计算R中加权离散随机变量的均值和方差

Question

I have the following data frame:

dat <- read.table(text="  X prob
1 1  0.1
2 2  0.2
3 3  0.4
4 4  0.3", header=TRUE)

Is there any built-in function or elegant way to calulate mean and variance for discrete random variables in R?

Answer 1

There is a weighted.mean function in base R and the Hmisc package has a bunch of wtd.* functions.

> with(dat, weighted.mean(X, prob))
[1] 2.9

require(Hmisc)
>  wtd.var(x=dat$X, weights=dat$prob)
[1] Inf
# Huh ?  On investigation the weights argument is suppsed to be replicate weights
# So it's more appropriate to use normwt=TRUE
> wtd.var(x=dat$X, weights=dat$prob, normwt=TRUE)
[1] 1.186667

The survey package from Thomas Lumley provides much more than this simplistic example illustrates. It has the mechanism for handling complex weighting schemes for a variety of statistical modeling procedures:

require(survey)
> dclus1<-svydesign(id=~1, weights=~prob, data=dat)
>   v<-svyvar(~X, dclus1)
> v
  variance     SE
X   1.1867 0.7011

These are sample statistics rather than the variances that would be calculated for abstract random variables. This result does seem appropriate for a statistical system, but might not be the correct answer for a probability homework question.