Nothing
propCI_exact <-
function(x, n, l){
if (x == 0){
lw <- 0
up <- 1 - l[3] ^ (1/n)
} else if (x == n){
lw <- l[3] ^ (1/n)
up <- 1
} else{
lw <- qbeta(l[1], x, n - x + 1, lower.tail = T)
up <- qbeta(l[2], x + 1, n - x, lower.tail = T)
}
return(c(lw, up))
}
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