I feel there is something wrong in definition in weighted variance.
Say for a fair dice the variance of outcome should be : 2.92 (
http://en.wikipedia.org/wiki/Variance)
However if I use cov.wt() or weighted.var() by Gavin, I get :
cov.wt(as.data.frame(1:6), rep(0.6, 6))
$cov
1:6
1:6 3.5
$center
1:6
3.5
$n.obs
[1] 6
$wt
[1] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
i.e. 3.5
Therefore if I want to calculate Variance for a r.v. with different prob for
different values then should not use those formulae. Is it the case?
On Sun, Jul 27, 2008 at 2:30 PM, Patrick Burns <[EMAIL PROTECTED]>wrote:
> Have you seen 'cov.wt'?
>
>
> Patrick Burns
> [EMAIL PROTECTED]
> +44 (0)20 8525 0696
> http://www.burns-stat.com
> (home of S Poetry and "A Guide for the Unwilling S User")
>
> Arun Kumar Saha wrote:
>
>> 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 <[EMAIL PROTECTED]
>> >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/>
>>> <http://www.ucl.ac.uk/%7Eucfagls/>
>>> UK. WC1E 6BT. [w] http://www.freshwaters.org.uk
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>>>
>>>
>>>
>>>
>>
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>>
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