Weighted mean from exact sums

xsum_weighted_mean() computes sum(w * x) and sum(w) exactly, each rounded once, and divides. The result therefore has three roundings: the two sums and the division. Each sum is exact, which removes the cancellation and accumulation error that dominates sum(w * x) / sum(w); an exact ratio of two superaccumulators is not available.

Usage

xsum_weighted_mean(x, w, na.rm = FALSE)

Arguments

x

A numeric or logical vector.

w

Weights, of the same length as x.

na.rm

Remove NA and NaN values before summing?

Value

A double of length one.

Details

With na.rm = TRUE, pairs where x is NA or NaN are removed, as in stats::weighted.mean(); NA weights are not removed.

See also

Other means: xsum_mean()

Examples

xsum_weighted_mean(c(1e16, 1, -1e16), c(1, 1, 1))
#> [1] 0.3333333