IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v143y2020ics0167947319301938.html
   My bibliography  Save this article

The Zipf–Poisson-stopped-sum distribution with an application for modeling the degree sequence of social networks

Author

Listed:
  • Duarte-López, Ariel
  • Pérez-Casany, Marta
  • Valero, Jordi

Abstract

Under the Zipf Distribution, the frequency of a value is a power function of its size. Thus, when plotting frequencies versus size in log–log scale of data following that distribution, one obtains a straight line. The Zipf has been assumed to be appropriate for modeling highly skewed data from many different areas. Nevertheless, for many real data sets, the linearity is observed only in the tail; thus, the Zipf is fitted only for values larger than a given threshold and, consequently, there is a loss of information. The Zipf–Poisson-stopped-sum distribution is introduced as a more flexible alternative. It is proven that in log–log scale allows for top-concavity, maintaining the linearity in the tail. Consequently, the distribution fits properly many data sets in their entire range. To prove the suitability of our model 16 network degree sequences describing the interaction between members of a given platform have been fitted. The results have been compared with the fits obtained through other bi-parametric distributions.

Suggested Citation

  • Duarte-López, Ariel & Pérez-Casany, Marta & Valero, Jordi, 2020. "The Zipf–Poisson-stopped-sum distribution with an application for modeling the degree sequence of social networks," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:csdana:v:143:y:2020:i:c:s0167947319301938
    DOI: 10.1016/j.csda.2019.106838
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947319301938
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2019.106838?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. Ramon Ferrer‐i‐Cancho & Michael S. Vitevitch, 2018. "The origins of Zipf's meaning‐frequency law," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 69(11), pages 1369-1379, November.
    2. Wan Jing Low & Paul Wilson & Mike Thelwall, 2016. "Stopped sum models and proposed variants for citation data," Scientometrics, Springer;Akadémiai Kiadó, vol. 107(2), pages 369-384, May.
    3. Meng, Shengwang & Gao, Guangyuan, 2018. "Compound Poisson Claims Reserving Models: Extensions And Inference," ASTIN Bulletin, Cambridge University Press, vol. 48(3), pages 1137-1156, September.
    4. Boginski, Vladimir & Butenko, Sergiy & Pardalos, Panos M., 2005. "Statistical analysis of financial networks," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 431-443, February.
    5. Yeşim Güney & Yetkin Tuaç & Olcay Arslan, 2017. "Marshall–Olkin distribution: parameter estimation and application to cancer data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(12), pages 2238-2250, September.
    6. Assistant Professor G. Christopher Crawford & Professor Bill McKelvey, 2018. "Using maximum likelihood estimation methods and complexity science concepts to research power law-distributed phenomena," Chapters, in: Eve Mitleton-Kelly & Alexandros Paraskevas & Christopher Day (ed.), Handbook of Research Methods in Complexity Science, chapter 12, pages 227-253, Edward Elgar Publishing.
    7. Zornig, Peter & Altmann, Gabriel, 1995. "Unified representation of Zipf distributions," Computational Statistics & Data Analysis, Elsevier, vol. 19(4), pages 461-473, April.
    8. Panjer, Harry H., 1981. "Recursive Evaluation of a Family of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 22-26, June.
    9. Sundt, Bjørn & Jewell, William S., 1981. "Further Results on Recursive Evaluation of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 27-39, June.
    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. Valero, Jordi & Pérez-Casany, Marta & Duarte-López, Ariel, 2022. "The Zipf-Polylog distribution: Modeling human interactions through social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(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. Venegas-Martínez, Francisco & Franco-Arbeláez, Luis Ceferino & Franco-Ceballos, Luis Eduardo & Murillo-Gómez, Juan Guillermo, 2015. "Riesgo operativo en el sector salud en Colombia: 2013," eseconomía, Escuela Superior de Economía, Instituto Politécnico Nacional, vol. 0(43), pages 7-36, segundo s.
