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Positive reinforcement and 3-dimensional informetrics

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  • Leo Egghe

    (Limburgs Universitair Centrum (LUC), Universitaire Campus)

Abstract

We show that the composition of two information production processes (IPPs), where the items of the first IPP are the sources of the second, and where the ranks of the sources in the first IPP agree with the ranks of the sources in the second IPP, yields an IPP which is positively reinforced with respect to the first IPP. This means that the rank-frequency distribution of the composition is the composition of the rank-frequency distribution of the first IPP and an increasing function φ, which is explicitly calculable from the two IPPs' distributions. From the rank-frequency distribution of the composition, we derive its size-frequency distribution in terms of the size-frequency distribution of the first IPP and of the function φ. The paper also relates the concentration of the reinforced IPP to that of the original one. This theory solves part of the problem of the determination of a third IPP from two given ones (so-called three-dimensional informetrics). In this paper we solved the “linear” case, i.e., where the third IPP is the composition of the other two IPPs.

Suggested Citation

  • Leo Egghe, 2004. "Positive reinforcement and 3-dimensional informetrics," Scientometrics, Springer;Akadémiai Kiadó, vol. 60(3), pages 497-509, August.
    • Handle: RePEc:spr:scient:v:60:y:2004:i:3:d:10.1023_b:scie.0000034390.96418.bf
    DOI: 10.1023/B:SCIE.0000034390.96418.bf
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    References listed on IDEAS

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    1. Ronald Rousseau, 1992. "Concentration and diversity of availability and use in information systems: A positive reinforcement model," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 43(5), pages 391-395, June.
    2. S. R. Coleman, 1992. "The laboratory as a productivity and citation unit in the publications of an experimental‐psychology specialty," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 43(9), pages 639-643, October.
    3. 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.
    4. Carole J. Mankin & Jacqueline D. Bastille, 1981. "An analysis of the differences between density‐of‐use ranking and raw‐use ranking of library journal use," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 32(3), pages 224-228, May.
    5. Fellman, J, 1976. "The Effect of Transformations on Lorenz Curves," Econometrica, Econometric Society, vol. 44(4), pages 823-824, July.
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    Cited by:

    1. Egghe, L., 2007. "General evolutionary theory of information production processes and applications to the evolution of networks," Journal of Informetrics, Elsevier, vol. 1(2), pages 115-122.
    2. Bar-Ilan, Judit, 2008. "Informetrics at the beginning of the 21st century—A review," Journal of Informetrics, Elsevier, vol. 2(1), pages 1-52.
    3. Elias Sanz-Casado & Carlos García-Zorita & Ronald Rousseau, 2016. "Using h-cores to study the most-cited articles of the twenty-first century," Scientometrics, Springer;Akadémiai Kiadó, vol. 108(1), pages 243-261, July.

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