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. © 1993 Società Italiana di Statistica.
Concentration function and coefficients of divergence for signed measures
FORTINI, SANDRA;
1993
Abstract
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. © 1993 Società Italiana di Statistica.
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