# R/NormalESConfidenceInterval.R In Dowd: Functions Ported from 'MMR2' Toolbox Offered in Kevin Dowd's Book Measuring Market Risk

#### Documented in NormalESConfidenceInterval

```#' Generates Monte Carlo 95\% Confidence Intervals for normal ES
#'
#' Generates 95\% confidence intervals for normal ES using Monte Carlo simulation
#'
#' @param mu Mean of the P/L process
#' @param sigma Standard deviation of the P/L process
#' @param number.trials Number of trials used in the simulations
#' @param sample.size Sample drawn in each trial
#' @param cl Confidence Level
#' @param hp Holding Period
#'
#' @return 95\% confidence intervals for normal ES
#'
#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
#'
#' @author Dinesh Acharya
#'
#' @examples
#'
#'    # Generates 95\% confidence intervals for normal ES for given parameters
#'    NormalESConfidenceInterval(0, .5, 20, 20, .95, 90)
#'
#'
#' @export
NormalESConfidenceInterval <- function(mu, sigma, number.trials, sample.size, cl, hp){
ES <- double(number.trials)
for (k in 1:number.trials) {
z <- rnorm(sample.size)
x <- sigma * z + mu
ES[k] <- NormalES(returns = x, cl = cl, hp = hp)
}
ES <- sort(ES)
lower.order.stat <- floor(0.025 * number.trials)
upper.order.stat <- ceiling(0.975 * number.trials)
y <- c(ES[lower.order.stat], ES[upper.order.stat])
return(y)
}
```

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Dowd documentation built on May 30, 2017, 1:30 a.m.