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dMW.R
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dMW.R
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#' The Modified Weibull 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 modified 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 shape parameter one.
#' @param sigma parameter two.
#' @param nu scale parameter three.
#' @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 modified weibull distribution with parameters \code{mu}, \code{sigma}
#' and \code{nu} has density given by
#'
#' \eqn{f(x) = \mu (\sigma + \nu x) x^{\sigma - 1} \exp(\nu x) \exp(-\mu x^{\sigma} \exp(\nu x))}
#'
#' for \eqn{x > 0}, \eqn{\mu > 0}, \eqn{\sigma \geq 0} and \eqn{\nu \geq 0}.
#'
#' @return
#' \code{dMW} gives the density, \code{pMW} gives the distribution
#' function, \code{qMW} gives the quantile function, \code{rMW}
#' generates random deviates and \code{hMW} gives the hazard function.
#'
#' @example examples/examples_dMW.R
#'
#' @references
#'\insertRef{almalki2014modifications}{RelDists}
#'
#'\insertRef{lai2003modified}{RelDists}
#'
#' @export
dMW <- 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(mu) + log(sigma + nu*x) + (sigma-1)*log(x) +
nu*x - mu*(x^sigma)*exp(nu*x)
if (log == FALSE) density<- exp(loglik)
else density <- loglik
return(density)
}
#' @export
#' @rdname dMW
pMW <- 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*(q^sigma) * exp(nu*q))
if (lower.tail == TRUE) cdf <- cdf
else cdf <- 1 - cdf
if (log.p == FALSE) cdf <- cdf
else cdf <- log(cdf)
cdf
}
#' @export
#' @rdname dMW
qMW <- 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- exp(-mu*(x^sigma) * exp(nu*x))
}
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(0,99999), mu, sigma, nu, p)$root
}
r_de_la_funcion <- Vectorize(r_de_la_funcion)
q <- r_de_la_funcion(mu, sigma, nu, p)
q
}
#' @export
#' @rdname dMW
rMW <- 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 <- qMW(p, mu, sigma, nu)
r
}
#' @export
#' @rdname dMW
hMW<-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 <- dMW(x, mu, sigma, nu, log = FALSE)/
pMW(q=x, mu, sigma, nu, lower.tail=FALSE, log.p = FALSE)
h
}