R/piest2.R

In austinragotzy/mathstat: Introduction to Mathematical Statistics R Package

#' @title Estimation of Pi by Monte Carlo Integration
#'
#' @description Uses Monte Carlo integration to estimate pi given a simulation
#' size.
#' See example 4.8.4 on page 295 and 296 of the book.
#'
#' @param n simulation size.
#'
#' @return Tuple containing estimate value of pi and the standard error.
#'
#' @references Hogg, R. McKean, J. Craig, A (2018) Introduction to
#' Mathematical Statistics, 8th Ed. Boston: Pearson
#'
#' @examples
#' # Example where parameters are passed in as variables.
#' n <- 1000
#' result <- piest2(n)
#'
#' # Example where parameters are passed in as values.
#' result <- piest2(1000)
#'
#' @export piest2

piest2 <- function(n) {
  
  # INPUT VALIDATION
  errors <- makeAssertCollection()
  # argument 1: n
  errors$push(has_nonan(n, 1))
  errors$push(is_oneelement(n, 1))
  reportAssertions(errors)
  
  errors$push(is_numeric(n, 1))
  errors$push(has_noinf(n, 1))
  errors$push(is_positive(n, 1))
  errors$push(is_nonzero(n, 1))
  reportAssertions(errors)
  
  # FUNCTION BEGINS
  
  sample <- 4 * sqrt(1 - runif(n)^2)
  estimate <- mean(sample)
  standard_error <- sqrt(var(sample)/n)
  
  return(list(estimate = estimate, standard_error = standard_error))
}