# Re: [R] Weighted variance function?

From: Arun Kumar Saha <arun.kumar.saha_at_gmail.com>
Date: Sun, 27 Jul 2008 13:17:56 +0530

ur prog gives following result:

weighted.var(c(1,-1), c(0.5,0.5))
[1] 2

is it ok?

On Thu, Jul 24, 2008 at 7:57 PM, Gavin Simpson <gavin.simpson_at_ucl.ac.uk>wrote:

> On Thu, 2008-07-24 at 02:25 +0530, Arun Kumar Saha wrote:
> > There is a R function to calculate weighted mean : weighted.mean() under
> > stats package. Is there any direct R function for calculating weighted
> > variance as well?
>
> Here are two ways; weighted.var() is via the usual formula and
> weighted.var2() uses a running sums approach. The formulae for which are
> both on the weighted mean entry page on wikipedia for example.
>
> The removal of NA is as per weighted.mean, but I have not included any
> of the sanity checks that that functions contains.
>
> weighted.var <- function(x, w, na.rm = FALSE) {
> if (na.rm) {
> w <- w[i <- !is.na(x)]
> x <- x[i]
> }
> sum.w <- sum(w)
> sum.w2 <- sum(w^2)
> mean.w <- sum(x * w) / sum(w)
> (sum.w / (sum.w^2 - sum.w2)) * sum(w * (x - mean.w)^2, na.rm =
> na.rm)
> }
>
> weighted.var2 <- function(x, w, na.rm = FALSE) {
> if (na.rm) {
> w <- w[i <- !is.na(x)]
> x <- x[i]
> }
> sum.w <- sum(w)
> (sum(w*x^2) * sum.w - sum(w*x)^2) / (sum.w^2 - sum(w^2))
> }
>
> ## from example section in ?weighted.mean
> ## GPA from Siegel 1994
> wt <- c(5, 5, 4, 1)/15
> x <- c(3.7,3.3,3.5,2.8)
> weighted.mean(x,wt)
>
> weighted.var(x, wt)
>
> weighted.var2(x, wt)
>
> And some timings:
>
> > system.time(replicate(100000, weighted.var(x, wt)))
> user system elapsed
> 2.679 0.014 2.820
> > system.time(replicate(100000, weighted.var2(x, wt)))
> user system elapsed
> 2.224 0.010 2.315
>
> HTH
>
> G
> --
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> Dr. Gavin Simpson [t] +44 (0)20 7679 0522
> ECRC, UCL Geography, [f] +44 (0)20 7679 0565
> Pearson Building, [e] gavin.simpsonATNOSPAMucl.ac.uk
> Gower Street, London [w] http://www.ucl.ac.uk/~ucfagls/<http://www.ucl.ac.uk/%7Eucfagls/>
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>
>

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