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dEOFNH.R
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dEOFNH.R
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#' The Extended Odd Frechet-Nadarajah-Haghighi
#'
#' @author Helber Santiago Padilla
#'
#' @description
#' Density, distribution function, quantile function,
#' random generation and hazard function for the Extended Odd Fr?chet-Nadarajah-Haghighi 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 parameter.
#' @param sigma parameter.
#' @param nu parameter.
#' @param tau 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
#' Tthe Extended Odd Frechet-Nadarajah-Haghighi \code{mu},
#' \code{sigma}, \code{nu} and \code{tau} has density given by
#'
#' \eqn{f(x)= \frac{\mu\sigma\nu\tau(1+\nu x)^{\sigma-1}e^{(1-(1+\nu x)^\sigma)}[1-(1-e^{(1-(1+\nu x)^\sigma)})^{\mu}]^{\tau-1}}{(1-e^{(1-(1+\nu x)^{\sigma})})^{\mu\tau+1}} e^{-[(1-e^{(1-(1+\nu x)^\sigma)})^{-\mu}-1]^{\tau}},}
#'
#' for \eqn{x > 0}, \eqn{\mu > 0}, \eqn{\sigma > 0}, \eqn{\nu > 0} and \eqn{\tau > 0}.
#'
#' @return
#' \code{dEOFNH} gives the density, \code{pEOFNH} gives the distribution
#' function, \code{qEOFNH} gives the quantile function, \code{rEOFNH}
#' generates random numbers and \code{hEOFNH} gives the hazard function.
#'
#' @example examples/examples_dEOFNH.R
#'
#' @references
#'\insertRef{nasiru2018extended}{RelDists}
#'
#' @export
dEOFNH <- 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", ""))
term1 <- 1+nu*x
term2 <- exp(1-(term1)^sigma)
term3 <- 1-term2
term4 <- exp(-(term3^(-mu)-1)^tau)
lik <- term4*(mu*sigma*tau*nu*term1^(sigma-1)*term2*(1-term3^mu)^(tau-1))/(term3^(mu*tau+1))
if (log == FALSE)
density <- lik
else density <- log(lik)
return(density)
}
#' @export
#' @rdname dEOFNH
pEOFNH <- 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", ""))
term1 <- 1+nu*q
term2 <- exp(1-(term1)^sigma)
term3 <- 1-term2
term5 <- (1-term3^mu)/(term3^mu)
cdf <- exp(-(term5)^tau)
if (lower.tail == TRUE) cdf <- cdf
else cdf <- 1 - cdf
if (log.p == FALSE) cdf <- cdf
else cdf <- log(cdf)
cdf
}
#' @export
#' @rdname dEOFNH
qEOFNH <- 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", ""))
term1 <- (-log(p))^(1/tau)
term2 <- (1+term1)^(-1/mu)
term3 <- log(1-term2)
term4 <- (1-term3)^(1/sigma)
term5 <- (term4-1)/(nu)
q <- term5
q
}
#' @importFrom stats runif
#' @export
#' @rdname dEOFNH
rEOFNH <- function(n, mu, sigma, nu, tau){
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 <= 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 <- qEOFNH(p, mu, sigma, nu, tau)
r
}
#' @export
#' @rdname dEOFNH
hEOFNH <- function(x, mu, sigma, nu, tau){
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 <- dEOFNH(x, mu, sigma, nu, tau, log=FALSE) / pEOFNH(x, mu, sigma, nu, tau, lower.tail=FALSE, log.p=FALSE)
h
}