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var.variance = function(V) {
# Calculate the approximate variance of the categorical variance estimator
# V should be a frequency vector
# Based off of Blair and Lacy 2000: 274
k = length(V)
N = sum (V)
p = V / N
mu = mean(expand(V))
const = -sum(2*p*((1:k)-mu))
a = (N / (N - 1)) * ((1:k) * const + ((1:k) - mu)^2)
var.var = (sum(p * a^2) - (sum(p * a))^2)/N
return(var.var)
}
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