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Multidistances and Dispersion Measures
Producción CientíficaIn this paper, we provide a formal notion of absolute dispersion measure that
is satisfied by some classical dispersion measures used in Statistics, such as the
range, the variance, the mean deviation and the standard deviation, among others,
and also by the absolute Gini index, used in Welfare Economics for measuring
inequality. The notion of absolute dispersion measure shares some properties
with the notion of multidistance introduced and analyzed by Mart´ın and
Mayor in several recent papers. We compare absolute dispersion measures and
multidistances and we establish that these two notions are compatible by showing
some functions that are simultaneously absolute dispersion measures and
multidistances. We also establish that remainders obtained through the dual decomposition
of exponential means, introduced by Garc´ıa-Lapresta and Marques
Pereira, are absolute dispersion measures up to signMinisterio de Economía, Industria y Competitividad (ECO2012-32178)Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA066U13