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Concentration function and coefficients of divergence for signed measures

  • Sandra Fortini
  • Fabrizio Ruggeri
Article

Summary

Comparisons among probability measures are rather frequent in many statistical problems and they are sometimes performed through the coefficients of divergence or the concentration functions with respect to a reference measure. Extending the notion of Lorenz-Gini curve, the concentration function studies the discrepancy between two probability measures Π and Π0.

In this paper, both the concentration function and the coefficients have been defined and studied for a signed measure Π, as an extension of the concentration curve for real valued statistical variables. Signed measures are relevant in statistical analysis, even if unusual, because real problems require them, especially in descriptive statistics, like the simple one presented here.

Keywords

Concentration function coefficients of divergence Gini's concentration ratio Pietra index signed measure 

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Copyright information

© Società Italiana di Statistica 1993

Authors and Affiliations

  • Sandra Fortini
    • 1
  • Fabrizio Ruggeri
    • 1
  1. 1.Consiglio Nazionale delle RicercheIstituto per le Applicazioni della Matematica e dell'InformaticaMilanoItaly

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