#' @rdname f0
#'
#' @export
ACE <- function(f) {
x <- f.stats(f)
if(length(f) < 10) f <- c(f, rep(0, 10 - length(f)))
s.rare <- sum(f[1:10])
x.rare <- sum(1:10 * f[1:10])
c.ace <- 1 - f[1] / x.rare
term.1 <- s.rare / c.ace
term.2 <- sum(1:10 * 0:9 * f[1:10])
term.3 <- x.rare * (x.rare - 1)
term.4 <- (term.1 * term.2 / term.3) - 1
cv.ace <- max(c(term.4, 0))
f0 <- term.1 + (f[1] * cv.ace / c.ace) - s.rare
f0 <- f0 * (x["n"] - 1) / x["n"]
c(s.est = unname(f0 + x["s.obs"]), f0 = unname(f0), x)
}
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