Symmetric and asymmetric theory of relative concentration and applications

Citation
L. Egghe et R. Rousseau, Symmetric and asymmetric theory of relative concentration and applications, SCIENTOMETR, 52(2), 2001, pp. 261-290
Citations number
20
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Library & Information Science
Journal title
SCIENTOMETRICS
ISSN journal
0138-9130 → ACNP
Volume
52
Issue
2
Year of publication
2001
Pages
261 - 290
Database
ISI
SICI code
0138-9130(200110)52:2<261:SAATOR>2.0.ZU;2-P
Abstract
Relative concentration theory studies the degree of inequality between two vectors (a(1),....,a(N)) and (alpha (1),....,alpha (N)). It extends concent ration theory in the sense that, in the latter theory, one of the above vec tors is (1/N,....,1/N) (N coordinates). When studying relative concentration one can consider the vectors (a(1),... .,a(N)) and (alpha (1),.....,alpha (N)) as interchangeable (equivalent) or not. In the former case this means that the relative concentration of (a(1) ,....,a(N)) versus (alpha (1),....,alpha (N)) is the same as the relative c oncentration of (alpha (1),.....,alpha (N)) versus (a(1),....,a(N)). We dea l here with a symmetric theory of relative concentration. In the other case one wants to consider (a(1),....,a(N)) as having a different role as and h ence the results can be different when interchanging the vectors. This lead s to an asymmetric theory of relative concentration. In this paper we elaborate both models, As they extend concentration theory , both models use the Lorenz order and Lorenz curves. For each theory we present good measures of relative concentration and give applications of each model.