IDEAS home Printed from https://ideas.repec.org/a/eee/infome/v3y2009i4p290-295.html
   My bibliography  Save this article

Mathematical derivation of the impact factor distribution

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S175115770900011X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.joi.2009.01.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Huang, Ding-wei, 2017. "Impact factor distribution revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 173-180.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    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. 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.
    10. 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.
    11. L. Egghe, 2011. "The impact factor rank-order distribution revisited," Scientometrics, Springer;Akadémiai Kiadó, vol. 87(3), pages 683-685, June.
    12. Brzezinski, Michal, 2014. "Empirical modeling of the impact factor distribution," Journal of Informetrics, Elsevier, vol. 8(2), pages 362-368.
    13. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Wolfgang Glänzel, 2009. "The multi-dimensionality of journal impact," Scientometrics, Springer;Akadémiai Kiadó, vol. 78(2), pages 355-374, February.
    3. 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.
    4. Zewen Hu & Yishan Wu & Jianjun Sun, 2018. "A quantitative analysis of determinants of non-citation using a panel data model," Scientometrics, Springer;Akadémiai Kiadó, vol. 116(2), pages 843-861, August.
    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. Burrell, Quentin L., 2013. "A stochastic approach to the relation between the impact factor and the uncitedness factor," Journal of Informetrics, Elsevier, vol. 7(3), pages 676-682.
    7. Waltman, L. & van Eck, N.J.P., 2009. "A Taxonomy of Bibliometric Performance Indicators Based on the Property of Consistency," ERIM Report Series Research in Management ERS-2009-014-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    8. Bouyssou, Denis & Marchant, Thierry, 2011. "Bibliometric rankings of journals based on Impact Factors: An axiomatic approach," Journal of Informetrics, Elsevier, vol. 5(1), pages 75-86.
    9. Cerqueti, Roy & Lupi, Claudio & Pietrovito, Filomena & Pozzolo, Alberto Franco, 2022. "Rank–size distributions for banks: A cross-country analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    10. Rongying Zhao & Mingkun Wei, 2017. "Academic impact evaluation of Wechat in view of social media perspective," Scientometrics, Springer;Akadémiai Kiadó, vol. 112(3), pages 1777-1791, September.
    11. Elio Roca-Flores & Gerardo G. Naumis, 2021. "Assessing statistical hurricane risks: nonlinear regression and time-window analysis of North Atlantic annual accumulated cyclonic energy rank profile," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 108(3), pages 2455-2465, September.
    12. 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.
    13. Yutao Sun & Seamus Grimes, 2016. "The emerging dynamic structure of national innovation studies: a bibliometric analysis," Scientometrics, Springer;Akadémiai Kiadó, vol. 106(1), pages 17-40, January.
    14. Ji-ping Gao & Cheng Su & Hai-yan Wang & Li-hua Zhai & Yun-tao Pan, 2019. "Research fund evaluation based on academic publication output analysis: the case of Chinese research fund evaluation," Scientometrics, Springer;Akadémiai Kiadó, vol. 119(2), pages 959-972, May.
    15. Giovanni Abramo & Ciriaco Andrea D’Angelo & Flavia Costa, 2023. "Correlating article citedness and journal impact: an empirical investigation by field on a large-scale dataset," Scientometrics, Springer;Akadémiai Kiadó, vol. 128(3), pages 1877-1894, March.
    16. Bertoli-Barsotti, Lucio & Lando, Tommaso, 2019. "How mean rank and mean size may determine the generalised Lorenz curve: With application to citation analysis," Journal of Informetrics, Elsevier, vol. 13(1), pages 387-396.
    17. 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.
    18. Máxima Bolaños-Pizarro & Bart Thijs & Wolfgang Glänzel, 2010. "Cardiovascular research in Spain. A comparative scientometric study," Scientometrics, Springer;Akadémiai Kiadó, vol. 85(2), pages 509-526, November.
    19. Sangwal, Keshra, 2013. "Citation and impact factor distributions of scientific journals published in individual countries," Journal of Informetrics, Elsevier, vol. 7(2), pages 487-504.
    20. Nowak, Przemysław & Santolini, Marc & Singh, Chakresh & Siudem, Grzegorz & Tupikina, Liubov, 2024. "Beyond Zipf’s law: Exploring the discrete generalized beta distribution in open-source repositories," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 649(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:infome:v:3:y:2009:i:4:p:290-295. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/joi .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.