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On the Decomposition of the Gini’s Mean Difference and Concentration Ratio

digital On the Decomposition of the Gini’s
Mean Difference and Concentration Ratio
Article
journal STATISTICA & APPLICAZIONI
issue STATISTICA & APPLICAZIONI - 2005 - 2
title On the Decomposition of the Gini’s Mean Difference and Concentration Ratio
authors
publisher Vita e Pensiero
format Article | Pdf
language English
online since 06-2016
issn 18246672 (print)
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In this paper we propose a decomposition for the Gini’s mean difference of a real variate obtained as the sum of c variates observed on a finite population. The decomposition is mainly based on two different sortings of the values of each variate: one is the natural sorting of the values, the other one is obtained by ranking the values according to the corresponding totals. The obtained result is then applied to get a similar decomposition for the Gini’s concentration ratio. This latter decomposition is then compared with other decompositions proposed in literature. Finally the decompositions for the Gini’s mean difference and concentration ratio are extended to the more general case of a linear combination of variates.

Keywords: mean difference, concentration ratio, decomposition, uniform ranking.

Authors biography

Paolo Radaelli, Dipartimento di Metodi Quantitativi per le Scienze Economiche ed Aziendali – Università degli Studi di Milano-Bicocca – P.zza dell’Ateneo Nuovo, 1, 20126 Milano (e-mail: paolo.radaelli@unimib.it
Michele Zenga, Dipartimento di Metodi Quantitativi per le Scienze Economiche ed Aziendali – Università degli Studi di Milano-Bicocca – P.zza dell’Ateneo Nuovo, 1, 20126 Milano (e-mail: michele.zenga@unimib.it).