Multidistances and Dispersion Measures

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 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 sign