In this paper, we suggest an alternative way to calculate the concentration index by means of a new matrix form approach, which can be applied to both the Gini and the concentration index. For both indices, the proposed matrix approach yields expressions that are decomposable by groups and easily comparable. Our findings are illustrated by applying them to the Atkinson Plotnick Kakwani (APK) reranking measure, thereby enabling to decompose this reranking measure by groups.
A Gini and concentration index decomposition with an application to the APK reranking measure / A. Vernizzi, M.G. Monti, M. Mussini - In: Proceedings of the international scientific conference : AMSE 2010 / [a cura di] R. Zimka. - Banská Bystrica : Občianske združenie Financ, 2010. - ISBN 978-80-89438-02-0. - pp. 397-407 (( Intervento presentato al 13. convegno AMSE 2010 : applications of mathematics and statistics in economy tenutosi a Demänovská Dolina nel 2010.
A Gini and concentration index decomposition with an application to the APK reranking measure
A. VernizziPrimo
;M.G. MontiSecondo
;
2010
Abstract
In this paper, we suggest an alternative way to calculate the concentration index by means of a new matrix form approach, which can be applied to both the Gini and the concentration index. For both indices, the proposed matrix approach yields expressions that are decomposable by groups and easily comparable. Our findings are illustrated by applying them to the Atkinson Plotnick Kakwani (APK) reranking measure, thereby enabling to decompose this reranking measure by groups.
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