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 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.

Measuring Dispersion in the Context of Ordered Qualitative Scales

“…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 [7] in a quantitative context. 5 Invariance for translations: if π is totally uniform, then D R (T k (x 1 ), .…”

“…These estimator has attractive properties (see Maronna, et al**) **Some absolute dispersion measures used in Statistics are the range, the variance, the mean deviation, the standard deviation, the absolute Gini index, etc. (see Martínez-Panero et al [7]).…”