#' Simulate homogeneous Poisson process on the real line.
#'
#' @param rate non-negative number giving the rate parameter of the process
#' @param min lower limit of the observation interval
#' @param max upper limit of the observation interval
#'
#' @return a vector containing the points of the realization within the given observation interval
#' @export
#'
#' @examples
#' # A realization from a Poisson process with rate 10 observed over the unit interval [0,1]
#' y <- sim_hpp(rate = 10, min = 0, max = 1)
sim_hpp <- function(rate, min, max){
assertthat::assert_that(assertthat::is.number(rate),
rate >= 0,
assertthat::is.number(min),
assertthat::is.number(max),
max > min)
width = max - min
y <- stats::rpois(1, lambda = rate*width)
result <- stats::runif(y, min=min, max = max)
return(result)
}
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