# Simultaneous confidence intervals for probabilities/proportions.
# The program offers two options:
# - Input of a raw data vector (factor):
#     MultinomSimCBs(NULL, X, your.alpha)
#     MultinomSimCBs(RawData=X, alpha=your.alpha)
#     ...
# - Input of a vector (table) of absolute frequencies:
#     MultinomSimCBs(N, Null, your.alpha)
#     MultinomSimCBs(Table=N, alpha=your.alpha)
#     ...

MultinomSimCBs <- function(Table=NULL,RawData=NULL,alpha=0.05)
{
	if (is.null(Table))
	{
		Table = table(RawData)
	}
	n <- sum(Table)
	q <-length(Table)

	# Initialize output vectors:
	p.est <- rep(0, times=q)
	a <- rep(0, times=q)
	b <- rep(1, times=q)
	
	conf.level.indiv <- 1 - alpha/q
	for (j in 1:q)
	{
		tmp<- binom.test(Table[j],n,conf.level=conf.level.indiv)
		a[j] <- tmp$conf.int[1]
		b[j] <- tmp$conf.int[2]
		p.est[j] <- tmp$estimate
	}
	G <- cbind(Table,p.est,a,b)
	return(list(summarized.data.and.bounds=G,
		simult.conf.level=1-alpha,
		indiv.conf.level=conf.level.indiv,
		sample.size=n))
}