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Two-step competition process leads to quasi power-law income distributions

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  • van Raan, Anthony F.J.

Abstract

We apply a two-step competition process as a model to explain the distribution of citations (‘income’) over publications (‘work’). The first step is the competition amongst scientists to get their work published in better journals, and the second to get this work cited in these journals. Generally, citation distributions are supposed to follow a power law, like most other ‘income’ distributions. So far, no satisfactory theoretical model of citation distribution has been developed. On the basis of two Boltzmann type distribution functions of source publications, we derive a distribution function of citing publications over source publications. This distribution function corresponds very well to the empirical data. It is not a power law, but a modified Bessel-function. In our view, the model presented in this article has a more generic value, particularly in economics to explain observed income distributions.

Suggested Citation

  • van Raan, Anthony F.J., 2001. "Two-step competition process leads to quasi power-law income distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 298(3), pages 530-536.
    • Handle: RePEc:eee:phsmap:v:298:y:2001:i:3:p:530-536
    DOI: 10.1016/S0378-4371(01)00254-0
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    References listed on IDEAS

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    1. Per O. Seglen, 1992. "The skewness of science," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 43(9), pages 628-638, October.
    2. Anthony F. J. Van Raan, 2001. "Competition amongst scientists for publication status:Toward a model of scientific publication and citation distributions," Scientometrics, Springer;Akadémiai Kiadó, vol. 51(1), pages 347-357, April.
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    Cited by:

    1. S. R. Goldberg & H. Anthony & T. S. Evans, 2015. "Modelling citation networks," Scientometrics, Springer;Akadémiai Kiadó, vol. 105(3), pages 1577-1604, December.
    2. Sangwal, Keshra, 2013. "Comparison of different mathematical functions for the analysis of citation distribution of papers of individual authors," Journal of Informetrics, Elsevier, vol. 7(1), pages 36-49.
    3. Tol, Richard S.J., 2013. "The Matthew effect for cohorts of economists," Journal of Informetrics, Elsevier, vol. 7(2), pages 522-527.
    4. Saralees Nadarajah & Samuel Kotz, 2007. "Models for citation behavior," Scientometrics, Springer;Akadémiai Kiadó, vol. 72(2), pages 291-305, August.
    5. Thelwall, Mike, 2016. "Are there too many uncited articles? Zero inflated variants of the discretised lognormal and hooked power law distributions," Journal of Informetrics, Elsevier, vol. 10(2), pages 622-633.
    6. Bertoli-Barsotti, Lucio & Lando, Tommaso, 2015. "On a formula for the h-index," Journal of Informetrics, Elsevier, vol. 9(4), pages 762-776.
    7. Lambiotte, R. & Ausloos, M. & Thelwall, M., 2007. "Word statistics in Blogs and RSS feeds: Towards empirical universal evidence," Journal of Informetrics, Elsevier, vol. 1(4), pages 277-286.
    8. Thelwall, Mike, 2016. "The discretised lognormal and hooked power law distributions for complete citation data: Best options for modelling and regression," Journal of Informetrics, Elsevier, vol. 10(2), pages 336-346.
    9. Vieira, E.S. & Gomes, J.A.N.F., 2010. "Citations to scientific articles: Its distribution and dependence on the article features," Journal of Informetrics, Elsevier, vol. 4(1), pages 1-13.

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