Chapter

Multidistances and Dispersion Measures

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Abstract

In 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 Martín 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 García-Lapresta and Marques Pereira, are absolute dispersion measures up to sign.

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... In the following proposition we establish some properties of the mappings introduced in (2) and (3). They are related to the ones considered in Martínez-Panero et al. [13] in a quantitative context. 3 Minimum dispersion: D R (x) = δ 1 ⇔ x 1 = · · · = x n , for every x ∈ L n ; and D G (l r , . . . ...
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  • J Martín
  • G Mayor
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