An (almost) unbiased estimator for the S-Gini index∗

This note provides an unbiased estimator for the absolute S-Gini and an almost unbiased estimator for the relative S-Gini for integer parameter values. Simulations indicate that these estimators perform considerably better then the usual estimators, especially for small sample sizes. 1 The absolute and relative S-gini indices Assume that income is distributed according to a continuous and differentiable cumulative distribution function (cdf) F : [0,∞]→ [0, 1] with finite mean, μ, and continuous population density function (pdf) f . The absolute single-series Gini (absolute S-Gini), A∞, and the Relative single series Gini (relative S-Gini), R ∞, with parameter δ ∈ R++ are given by: A∞ = μ−H ∞ and R ∞ = 1− H ∞ μ ,