R/NormalQuantileStandardError.R

In Dowd: Functions Ported from 'MMR2' Toolbox Offered in Kevin Dowd's Book Measuring Market Risk

#' Standard error of normal quantile estimate
#'
#' Estimates standard error of normal quantile estimate
#'  
#' @param prob Tail probability. Can be a vector or scalar
#' @param n Sample size
#' @param mu Mean of the normal distribution
#' @param sigma Standard deviation of the distribution
#' @param bin.size Bin size. It is optional parameter with default value 1
#' @return Vector or scalar 
#' depending on whether the probability is a vector
#' or scalar
#' 
#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
#'
#' @author Dinesh Acharya
#' @examples
#' 
#'    # Estimates standard error of normal quantile estimate
#'    NormalQuantileStandardError(.8, 100, 0, .5, 3)
#'
#' @export
NormalQuantileStandardError <- function(prob, n, mu, sigma, bin.size){
  # Check that inputs obey sign and value restrictions
  if (prob < 0|prob>1) {
    stop("Probability must be nonnegative and no greater than 1")
  }
  if (n <= 0){
    stop("Sample size must be positive")
  }
  if (bin.size <= 0){
    stop("Bin size must be greater than 0")
  }
  # Determination of frequency 
  x <- qnorm(prob, mu, sigma)
  freq <- pnorm(x+.5*bin.size,mu,sigma) - pnorm(x - 0.5*bin.size, mu, sigma)
  y <- sqrt(prob*(1 - prob)/(n*freq^2)) # Standard Error
  return(y)
}