ENBIS-16 in Sheffield

11 – 15 September 2016; Sheffield Abstract submission: 20 March – 4 July 2016

A Location-Dispersion Index for the Analysis of Lower and Upper Bounded Variables

13 September 2016, 14:30 – 14:50

Abstract

Submitted by
Stefano Barone
Authors
Stefano Barone (University of Palermo)
Abstract
The concept of concentration in statistics is well known and consolidated. Concentration is a way to quantify how a generic resource is allocated between a number of subjects.
It is well motivated in the economics field: the more resources lie in the hands of few, the more concentration is present.
The most adopted indicator for concentration is the so called Gini index.
The concept of concentration is quite far away from the concept of robustness, this latter having to do with the two aspects of location and dispersion taken together, and meaning closeness to a target value with smallest possible variation.
None has so far felt the need to relate the concept of concentration to the concept of robustness.
However, it is possible to show that in some special circumstances the two concepts become equivalent and a well-studied modification of the Gini index is a robustness index (hereby called Location-Dispersion Index, LDI).
The “special” circumstances are actually not so rare in statistical analysis since they refer to cases in which the characteristic of interest in the statistical units is theoretically continue (even though it can be measured on a discrete scale) and lower- and upper-bounded. An example can be the “charge of a cellphone battery”.
The LDI was previously formulated in another context, where the measurement of the characteristic of interest (the satisfaction) was made on a discrete scale (0,1,2,…,10 scale).
In this work the author presents the LDI in the most general framework and illustrates some interesting properties.
Insights on the collocation of the index in the current literature, and suggestions of possible exploitation and application fields will complete the work.

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