#' @name MW
#'
#' @title
#' The Modified Weibull Distribution
#'
#' @description
#' Density, distribution function, quantile function,
#' random generation and hazard function for the modified weibull distribution with
#' parameters \code{beta}, \code{gamma} and \code{lambda}.
#'
#' @param x,q vector of quantiles.
#' @param p vector of probabilities.
#' @param n number of observations.
#' @param beta shape parameter one.
#' @param gamma parameter two.
#' @param lambda 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{beta}, \code{gamma}
#' and \code{lambda} has density given by
#'
#' f(x) = beta*(gamma+lambda*x)*x^(gamma-1)*exp(lambda*x)*exp(-beta*x^(gamma)*exp(lambda*x))
#'
#' for x > 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.
#'
#' @export
#' @examples
#' ## The probability density function
#' curve(dMW(x, beta = 2, gamma = 1.5, lambda = 0.2), from=0, to=2, ylim=c(0,1.5), col="red", las=1, ylab="The probability density function")
#'
#' ## The cumulative distribution and the Reliability function
#' par(mfrow = c(1, 2))
#' curve(pMW(x, beta = 2, gamma = 1.5, lambda = 0.2), from = 0, to = 2, ylim = c(0, 1), col = "red", las = 1, ylab = "The cumulative distribution function")
#' curve(pMW(x, beta = 2, gamma = 1.5, lambda = 0.2, lower.tail = FALSE), from = 0, to = 2, ylim = c(0, 1), col = "red", las = 1, ylab = "The Reliability function")
#'
#' ## The quantile function
#' p <- seq(from = 0, to = 0.998, length.out = 100)
#' plot(x = qMW(p = p, beta = 2, gamma = 1.5, lambda = 0.2), y = p, xlab = "Quantile", las = 1, ylab = "Probability")
#' curve(pMW(x, beta = 2, gamma = 1.5, lambda = 0.2), from = 0, add = TRUE, col = "red")
#'
#' ## The random function
#' hist(rMW(n = 1000, beta = 2, gamma = 1.5, lambda = 0.2), freq = FALSE, , ylim=c(0,1.5),xlab = "x", las = 1, main = "")
#' curve(dMW(x, beta = 2, gamma = 1.5, lambda = 0.2), from = 0, , ylim=c(0,1.5), add = T, col = "red")
#'
#' ## The Hazard function
#' curve(hMW(x, beta = 2, gamma = 1.5, lambda = 0.2), from = 0, to = 1.5, ylim = c(0, 5), col = "red", las = 1, ylab = "The Hazard function")
dMW<-function(x,beta,gamma,lambda, log = FALSE){
if (any(x<0))
stop(paste("x must be positive", "\n", ""))
if (any(beta<=0 ))
stop(paste("beta must be positive", "\n", ""))
if (any(gamma<0))
stop(paste("gamma must be positive", "\n", ""))
if (any(lambda<0))
stop(paste("lambda must be positive", "\n", ""))
loglik<- log(beta) + log(gamma + lambda*x) + (gamma-1)*log(x) +
lambda*x - beta*(x^gamma)*exp(lambda*x)
if (log == FALSE)
density<- exp(loglik)
else
density <- loglik
return(density)
}
#' @export
#' @rdname MW
pMW <- function(q,beta,gamma,lambda, lower.tail=TRUE, log.p = FALSE){
if (any(q<0))
stop(paste("q must be positive", "\n", ""))
if (any(beta<=0 ))
stop(paste("beta must be positive", "\n", ""))
if (any(gamma<0))
stop(paste("gamma must be positive", "\n", ""))
if (any(lambda<0))
stop(paste("lambda must be positive", "\n", ""))
cdf <- 1- exp(-beta*(q^gamma)*exp(lambda*q))
if (lower.tail == TRUE)
cdf <- cdf
else cdf <- 1 - cdf
if (log.p == FALSE)
cdf <- cdf
else cdf <- log(cdf)
cdf
}
#' @export
#' @rdname MW
qMW <- function(p, beta,gamma,lambda, lower.tail = TRUE, log.p = FALSE){
if (any(beta<=0 ))
stop(paste("beta must be positive", "\n", ""))
if (any(gamma<0))
stop(paste("gamma 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", ""))
fda <- function(x,beta,gamma,lambda){
1- exp(-beta*(x^gamma)*exp(lambda*x))
}
fda1 <- function(x, beta,gamma,lambda, p) {fda(x, beta,gamma,lambda) - p}
r_de_la_funcion <- function(beta,gamma,lambda, p) {
uniroot(fda1, interval=c(0,99999), beta,gamma,lambda, p)$root
}
r_de_la_funcion <- Vectorize(r_de_la_funcion)
q <- r_de_la_funcion(beta,gamma,lambda, p)
q
}
#' @export
#' @rdname MW
rMW <- function(n, beta,gamma,lambda){
if (any(beta<=0 ))
stop(paste("beta must be positive", "\n", ""))
if (any(gamma<0))
stop(paste("gamma must be positive", "\n", ""))
if (any(lambda<0))
stop(paste("lambda must be positive", "\n", ""))
n <- ceiling(n)
p <- runif(n)
r <- qMW(p,beta,gamma,lambda)
r
}
#' @export
#' @rdname MW
hMW<-function(x,beta,gamma,lambda){
if (any(x<0))
stop(paste("x must be positive", "\n", ""))
if (any(beta<=0 ))
stop(paste("beta must be positive", "\n", ""))
if (any(gamma<0))
stop(paste("gamma must be positive", "\n", ""))
if (any(lambda<0))
stop(paste("lambda must be positive", "\n", ""))
h <- dMW(x,beta,gamma,lambda, log = FALSE)/pMW(q=x,beta,gamma,lambda, lower.tail=FALSE, log.p = FALSE)
h
}
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