On Friday, 12/21/2012, The American Statistician published a paper by Stavros Kourouklis in which he proposed a new correction factor for estimating the standard deviation of a distribution based on a finite sample. The article describes the surprisingly simple formula for calculating the correction term and provides a proof that this formula at…

gistfile1.jl

  n_sims = 1_000_000

	mle_se = zeros(n_sims)
	unbiased_se = zeros(n_sims)
	yatracos_std_se = zeros(n_sims)
	kourouklis_std_se = zeros(n_sims)

	for sim in 1:n_sims
		n = 10
		x = randn(n)

		c1 = ((n + 2) * (n - 1)) / (n * (n + 1))
		c2 = (n * (n - 1)) / (n * (n - 1) + 2)

		mle = ((n - 1) / n) * std(x)
		unbiased = std(x)
		yatracos_std = c1 * std(x)
		kourouklis_std = c2 * std(x)

		mle_se[sim] = (mle - 1.0)^2
		unbiased_se[sim] = (unbiased - 1.0)^2
		yatracos_std_se[sim] = (yatracos_std - 1.0)^2
		kourouklis_std_se[sim] = (kourouklis_std - 1.0)^2
	end

	mean(mle_se)
	mean(unbiased_se)
	mean(yatracos_std_se)
	mean(kourouklis_std_se)