R/buffon.R

In Katrinebch/ExamST516:

#' @export
#' @title Buffon's Neddle experiment
#' @usage buffon(N,l,d)
#' @keywords buffon
#' @description This function estimates the probability of a needle to hit a line, P(hit), and pi by performing Buffon's experiment.
#' @param N number of needles to be thrown on the floor.
#' @param l length of the needle.
#' @param d distance between the stripes on the floor.
#' @return P(hit)\cr
#' pi
#' @author Katrine Eriksen and Katrine Bach \cr
#' Department of mathematics and computer science (IMADA) \cr
#' University of Southern Denmark \cr
#' \email{kater13@student.sdu.dk} and \email{kabac13@student.sdu.dk}
#' @examples buffon(1000,1,1)


buffon <- function(N,l,d){
  
  #warning and stop
  if(l>d){warning("l must be smaller than or equal to d")}
  if(!is.numeric(N)){stop("N must be a numeric")}
  if(!is.numeric(l)){stop("l must be a numeric")}
  if(!is.numeric(d)){stop("d must be a numeric")}
  if(N<1){stop("N must be larger or equal to 1")}
  if(d==0){warning("d should be bigger than zero")}
  if (d<1){stop("You cannot have a negative distance")}
  if (l==0){warning("It seems illogical to have a zero length")}
  if (l<0){stop("Not possible to have a negative length")}
  
  a <- 0
  b <- pi
  U <- runif(N)
  theta <- (b-a)*U+a
  f <- l*sin(theta)
  integralet <- sum((f/N))*(b-a) #the estiamtion
  Phit<- integralet/(pi*d)
  pie <- (2*l)/(Phit*d)
  return(pie)
}