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A Heuristic Study of the First-Citation Distribution

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  • Leo Egghe

    (LUC
    UIA)

Abstract

The first-citation distribution, i.e. the cumulative distribution of the time period between publication of an article and the time it receives its first citation, has never been modelled by using well-known informetric distributions. An attempt to this is given in this paper. For the diachronous aging distribution we use a simple decreasing exponential model. For the distribution of the total number of received citations we use a classical Lotka function. The combination of these two tools yield new first-citation distributions. The model is then tested by applying nonlinear regression techniques. The obtained fits are very good and comparable with older experimental results of Rousseau and of Gupta and Rousseau. However our single model is capable of fitting all first-citation graphs, concave as well as S-shaped; in the older results one needed two different models for it. Our model is the function $$\Phi {\text{(t}}_{\text{1}} {\text{) = }}\gamma (1 - a^{{\text{t}}_{\text{1}} } )^{\alpha - 1} {\text{ }}.$$ Here γ is the fraction of the papers that eventually get cited, t1 is the time of the first citation, a is the aging rate and α is Lotka's exponent. The combination of a and α in one formula is, to the best of our knowledge, new. The model hence provides estimates for these two important parameters.

Suggested Citation

  • Leo Egghe, 2000. "A Heuristic Study of the First-Citation Distribution," Scientometrics, Springer;Akadémiai Kiadó, vol. 48(3), pages 345-359, July.
  • Handle: RePEc:spr:scient:v:48:y:2000:i:3:d:10.1023_a:1005688404778
    DOI: 10.1023/A:1005688404778
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    Citations

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    Cited by:

    1. Mingers, John & Leydesdorff, Loet, 2015. "A review of theory and practice in scientometrics," European Journal of Operational Research, Elsevier, vol. 246(1), pages 1-19.
    2. Leo Egghe & I. K. R. Ravichandra Rao, 2002. "Theory and experimentation on the most-recent-reference distribution," Scientometrics, Springer;Akadémiai Kiadó, vol. 53(3), pages 371-387, March.
    3. Bornmann, Lutz & Daniel, Hans-Dieter, 2010. "Citation speed as a measure to predict the attention an article receives: An investigation of the validity of editorial decisions at Angewandte Chemie International Edition," Journal of Informetrics, Elsevier, vol. 4(1), pages 83-88.
    4. Ugo Finardi, 2017. "Long time series of highly cited articles: an empirical study," IRCrES Working Paper 201712, CNR-IRCrES Research Institute on Sustainable Economic Growth - Moncalieri (TO) ITALY - former Institute for Economic Research on Firms and Growth - Torino (TO) ITALY.
    5. Egghe, L., 2013. "The functional relation between the impact factor and the uncitedness factor revisited," Journal of Informetrics, Elsevier, vol. 7(1), pages 183-189.
    6. Leo Egghe, 2007. "Probabilities for encountering genius, basic, ordinary or insignificant papers based on the cumulative nth citation distribution," Scientometrics, Springer;Akadémiai Kiadó, vol. 70(1), pages 167-181, January.
    7. Soo Jeung Lee & Christian Schneijderberg & Yangson Kim & Isabel Steinhardt, 2021. "Have Academics’ Citation Patterns Changed in Response to the Rise of World University Rankings? A Test Using First-Citation Speeds," Sustainability, MDPI, vol. 13(17), pages 1-19, August.
    8. Wen-Yau Cathy Lin, 2021. "Effects of open access and articles-in-press mechanisms on publishing lag and first-citation speed: a case on energy and fuels journals," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(6), pages 4841-4869, June.
    9. Saralees Nadarajah & Samuel Kotz, 2007. "Models for citation behavior," Scientometrics, Springer;Akadémiai Kiadó, vol. 72(2), pages 291-305, August.
    10. J Mingers, 2008. "Exploring the dynamics of journal citations: Modelling with s-curves," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(8), pages 1013-1025, August.
    11. Wallace, Matthew L. & Larivière, Vincent & Gingras, Yves, 2009. "Modeling a century of citation distributions," Journal of Informetrics, Elsevier, vol. 3(4), pages 296-303.
    12. Hu, Zewen & Wu, Yishan, 2014. "Regularity in the time-dependent distribution of the percentage of never-cited papers: An empirical pilot study based on the six journals," Journal of Informetrics, Elsevier, vol. 8(1), pages 136-146.
    13. Xin Li & Xuli Tang & Wei Lu, 2024. "How biomedical papers accumulated their clinical citations: a large-scale retrospective analysis based on PubMed," Scientometrics, Springer;Akadémiai Kiadó, vol. 129(6), pages 3315-3339, June.
    14. Bar-Ilan, Judit, 2008. "Informetrics at the beginning of the 21st century—A review," Journal of Informetrics, Elsevier, vol. 2(1), pages 1-52.
    15. Aristoklis D. Anastasiadis & Marcelo P. Albuquerque & Marcio P. Albuquerque & Diogo B. Mussi, 2010. "Tsallis q-exponential describes the distribution of scientific citations—a new characterization of the impact," Scientometrics, Springer;Akadémiai Kiadó, vol. 83(1), pages 205-218, April.
    16. Rosenstreich, Daniela & Wooliscroft, Ben, 2009. "Measuring the impact of accounting journals using Google Scholar and the g-index," The British Accounting Review, Elsevier, vol. 41(4), pages 227-239.
    17. Finardi, Ugo, 2014. "On the time evolution of received citations, in different scientific fields: An empirical study," Journal of Informetrics, Elsevier, vol. 8(1), pages 13-24.
    18. Quentin L. Burrell, 2002. "The nth-citation distribution and obsolescence," Scientometrics, Springer;Akadémiai Kiadó, vol. 53(3), pages 309-323, March.
    19. Quentin L. Burrel, 2001. "Stochastic modelling of the first-citation distribution," Scientometrics, Springer;Akadémiai Kiadó, vol. 52(1), pages 3-12, September.

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