Symmetric and Asymmetric Theory of Relative Concentration and Applications.

Autor/inn/en	Egghe, Leo; Rousseau, Ronald
Titel	Symmetric and Asymmetric Theory of Relative Concentration and Applications.
Quelle	In: Scientometrics, (2001) 2, S.261-290 PDF als Volltext Verfügbarkeit
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0138-9130
DOI	10.1023/A:1017967807504
Schlagwörter	Information Retrieval; Relative Concentration; Good Measure; Gini Index; Lorenz Curve
Abstract	Abstract Relative concentration theory studies the degree of inequality between two vectors ($ a_{1} $,...,$ a_{N} $) and ($ α_{1} $,...,$ α_{N} $). It extends concentration theory in the sense that, in the latter theory, one of the above vectors is (1/N,...,1/N) (N coordinates). When studying relative concentration one can consider the vectors ($ a_{1} $,...,$ a_{N} $) and ($ α_{1} $,...,$ α_{N} $) as interchangeable (equivalent) or not. In the former case this means that the relative concentration of ($ a_{1} $,...,$ a_{N} $) versus ($ α_{1} $,...,$ α_{N} $) is the same as the relative concentration of ($ α_{1} $,...,$ α_{N} $) versus ($ a_{1} $,...,$ a_{N} $). We deal here with a symmetric theory of relative concentration. In the other case one wants to consider ($ a_{1} $,...,$ a_{N} $) as having a different role as ($ α_{1} $,...,$ α_{N} $) and hence the results can be different when interchanging the vectors. This leads 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.
Erfasst von	OLC
Update	2023/2/05