R/EW.R

In ousuga/reldist: Reliability and survival distributions

#' @name EW
#' 
#' @title 
#' The Exponentiated Weibull Distribution
#' 
#' @description 
#' Density, distribution function, quantile function, 
#' random generation  and hazard function for the exponentiated weibull  distribution with
#' parameters \code{alpha}, \code{theta} and \code{lambda}.
#' 
#' @param x,q	vector of quantiles.
#' @param p vector of probabilities.
#' @param n number of observations. 
#' @param alpha scale parameter.
#' @param theta,lambda 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 Exponentiated Weibull Distribution with parameters \code{alpha}, 
#' \code{theta} and \code{lambda} has density given by
#' 
#' f(x)=lambda*alpha*theta*x^(theta-1)*exp(-alpha*(x^theta))*(1-exp(-alpha*(x^theta)))^(lambda-1)
#' 
#' for x > 0. 
#' 
#' #' @return 
#' \code{dEW} gives the density, \code{pEW} gives the distribution 
#' function, \code{qEW} gives the quantile function, \code{rEW}
#' generates random deviates and \code{hEW} gives the hazard function.
#'
#' @export
#' @examples  
#' ## The probability density function
#' curve(dEW(x, alpha = 2, theta = 1.5, lambda = 0.5), from = 0, to = 2, ylim = c(0, 2.5), col = "red", las = 1, ylab = "The probability density function") 
#' 
#' ## The cumulative distribution and the Reliability function
#' par(mfrow = c(1, 2))
#' curve(pEW(x, alpha = 2, theta = 1.5, lambda = 0.5), from = 0, to = 2,  col = "red", las = 1, ylab = "The cumulative distribution function")
#' curve(pEW(x, alpha = 2, theta = 1.5, lambda = 0.5, lower.tail = FALSE), from = 0, to = 2,  col = "red", las = 1, ylab = "The Reliability function")
#' 
#' ## The quantile function
#' p <- seq(from = 0, to = 0.99999, length.out = 100)
#' plot(x = qEW(p, alpha = 2, theta = 1.5, lambda = 0.5), y = p, xlab = "Quantile", las = 1, ylab = "Probability")
#' curve(pEW(x, alpha = 2, theta = 1.5, lambda = 0.5),  from = 0, add = TRUE, col = "red")
#' 
#' ## The random function
#' hist(rEW(n = 10000, alpha = 2, theta = 1.5, lambda = 0.5), freq = FALSE, xlab = "x", las = 1, main = "")
#' curve(dEW(x, alpha = 2, theta = 1.5, lambda = 0.5),  from = 0, add = TRUE, col = "red") 
#' 
#' ## The Hazard function
#' curve(hEW(x, alpha = 2,theta = 1.5, lambda = 0.5), from = 0, to = 2, ylim = c(0, 7), col = "red", ylab = "The Hazard function")
#' 

dEW<-function(x,alpha,theta,lambda, log = FALSE){
  if (any(x<0)) 
    stop(paste("x must be positive", "\n", ""))
  if (any(alpha<=0 )) 
    stop(paste("alpha must be positive", "\n", ""))
  if (any(theta<=0)) 
    stop(paste("theta must be positive", "\n", ""))
  if (any(lambda<=0)) 
    stop(paste("lambda must be positive", "\n", ""))
  
  loglik<- log(lambda) +log(alpha) + log(theta) + (theta-1)*log(x)-
    alpha*(x^theta) + (lambda-1)*log(1-exp(-alpha*(x^theta)))
  
  if (log == FALSE) 
    density<- exp(loglik)
  else 
    density <- loglik
  return(density)
}

#' @export
#' @rdname EW
pEW <- function(q,alpha,theta,lambda, lower.tail=TRUE, log.p = FALSE){
  if (any(q<0)) 
    stop(paste("q must be positive", "\n", ""))
  if (any(alpha<=0 )) 
    stop(paste("alpha must be positive", "\n", ""))
  if (any(theta<=0)) 
    stop(paste("theta must be positive", "\n", ""))
  if (any(lambda<=0)) 
    stop(paste("lambda must be positive", "\n", ""))
  
  cdf <- (1-exp(-alpha*(q^theta)))^lambda
  if (lower.tail == TRUE) 
    cdf <- cdf
  else cdf <- 1 - cdf
  if (log.p == FALSE) 
    cdf <- cdf
  else cdf <- log(cdf)
  cdf
}

#' @export
#' @rdname EW
qEW <- function(p,alpha,theta,lambda, lower.tail = TRUE, log.p = FALSE){
  if (any(alpha<=0 )) 
    stop(paste("alpha must be positive", "\n", ""))
  if (any(theta<=0)) 
    stop(paste("theta must be positive", "\n", ""))
  if (any(lambda<=0)) 
    stop(paste("lambda 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/alpha)*log(1-p^(1/lambda)))^(1/theta)
  q
}
#' @export
#' @rdname EW
rEW <- function(n,alpha,theta, lambda){
  if(any(n<=0))
    stop(paste("n must be positive","\n",""))
  if (any(alpha<=0 )) 
    stop(paste("alpha must be positive", "\n", ""))
  if (any(theta<=0)) 
    stop(paste("theta must be positive", "\n", ""))
  if (any(lambda<=0)) 
    stop(paste("lambda must be positive", "\n", ""))
  
  n <- ceiling(n)
  p <- runif(n)
  r <- qEW(p, alpha,theta,lambda)
  r
}
#' @export
#' @rdname EW
hEW<-function(x,alpha,theta, lambda){
  if (any(x<0)) 
    stop(paste("x must be positive", "\n", ""))
  if (any(alpha<=0 )) 
    stop(paste("alpha must be positive", "\n", ""))
  if (any(theta<=0)) 
    stop(paste("theta must be positive", "\n", ""))
  if (any(lambda<=0)) 
    stop(paste("lambda must be positive", "\n", ""))
  
  h <- dEW(x,alpha,theta, lambda, log = FALSE)/pEW(q=x,alpha,theta, lambda, lower.tail=FALSE, log.p = FALSE)
  h
}