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Symmetric and Asymmetric Theory of Relative Concentration and Applications

Author

Listed:
  • Leo Egghe

    (LUC
    UIA, IBW)

  • Ronald Rousseau

    (UIA, IBW
    KHBO)

Abstract

Relative concentration theory studies the degree of inequality between two vectors (a1,...,aN) and (α1,...,αN). 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 (a1,...,aN) and (α1,...,αN) as interchangeable (equivalent) or not. In the former case this means that the relative concentration of (a1,...,aN) versus (α1,...,αN) is the same as the relative concentration of (α1,...,αN) versus (a1,...,aN). We deal here with a symmetric theory of relative concentration. In the other case one wants to consider (a1,...,aN) as having a different role as (α1,...,αN) 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.

Suggested Citation

  • Leo Egghe & Ronald Rousseau, 2001. "Symmetric and Asymmetric Theory of Relative Concentration and Applications," Scientometrics, Springer;Akadémiai Kiadó, vol. 52(2), pages 261-290, October.
    • Handle: RePEc:spr:scient:v:52:y:2001:i:2:d:10.1023_a:1017967807504
    DOI: 10.1023/A:1017967807504
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    References listed on IDEAS

    as
    1. L. Egghe, 1988. "The relative concentration of a journal with respect to a subject and the use of online services in calculating it," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 39(4), pages 281-284, July.
    2. L. Egghe & R. Rousseau, 1991. "Transfer principles and a classification of concentration measures," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 42(7), pages 479-489, August.
    3. Mark P. Carpenter, 1979. "Similarity of Pratt's measure of class concentration to the Gini index," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 30(2), pages 108-110, March.
    4. Leo Egghe & Ronald Rousseau, 1998. "Topological aspects of information retrieval," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 49(13), pages 1144-1160.
    5. Allan D. Pratt, 1977. "A measure of class concentration in bibliometrics," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 28(5), pages 285-292, September.
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    Cited by:

    1. Leo Egghe & Ronald Rousseau, 2004. "How to measure own-group preference? A novel approach to a sociometric problem," Scientometrics, Springer;Akadémiai Kiadó, vol. 59(2), pages 233-252, February.
    2. Leo Egghe & Ronald Rousseau, 2002. "A proposal to define a core of a scientific subject: A definition using concentration and fuzzy sets," Scientometrics, Springer;Akadémiai Kiadó, vol. 54(1), pages 51-62, April.
    3. Bar-Ilan, Judit, 2008. "Informetrics at the beginning of the 21st century—A review," Journal of Informetrics, Elsevier, vol. 2(1), pages 1-52.

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