    2. Gathy, Maude & Lefèvre, Claude, 2010. "On the Lagrangian Katz family of distributions as a claim frequency model," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 76-83, August.
    3. Marios N. Kyriacou, 2015. "Credit Risk Measurement in Financial Institutions: Going Beyond Regulatory Compliance," Cyprus Economic Policy Review, University of Cyprus, Economics Research Centre, vol. 9(1), pages 31-72, June.
    4. James D. Englehardt & Chengjun Peng, 1996. "A Bayesian Benefit‐Risk Model Applied to the South Florida Building Code," Risk Analysis, John Wiley & Sons, vol. 16(1), pages 81-91, February.
    5. Paul Embrechts & Marco Frei, 2009. "Panjer recursion versus FFT for compound distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 497-508, July.
    6. Sundt, Bjorn, 2002. "Recursive evaluation of aggregate claims distributions," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 297-322, June.
    7. Janecskó, Balázs, 2002. "Portfóliószemléletű hitelkockázat szimulációs meghatározása [Simulated determination of credit risk in portfolio terms]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 664-676.
    8. Anh Ninh, 2021. "Robust newsvendor problems with compound Poisson demands," Annals of Operations Research, Springer, vol. 302(1), pages 327-338, July.
    9. Aleksandr Beknazaryan & Peter Adamic, 2022. "On a stochastic order induced by an extension of Panjer’s family of discrete distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(1), pages 67-91, January.
    10. Ambagaspitiya, R. S., 1995. "A family of discrete distributions," Insurance: Mathematics and Economics, Elsevier, vol. 16(2), pages 107-127, May.
    11. A.Hernández-Bastida & J. M. Pérez–Sánchez & E. Gómez-Deniz, 2007. "Bayesian Analysis Of The Compound Collective Model: The Net Premium Principle With Exponential Poisson And Gamma–Gamma Distributions," FEG Working Paper Series 07/03, Faculty of Economics and Business (University of Granada).
    12. Wu, Xueyuan & Yuen, Kam C., 2003. "A discrete-time risk model with interaction between classes of business," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 117-133, August.
    13. Franco-Arbeláez, Luis Ceferino & Franco-Ceballos, Luis Eduardo & Murillo-Gómez, Juan Guillermo & Venegas-Martínez, Francisco, 2015. "Riesgo operativo en el sector salud en Colombia [Operational Risk in the Health Sector in Colombia]," MPRA Paper 63149, University Library of Munich, Germany.
    14. Brendan P. M. McCabe & Christopher L. Skeels, 2020. "Distributions You Can Count On …But What’s the Point?," Econometrics, MDPI, vol. 8(1), pages 1-36, March.
    15. den Iseger, P. W. & Smith, M. A. J. & Dekker, R., 1997. "Computing compound distributions faster!," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 23-34, June.
    16. Valero, Jordi & Pérez-Casany, Marta & Duarte-López, Ariel, 2022. "The Zipf-Polylog distribution: Modeling human interactions through social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    17. Sundt, Bjorn, 2003. "Some recursions for moments of compound distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 487-496, December.
    18. Cordelia Rudolph & Uwe Schmock, 2020. "Multivariate Collective Risk Model: Dependent Claim Numbers and Panjer’s Recursion," Risks, MDPI, vol. 8(2), pages 1-31, May.
    19. Kitano, Masashi & Shimizu, Kunio & Ong, S.H., 2005. "The generalized Charlier series distribution as a distribution with two-step recursion," Statistics & Probability Letters, Elsevier, vol. 75(4), pages 280-290, December.
    20. D'Arcangelis, Anna Maria & Rotundo, Giulia, 2021. "Herding in mutual funds: A complex network approach," Journal of Business Research, Elsevier, vol. 129(C), pages 679-686.

    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:csdana:v:143:y:2020:i:c:s0167947319301938. 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/csda .

    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.