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dGMW.R
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dGMW.R
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#' The Generalized modified Weibull distribution
#'
#' @description
#' Density, distribution function, quantile function,
#' random generation and hazard function for the generalized
#' modified weibull distribution with parameters \code{mu},
#' \code{sigma}, \code{nu} and \code{tau}.
#'
#' @param x,q vector of quantiles.
#' @param p vector of probabilities.
#' @param n number of observations.
#' @param mu scale parameter.
#' @param sigma shape parameter.
#' @param nu shape parameter.
#' @param tau acceleration 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 generalized modified weibull with parameters \code{mu},
#' \code{sigma}, \code{nu} and \code{tau} has density given by
#'
#' \eqn{f(x)= \mu \sigma x^{\nu - 1}(\nu + \tau x) \exp(\tau x - \mu x^{\nu} e^{\tau x})
#' [1 - \exp(- \mu x^{\nu} e^{\tau x})]^{\sigma-1},}
#'
#' for x>0.
#'
#' @return
#' \code{dGMW} gives the density, \code{pGMW} gives the distribution
#' function, \code{qGMW} gives the quantile function, \code{rGMW}
#' generates random deviates and \code{hGMW} gives the hazard function.
#'
#' @example examples/examples_dGMW.R
#'
#' @export
dGMW <- function(x, mu, sigma, nu, tau, 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", ""))
if (any(tau<0))
stop(paste("tau must be positive", "\n", ""))
loglik <- log(mu*sigma) + (nu-1)*log(x) + log(nu + tau*x) +
tau*x - mu*(x^nu)*exp(tau*x) +
(sigma-1)*log(1-exp(-mu*(x^nu)*exp(tau*x) ))
if (log==FALSE)
density <- exp(loglik)
else density <- loglik
return(density)
}
#' @export
#' @rdname dGMW
pGMW <- function(q, mu, sigma, nu, tau, 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", ""))
if (any(tau<0))
stop(paste("tau must be positive", "\n", ""))
cdf <- (1-exp(-mu*(q^nu)*exp(tau*q)))^sigma
if (lower.tail==TRUE)
cdf <- cdf
else cdf <- 1 - cdf
if (log.p==FALSE)
cdf <- cdf
else cdf <- log(cdf)
cdf
}
#' @export
#' @rdname dGMW
qGMW <- function(p, mu, sigma, nu, tau, 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 (any(tau<0))
stop(paste("tau 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", ""))
cdf <- function(x, mu, sigma, nu, tau){
(1-exp((-mu*(x^nu))*exp(tau*x)))^sigma
}
cdf1 <- function(x, mu, sigma, nu, tau, p) {cdf(x, mu, sigma, nu, tau) - p}
root.cdf1 <- function(mu, sigma, nu, tau, p) {
uniroot(cdf1, interval=c(0,1e+06), mu, sigma, nu, tau, p)$root
}
root.cdf1 <- Vectorize(root.cdf1)
q <- root.cdf1(mu, sigma, nu, tau, p)
q
}
#' @importFrom stats runif
#' @export
#' @rdname dGMW
rGMW <- function(n, mu, sigma, nu, tau){
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 (any(tau<0))
stop(paste("tau must be positive", "\n", ""))
n <- ceiling(n)
p <- runif(n)
r <- qGMW(p, mu, sigma, nu, tau)
r
}
#' @export
#' @rdname dGMW
hGMW <- function(x, mu, sigma, nu, tau, 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", ""))
if (any(tau<0))
stop(paste("tau must be positive", "\n", ""))
h <- dGMW(x, mu, sigma, nu, tau, log=FALSE) /
pGMW(q=x, mu, sigma, nu, tau, lower.tail=FALSE, log.p=FALSE)
h
}