R/pdfbsgdp.R

In ERPeq: Probabilistic Hazard Assessment

#' @title Probability density function of the Birnbaum-Saunders-Generalized Pareto distribution
#' @param par parameter vector of the Birnbaum-Saunders-Generalized Pareto distribution.
#' First parameter is the shape, second parameter is the scale parameter. Third parameter is the lower bound parameter.
#' @param x vector of observations or single value
#'
#' @return return the value of the pdf of the Birnbaum-Saunders-Generalized Pareto  distribution.
#' @export
#' @importFrom VGAM dgumbel pgumbel
#' @references Altun, E., Ozel, G. A novel approach to probabilistic hazard assessment: BSGPD model. (Under Review)
#' @examples
#' pdfbsgdp(c(2,0.5,0.5),1)

pdfbsgdp=function(par,x){
  alpha=par[1]
  gamma=par[2]
  beta=par[3]
  at=(sqrt(x/beta)-sqrt(beta/x))/alpha
  att=x^(-3/2)*(x+beta)/(2*alpha*sqrt(beta))

  f=(1+gamma*at)^(-(1/gamma+1))*att
  return(f)
}