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Mathematical derivation of the impact factor distribution

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  • Egghe, L.

Abstract

Experimental data [Mansilla, R., Köppen, E., Cocho, G., & Miramontes, P. (2007). On the behavior of journal impact factor rank-order distribution. Journal of Informetrics, 1(2), 155–160] reveal that, if one ranks a set of journals (e.g. in a field) in decreasing order of their impact factors, the rank distribution of the logarithm of these impact factors has a typical S-shape: first a convex decrease, followed by a concave decrease. In this paper we give a mathematical formula for this distribution and explain the S-shape. Also the experimentally found smaller convex part and larger concave part is explained. If one studies the rank distribution of the impact factors themselves, we now prove that we have the same S-shape but with inflection point in μ, the average of the impact factors. These distributions are valid for any type of impact factor (any publication period and any citation period). They are even valid for any sample average rank distribution.

Suggested Citation

  • Egghe, L., 2009. "Mathematical derivation of the impact factor distribution," Journal of Informetrics, Elsevier, vol. 3(4), pages 290-295.
    • Handle: RePEc:eee:infome:v:3:y:2009:i:4:p:290-295
    DOI: 10.1016/j.joi.2009.01.004
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    1. Mansilla, R. & Köppen, E. & Cocho, G. & Miramontes, P., 2007. "On the behavior of journal impact factor rank-order distribution," Journal of Informetrics, Elsevier, vol. 1(2), pages 155-160.
    2. Leo Egghe, 2008. "The mathematical relation between the impact factor and the uncitedness factor," Scientometrics, Springer;Akadémiai Kiadó, vol. 76(1), pages 117-123, July.
    3. Thed N. van Leeuwen & Henk F. Moed, 2005. "Characteristics of journal impact factors: The effects of uncitedness and citation distribution on the understanding of journal impact factors," Scientometrics, Springer;Akadémiai Kiadó, vol. 63(2), pages 357-371, April.
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    1. L. Egghe, 2010. "The distribution of the uncitedness factor and its functional relation with the impact factor," Scientometrics, Springer;Akadémiai Kiadó, vol. 83(3), pages 689-695, June.
    2. Bárbara S. Lancho-Barrantes & Vicente P. Guerrero-Bote & Félix Moya-Anegón, 2010. "The iceberg hypothesis revisited," Scientometrics, Springer;Akadémiai Kiadó, vol. 85(2), pages 443-461, November.
    3. José Alberto Molina & David Iñiguez & Gonzalo Ruiz & Alfonso Tarancón, 2021. "Leaders among the leaders in Economics: a network analysis of the Nobel Prize laureates," Applied Economics Letters, Taylor & Francis Journals, vol. 28(7), pages 584-589, April.
    4. Copiello, Sergio, 2019. "Peer and neighborhood effects: Citation analysis using a spatial autoregressive model and pseudo-spatial data," Journal of Informetrics, Elsevier, vol. 13(1), pages 238-254.
    5. Huang, Ding-wei, 2017. "Impact factor distribution revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 173-180.
    6. L. Egghe, 2011. "The impact factor rank-order distribution revisited," Scientometrics, Springer;Akadémiai Kiadó, vol. 87(3), pages 683-685, June.
    7. Juan Miguel Campanario, 2018. "Are leaders really leading? Journals that are first in Web of Science subject categories in the context of their groups," Scientometrics, Springer;Akadémiai Kiadó, vol. 115(1), pages 111-130, April.
    8. Balakrishnan, N. & Sarabia, José María & Kolev, Nikolai, 2010. "A simple relation between the Leimkuhler curve and the mean residual life," Journal of Informetrics, Elsevier, vol. 4(4), pages 602-607.
    9. Perc, Matjaž, 2010. "Zipf’s law and log-normal distributions in measures of scientific output across fields and institutions: 40 years of Slovenia’s research as an example," Journal of Informetrics, Elsevier, vol. 4(3), pages 358-364.
    10. Sarabia, José María & Prieto, Faustino & Trueba, Carmen, 2012. "Modeling the probabilistic distribution of the impact factor," Journal of Informetrics, Elsevier, vol. 6(1), pages 66-79.
    11. Mishra, SK, 2010. "A note on empirical sample distribution of journal impact factors in major discipline groups," MPRA Paper 20747, University Library of Munich, Germany.
    12. B Ian Hutchins & Xin Yuan & James M Anderson & George M Santangelo, 2016. "Relative Citation Ratio (RCR): A New Metric That Uses Citation Rates to Measure Influence at the Article Level," PLOS Biology, Public Library of Science, vol. 14(9), pages 1-25, September.
    13. Brzezinski, Michal, 2014. "Empirical modeling of the impact factor distribution," Journal of Informetrics, Elsevier, vol. 8(2), pages 362-368.
    14. Mishra, SK, 2010. "Empirical probability distribution of journal impact factor and over-the-samples stability in its estimated parameters," MPRA Paper 20919, University Library of Munich, Germany.

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