\mu) exp\{{-(\nu x )^{\sigma}}\} \}^{2}},}
#'
#' for x > 0.
#'
#' @return
#' \code{dMOEW} gives the density, \code{pMOEW} gives the distribution
#' function, \code{qMOEW} gives the quantile function, \code{rMOEW}
#' generates random deviates and \code{hMOEW} gives the hazard function.
#'
#' @example examples/examples_dMOEW.R
#'
#' @references
#' \insertRef{almalki2014modifications}{RelDists}
#'
#' \insertRef{ghitany2005}{RelDists}
#'
#' @importFrom Rdpack reprompt
#'
#' @export
dMOEW <- 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", ""))
A <- log(mu) + log(sigma) + log(nu) + (sigma - 1) * log(nu * x) - (nu * x)^sigma
B <- 2 * log(1 - (1 - mu) * exp(-(nu * x)^sigma))
loglik <- A - B
if (log == FALSE)
density <- exp(loglik)
else
density <- loglik
return(density)
}
#' @export
#' @rdname dMOEW
pMOEW <- function(q, 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", ""))
A <- mu * exp(-(nu * q)^sigma)
B <- 1 - (1 - mu) * exp(-(nu * q)^sigma)
cdf <- 1 - (A / B)
if (lower.tail == TRUE)
cdf <- cdf
else cdf <- 1 - cdf
if (log.p == FALSE)
cdf <- cdf
else cdf <- log(cdf)
cdf
}
#' @export
#' @rdname dMOEW
qMOEW <- 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", ""))
fda <- function(x, mu, sigma, nu){
1 - (mu * exp(-(nu * x)^sigma)) / (1 - (1 - mu) * exp(-(nu * x)^sigma))
}
fda1 <- function(x, mu, sigma, nu, p) {
fda(x, mu, sigma, nu) - p
}
r_de_la_funcion <- function(mu, sigma, nu, p) {
uniroot(fda1, interval=c(0, 1e+06), mu, sigma, nu, p)$root
}
r_de_la_funcion <- Vectorize(r_de_la_funcion)
q <- r_de_la_funcion(mu, sigma, nu, p)
q
}
#' @importFrom stats runif
#' @export
#' @rdname dMOEW
rMOEW <- function(n, mu, sigma, nu){
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 <- qMOEW(p, mu, sigma, nu)
r
}
#' @export
#' @rdname dMOEW
hMOEW<-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 <- dMOEW(x, mu, sigma, nu, log=FALSE) /
pMOEW(q=x, mu, sigma, nu, lower.tail=FALSE, log.p=FALSE)
h
}