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

digital

Article

Magazine

STATISTICA & APPLICAZIONI

Section

Open Access

Title

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

Authors

Paolo Radaelli, Michele Zenga

Publisher

Vita e Pensiero

Format

Article |

Pdf

Pages

Language

English

Online from

06-2016

Issn

1824-6672 (print) | 2283-6659 (digital)

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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).

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