IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v606y2022ics0378437122006604.html
   My bibliography  Save this article

Power laws, the Price model, and the Pareto type-2 distribution

Author

Listed:
  • Siudem, Grzegorz
  • Nowak, Przemysław
  • Gagolewski, Marek

Abstract

We consider a version of D. Price’s model for the growth of a bibliographic network, where in each iteration, a constant number of citations is randomly allocated according to a weighted combination of the accidental (uniformly distributed) and the preferential (rich-get-richer) rule. Instead of relying on the typical master equation approach, we formulate and solve this problem in terms of the rank–size distribution. We show that, asymptotically, such a process leads to a Pareto-type 2 distribution with a new, appealingly interpretable parametrisation. We prove that the solution to the Price model expressed in terms of the rank–size distribution coincides with the expected values of order statistics in an independent Paretian sample. An empirical analysis of a large repository of academic papers yields a good fit not only in the tail of the distribution (as it is usually the case in the power law-like framework), but also across a significantly larger fraction of the data domain.

Suggested Citation

  • Siudem, Grzegorz & Nowak, Przemysław & Gagolewski, Marek, 2022. "Power laws, the Price model, and the Pareto type-2 distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    • Handle: RePEc:eee:phsmap:v:606:y:2022:i:c:s0378437122006604
    DOI: 10.1016/j.physa.2022.128059
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437122006604
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2022.128059?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Luceno, Alberto, 2006. "Fitting the generalized Pareto distribution to data using maximum goodness-of-fit estimators," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 904-917, November.
    2. Zoltán Néda & Levente Varga & Tamás S Biró, 2017. "Science and Facebook: The same popularity law!," PLOS ONE, Public Library of Science, vol. 12(7), pages 1-11, July.
    3. Gagolewski, Marek, 2013. "Scientific impact assessment cannot be fair," Journal of Informetrics, Elsevier, vol. 7(4), pages 792-802.
    4. Schubert, András & Glänzel, Wolfgang, 2007. "A systematic analysis of Hirsch-type indices for journals," Journal of Informetrics, Elsevier, vol. 1(3), pages 179-184.
    5. Chami Figueira, F. & Moura, N.J. & Ribeiro, M.B., 2011. "The Gompertz–Pareto income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 689-698.
    6. Chanania Steinbock & Ofer Biham & Eytan Katzav, 2019. "Analytical results for the distribution of shortest path lengths in directed random networks that grow by node duplication," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(6), pages 1-16, June.
    7. Mike Thelwall & Pardeep Sud, 2021. "Do new research issues attract more citations? A comparison between 25 Scopus subject categories," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 72(3), pages 269-279, March.
    8. Grzegorz Siudem & Barbara Żogała-Siudem & Anna Cena & Marek Gagolewski, 2020. "Three dimensions of scientific impact," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 117(25), pages 13896-13900, June.
    9. Alessandro Pluchino & Giulio Burgio & Andrea Rapisarda & Alessio Emanuele Biondo & Alfredo Pulvirenti & Alfredo Ferro & Toni Giorgino, 2019. "Exploring the role of interdisciplinarity in physics: Success, talent and luck," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-15, June.
    10. Alessandro Pluchino & Alessio Emanuele Biondo & Andrea Rapisarda, 2018. "Talent Versus Luck: The Role Of Randomness In Success And Failure," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 21(03n04), pages 1-31, May.
    11. Bourguignon, Marcelo & Saulo, Helton & Fernandez, Rodrigo Nobre, 2016. "A new Pareto-type distribution with applications in reliability and income data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 166-175.
    12. Dongqing Lyu & Xuanmin Ruan & Juan Xie & Ying Cheng, 2021. "The classification of citing motivations: a meta-synthesis," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(4), pages 3243-3264, April.
    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. Lucio Bertoli-Barsotti & Marek Gagolewski & Grzegorz Siudem & Barbara .Zoga{l}a-Siudem, 2023. "Equivalence of inequality indices: Three dimensions of impact revisited," Papers 2304.07479, arXiv.org.
    2. 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).
    3. Lucio Bertoli-Barsotti & Marek Gagolewski & Grzegorz Siudem & Barbara .Zoga{l}a-Siudem, 2023. "Gini-stable Lorenz curves and their relation to the generalised Pareto distribution," Papers 2304.07480, arXiv.org, revised Jan 2024.
    4. Żogała-Siudem, Barbara & Cena, Anna & Siudem, Grzegorz & Gagolewski, Marek, 2023. "Interpretable reparameterisations of citation models," Journal of Informetrics, Elsevier, vol. 17(1).
    5. Mrowinski, Maciej J. & Gagolewski, Marek & Siudem, Grzegorz, 2022. "Accidentality in journal citation patterns," Journal of Informetrics, Elsevier, vol. 16(4).
    6. Bertoli-Barsotti, Lucio & Gagolewski, Marek & Siudem, Grzegorz & Żogała-Siudem, Barbara, 2024. "Gini-stable Lorenz curves and their relation to the generalised Pareto distribution," Journal of Informetrics, Elsevier, vol. 18(2).
    7. D'Acci, Luca S., 2023. "Is housing price distribution across cities, scale invariant? Fractal distribution of settlements' house prices as signature of self-organized complexity," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

