QuantileCBs <- function(X,p=0.5,alpha=0.05)
# Computation of exact (1 - alpha)-confidence bounds
# for the p-quantile based on a sample X.
# 
# Lutz Duembgen, September 10, 2009

{
	n <- length(X)
	Xs <- sort(X)

	# Compute Indices:
	# Indices for one- and two-sided upper bound:
	ui1 <- qbinom(p=1-alpha,   size=n, prob=p) + 1
	ui2 <- qbinom(p=1-alpha/2, size=n, prob=p) + 1
	# Indices for one- and two-sided lower bound:
	li1 <- n - qbinom(p=1-alpha,   size=n, prob=1-p)
	li2 <- n - qbinom(p=1-alpha/2, size=n, prob=1-p)

	# One-sided lower bound:
	if (li1 == 0)
	{
		lb1 <- -Inf
	}
	else
	{
		lb1 <- Xs[li1]
	}

	# One-sided upper bound:
	if (ui1 == n+1)
	{
		ub1 <- Inf
	}
	else
	{
		ub1 <- Xs[ui1]
	}
	
	# Confidence interval:
	if (li2 == 0)
	{
		lb2 <- -Inf
	}
	else
	{
		lb2 <- Xs[li2]
	}
	if (ui2 == n+1)
	{
		ub2 <- Inf
	}
	else
	{
		ub2 <- Xs[ui2]
	}
	
	return(list(lower.bound=lb1,upper.bound=ub1,
		confidence.interval=c(lb2,ub2)))
}