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#' Hill Plot
#'
#' Displays a plot of the Hill Estimator against tail sample size.
#'
#' @param Ra The data set
#' @param maximum.tail.size maximum tail size and should be greater than a
#' quarter of the sample size.
#'
#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
#'
#'
#' @author Dinesh Acharya
#' @examples
#'
#' # Hill Estimator - Tail Sample Size Plot for random normal dataset
#' Ra <- rnorm(1000)
#' HillPlot(Ra, 180)
#'
#' @export
HillPlot <- function(Ra, maximum.tail.size){
data <- as.vector(Ra)
data <- sort(data)
n <- length(data)
i <- which(data <= 0)
i <- max(i)
max.k <- min(maximum.tail.size, n - i)
he <- double(max.k)
# Derivation of Hill Estimators and tail size series
for (k in 2:max.k){
he[k] <- HillEstimator(data,k)
}
# Plot of Hill Estimator against tail size
j <- which(he != 0)
he <- he[j]
k <- 2:max.k
plot(k, he, type = "l", col="red", main = "Hill Estimator against Tail Size",
xlab="Number of observations in tail (k)", ylab = "Hill estimator")
}
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