    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. Mrowinski, Maciej J. & Gagolewski, Marek & Siudem, Grzegorz, 2022. "Accidentality in journal citation patterns," Journal of Informetrics, Elsevier, vol. 16(4).
    2. Biró, Tamás S. & Telcs, András & Józsa, Máté & Néda, Zoltán, 2023. "Gintropic scaling of scientometric indexes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    3. Domma, Filippo & Condino, Francesca & Giordano, Sabrina, 2018. "A new formulation of the Dagum distribution in terms of income inequality and poverty measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 104-126.
    4. 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).
    5. Żogała-Siudem, Barbara & Cena, Anna & Siudem, Grzegorz & Gagolewski, Marek, 2023. "Interpretable reparameterisations of citation models," Journal of Informetrics, Elsevier, vol. 17(1).
    6. Cena, Anna & Gagolewski, Marek & Siudem, Grzegorz & Żogała-Siudem, Barbara, 2022. "Validating citation models by proxy indices," Journal of Informetrics, Elsevier, vol. 16(2).
    7. Faiza Qayyum & Harun Jamil & Naeem Iqbal & DoHyeun Kim & Muhammad Tanvir Afzal, 2022. "Toward potential hybrid features evaluation using MLP-ANN binary classification model to tackle meaningful citations," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(11), pages 6471-6499, November.
    8. Tuba Bircan & Almila Alkim Akdag Salah, 2022. "A Bibliometric Analysis of the Use of Artificial Intelligence Technologies for Social Sciences," Mathematics, MDPI, vol. 10(23), pages 1-17, November.
    9. Filip Gesiarz & Jan-Emmanuel De Neve & Tali Sharot, 2020. "The motivational cost of inequality: Opportunity gaps reduce the willingness to work," PLOS ONE, Public Library of Science, vol. 15(9), pages 1-18, September.
    10. Martin Ricker, 2017. "Letter to the Editor: About the quality and impact of scientific articles," Scientometrics, Springer;Akadémiai Kiadó, vol. 111(3), pages 1851-1855, June.
    11. Ilda Inácio & José Velhinho, 2022. "Comments on Mathematical Aspects of the Biró–Néda Model," Mathematics, MDPI, vol. 10(4), pages 1-10, February.
    12. Lukas Schneider & Johannes Scholten & Bulcsú Sándor & Claudius Gros, 2021. "Charting closed-loop collective cultural decisions: from book best sellers and music downloads to Twitter hashtags and Reddit comments," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(8), pages 1-13, August.
    13. Gangan Prathap, 2010. "Going much beyond the Durfee square: enhancing the h T index," Scientometrics, Springer;Akadémiai Kiadó, vol. 84(1), pages 149-152, July.
    14. Moura, N.J. & Ribeiro, Marcelo B., 2013. "Testing the Goodwin growth-cycle macroeconomic dynamics in Brazil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2088-2103.
    15. Pascal Bador & Thierry Lafouge, 2010. "Comparative analysis between impact factor and h-index for pharmacology and psychiatry journals," Scientometrics, Springer;Akadémiai Kiadó, vol. 84(1), pages 65-79, July.
    16. Tingcan Ma & Gui-Fang Wang & Ke Dong & Mukun Cao, 2012. "The Journal’s Integrated Impact Index: a new indicator for journal evaluation," Scientometrics, Springer;Akadémiai Kiadó, vol. 90(2), pages 649-658, February.
    17. Petridis, Konstantinos & Malesios, Chrisovalantis & Arabatzis, Garyfallos & Thanassoulis, Emmanuel, 2013. "Efficiency analysis of forestry journals: Suggestions for improving journals’ quality," Journal of Informetrics, Elsevier, vol. 7(2), pages 505-521.
    18. Roberto Todeschini, 2011. "The j-index: a new bibliometric index and multivariate comparisons between other common indices," Scientometrics, Springer;Akadémiai Kiadó, vol. 87(3), pages 621-639, June.
    19. Pedro Albarrán & Juan A. Crespo & Ignacio Ortuño & Javier Ruiz-Castillo, 2011. "The skewness of science in 219 sub-fields and a number of aggregates," Scientometrics, Springer;Akadémiai Kiadó, vol. 88(2), pages 385-397, August.
    20. Anna Tietze & Philip Hofmann, 2019. "The h-index and multi-author hm-index for individual researchers in condensed matter physics," Scientometrics, Springer;Akadémiai Kiadó, vol. 119(1), pages 171-185, April.

    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:phsmap:v:606:y:2022:i:c:s0378437122006604. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.