R/dOW.R

In RelDists: Estimation for some Reliability Distributions

#' The Odd Weibull Distribution
#' 
#' @author Jaime Mosquera Gutiérrez \email{jmosquerag@unal.edu.co}
#'
#' @description
#' Density, distribution function, quantile function,
#' random generation and hazard function for the Odd 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 one.
#' @param sigma parameter two.
#' @param nu 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[T <= t], otherwise, P[T > t].
#'
#' @details
#' The Odd Weibull with parameters \code{mu}, \code{sigma}
#' and \code{nu} has density given by
#'
#' \eqn{f(x) = \left( \frac{\sigma\nu}{x} \right) (\mu x)^\sigma
#'      e^{(\mu x)^\sigma} \left(e^{(\mu x)^{\sigma}}-1\right)^{\nu-1}
#'      \left[ 1 + \left(e^{(\mu x)^{\sigma}}-1\right)^\nu \right]^{-2}}
#'
#' for x > 0.
#'
#' @return
#' \code{dOW} gives the density, \code{pOW} gives the distribution
#' function, \code{qOW} gives the quantile function, \code{rOW}
#' generates random deviates and \code{hOW} gives the hazard function.
#'
#' @example examples/examples_dOW.R
#' 
#' @references
#' \insertRef{Cooray2006}{RelDists}
#' 
#' @export
dOW <- 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*nu <= 0))
    stop(paste("Product sigma*nu must be positive", "\n", ""))
  
  prod1 <- (mu*x)^sigma
  loglik <- log(sigma*nu) - log(x) + sigma*( log(mu) + log(x) ) +
    (mu*x)^sigma + ( nu - 1 )*log(expm1( prod1 )) -
    2*log1p( (expm1(prod1))^nu )
  
  if (log == FALSE)
    dens <- exp(loglik)
  else
    dens <- loglik
  return(dens)
}

#' @export
#' @rdname dOW
pOW <- 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*nu<=0))
    stop(paste("Product sigma*nu must be positive", "\n", ""))
  
  prod1 <- (mu*q)^sigma
  cdf <- 1 - ( 1 + (expm1(prod1))^nu )^(-1)
  
  if (lower.tail == TRUE)
    cdf <- cdf
  else cdf <- 1 - cdf
  if (log.p == FALSE)
    cdf <- cdf
  else cdf <- log(cdf)
  return(cdf)
}

#' @export
#' @rdname dOW
qOW <- 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*nu<=0))
    stop(paste("Product sigma*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/mu)*(log1p( (p*(1-p)^(-1))^(1/nu) ))^(1/sigma)
  return(q)
}

#' @export
#' @rdname dOW
rOW <- 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*nu<=0))
    stop(paste("Product sigma*nu must be positive", "\n", ""))
  
  n <- ceiling(n)
  p <- runif(n)
  r <- qOW(p, mu, sigma, nu)
  return(r)
}
#' @export
#' @rdname dOW
hOW<-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*nu<=0))
    stop(paste("Product sigma*nu must be positive", "\n", ""))
  
  h <- dOW(x, mu, sigma, nu, log=FALSE)/pOW(q=x, mu, sigma, nu,
                                            lower.tail=FALSE, log.p=FALSE)
  return(h)
}