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Symmetric and Asymmetric Theory of Relative Concentration and Applications

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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.

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References

  • Carpenter, M. P. (1979), Similarity of Pratt's measure of class concentration to the Gini index, Journal of the American Society for Information Science, 30: 108–110.

    Google Scholar 

  • Dalton, H. (1920), The measurement of the inequality of incomes, The Economic Journal, 30: 348–361.

    Article  Google Scholar 

  • Egghe, L. (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, 39(4): 281–284.

    Article  Google Scholar 

  • Egghe, L. (1990), A new method for information retrieval based on the theory of relative concentration, Proceedings of the 13th International Conference on Research and Development in Information Retrieval (SIGIR), Brussels, pp. 469–493.

  • Egghe, L., Rousseau, R. (1990a), Introduction to Informetrics. Quantitative Methods in Library, Documentation and Information Science, Elsevier, Amsterdam.

    Google Scholar 

  • Egghe, L., ROUSSEAU, R. (1990b), Elements of concentration theory, Informetrics 89/90, L. Egghe, R. Rousseau (Eds), pp. 97–137.

  • Egghe, L., Rousseau, R. (1991), Transfer principles and a classification of concentration measures, Journal of the American Society for Information Science, 42(7): 479–489.

    Article  Google Scholar 

  • Egghe, L., Rousseau, R. (1996), Average and global impact of a set of journals, Scientometrics, 36(1): 97–107.

    Article  Google Scholar 

  • Egghe, L., Rousseau, R. (1997), Duality in information retrieval and the hypergeometric distribution, Journal of Documentation, 53(5): 488–496.

    Article  Google Scholar 

  • Egghe, L., Rousseau, R. (1998), Topological aspects of information retrieval, Journal of the American Society for Information Science, 49(13): 1144–1160.

    Article  Google Scholar 

  • Gini, C. (1909), Il diverso accrescimento delle classi sociali e la concentrazione della ricchezza, Giornale degli Economisti, 11: 37.

    Google Scholar 

  • Hardy, G., Littlewood, J. E., PÓlya, G. (1988), Inequalities, Cambridge University Press, Cambridge.

    Google Scholar 

  • Krugman, P. (1991), Geography and Trade, University Press, Leuven.

    Google Scholar 

  • Nijssen, D., Rousseau, R., Van Hecke, P. (1998), The Lorenz curve: a graphical representation of evenness, Coenoses, 13: 33–38.

    Google Scholar 

  • Patil, G. P., Taillie, C. (1982), Diversity as a concept and its measurement, Journal of the American Statistical Association, 77: 548–561.

    Article  MATH  MathSciNet  Google Scholar 

  • Pratt, A. D. (1977), A measure of class concentration in bibliometrics, Journal of the American Society for Information Science, 28: 285–292.

    Google Scholar 

  • Rousseau, R. (1992), Concentration and Diversity in Informetric Research, Ph. D. Thesis, University of Antwerp (UIA).

  • Salton, G., Mc Gill, M. J. (1987), Introduction to Modern Information Retrieval, McGraw-Hill, Singapore.

    Google Scholar 

  • Theil, H. (1967), Economics and Information Theory, North-Holland, Amsterdam.

    Google Scholar 

  • Viles, C. L., French, J. C. (1999), Content locality in distributed digital libraries, Information Processing and Management, 35: 317–336.

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. LUC, Diepenbeeck, Belgium

    Leo Egghe

  2. UIA, IBW, Wilrijk, Belgium

    Leo Egghe & Ronald Rousseau

  3. Department of Industrial Sciences and Technology, KHBO, Oostende, Belgium

    Ronald Rousseau

Authors
  1. Leo Egghe
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  2. Ronald Rousseau
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Egghe, L., Rousseau, R. Symmetric and Asymmetric Theory of Relative Concentration and Applications. Scientometrics 52, 261–290 (2001). https://doi.org/10.1023/A:1017967807504

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