R/qgev_LT.R

In ckatom/ltmps: MPS estimation for left-truncated heavy-tailed data

#' @title  Left-truncated Generalized Extreme Value(GEV) Distribution
#' @description Cumulative probability, quantiles, density functions of left-truncated GEV distribution.
#' @usage pgev_LT(q, xi, sigma, u)
#' @usage qgev_LT(p, xi, sigma, u)
#' @usage dgev_LT(x,xi,sigma,u)
#' @param q vectors of quantiles.
#' @param p vectors of probabilities.
#' @param x vectors of values at which to evaluate density.
#' @param xi Shape parameter.
#' @param sigma Scale parameter.
#' @param u The left-truncated point.
#' @importFrom evir dgev
#' @importFrom evir pgev
#' @importFrom evir qgev
#' @return Probability (pgev), quantile (qgev), density (dgev) for the left-truncated GEV distribution.
#' @export
#'
#' @examples
#' pgev_LT(7,xi=1,sigma=2,u=4)
#' qgev_LT(0.7,xi=1,sigma=2,u=4)
#' dgev_LT(7,xi=1,sigma=2,u=4)

qgev_LT<-function (p,xi,sigma,u){
  if(!(max(p)<=1)&(min(p)>=0)){stop("Probability must lies between 0 and 1")}
  p_u = pgev(u,xi=xi,sigma=sigma,mu=sigma/xi)
  p0 = p*(1-p_u)+p_u
  sigma/xi + (sigma/xi) * ((-logb(p0))^(-xi) - 1)
}