Approximated Distributions of Sampling Inequality Indices

Often, in finite samples, the true level of the confidence intervals for natural estimators of inequality indices belonging to the Gini family differs greatly from their nominal level, which is based on the asymptotic confidence limits. This paper shows how the Gram-Charlier series can be used to obtain improved finite-sample confidence intervals. Our work focuses on the implementation in Mathematica 3.0 of computational procedures to compute the Gram-Charlier distribution for the following sampling inequality indices: R by Gini, P by Piesch and M by Mehran for the Dagum (Type I) distribution. The results of a Monte Carlo experiment confirm that, for the cases investigated, the Gram-Charlier distribution largely eliminates the problem of incorrect finite-sample level.