Variance of the weighted mean in R

var_of_weighted_mean.R

# Reference, see here: https://en.wikipedia.org/wiki/Weighted_arithmetic_mean#Variance_of_the_weighted_mean_(%CF%80-estimator_for_ratio-mean)

var_of_weighted_mean <- function(v, w = NULL, inf_rm = FALSE) {
  if (is.null(w)) {
    w <- rep(1, length(v))
  }
  if (inf_rm) {
    v <- replace(v, is.infinite(v), NA)
    w <- replace(w, is.infinite(w), NA)
  }
  w_mean <- sum(v * w) / sum(w)
  squared_sum_of_w <- sum(w) ^ 2
  w_var <- sum((w * (v - w_mean)) ^ 2) / squared_sum_of_w 
  return(w_var)
}


var_of_weighted_mean(1:4)
# 0.3125

sum((1:4 - mean(1:4))^2 / 4) / (4)
# 0.3125

var_of_weighted_mean(1:4, 1:4)
# 0.24