# Function to calculate the weighted variance
# x is a vector for which we want to compute the weighted variance
# w is a vector that contains the weights
#

weighted.var<-function(x,w) {
  x.wmean<-weighted.mean(x=x,w=w)
  w.mean<-mean(w)
  n<-length(x)
  wvar<-sum(w*(x-x.wmean)^2)/(n-1)*w.mean
  list(wvar=wvar)
}