R/SparseVec.R

In sunhfsc/SC19052: Functions for collective risk model and risk measures

#' @title Calculation of cumulative loss by sparse vector.
#' @description The prediction model is described in <Modern actuarial risk theory - based on R>.
#' @param p The probability distribution (NumericVector)
#' @param lambda The parameters of the poisson distribution (numeric)
#' @return The maximum possible cumulative loss and the probability of each value (list)
#' @examples
#' \dontrun{
#' p <- c(0.25,0.5,0.25)
#' lambda <- 4
#' fs <- SparseVec(p,lambda)
#' f <- SparseVec(p,lambda)$f
#' s <- SparseVec(p,lambda)$s
#' }
#' @export
SparseVec <- function(p,lambda){
  freq <- p*lambda
  if (any(freq<0)) stop("negative frequency")
  M <- length(freq)
  mu <- sum((1:M)*freq)
  sigma2 <- sum((1:M)^2*freq)
  MM <- ceiling(mu+10*sqrt(sigma2))+6
  fs <- dpois(0:(MM-1),freq[1])
  for(j in 2:M){
    MMM <- trunc((MM-1)/j)
    fj <- rep(0,MM)
    fj[(0:MMM)*j+1] <- dpois(0:MMM,freq[j])
    fs <- convolve(fs,rev(fj),type="o")
  }
  return(list(f=fs,s=length(fs)-1))
}