IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v27y2018i1d10.1007_s10260-017-0386-y.html
   My bibliography  Save this article

The Tempered Discrete Linnik distribution

Author

Listed:
  • Lucio Barabesi

    (Università di Siena)

  • Carolina Becatti

    (IMT Institute for Advanced Studies)

  • Marzia Marcheselli

    (Università di Siena)

Abstract

We introduce a new family of integer-valued distributions by considering a tempered version of the Discrete Linnik law. The proposal is actually a generalization of the well-known Poisson–Tweedie law. The suggested family is extremely flexible since it contains a wide spectrum of distributions ranging from light-tailed laws (such as the Binomial) to heavy-tailed laws (such as the Discrete Linnik). The main theoretical features of the Tempered Discrete Linnik distribution are explored by providing a series of identities in law, which describe its genesis in terms of mixture Poisson distribution and compound Negative Binomial distribution—as well as in terms of mixture Poisson–Tweedie distribution. Moreover, we give a manageable expression and a suitable recursive relationship for the corresponding probability function. Finally, an application to scientometric data—which deals with the scientific output of the researchers of the University of Siena—is considered.

Suggested Citation

  • Lucio Barabesi & Carolina Becatti & Marzia Marcheselli, 2018. "The Tempered Discrete Linnik distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 45-68, March.
    • Handle: RePEc:spr:stmapp:v:27:y:2018:i:1:d:10.1007_s10260-017-0386-y
    DOI: 10.1007/s10260-017-0386-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-017-0386-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10260-017-0386-y?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. Luca Pratelli & Alberto Baccini & Lucio Barabesi & Marzia Marcheselli, 2012. "Statistical Analysis of the Hirsch Index," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 681-694, December.
    2. Stefano Favaro & Bernardo Nipoti, 2014. "Discussion of “On simulation and properties of the stable law” by L. Devroye and L. James," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 365-369, August.
    3. A. Baccini & L. Barabesi & M. Cioni & C. Pisani, 2014. "Crossing the hurdle: the determinants of individual scientific performance," Scientometrics, Springer;Akadémiai Kiadó, vol. 101(3), pages 2035-2062, December.
    4. Luc Devroye & Lancelot James, 2014. "On simulation and properties of the stable law," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 307-343, August.
    5. Zhu, Rong & Joe, Harry, 2009. "Modelling heavy-tailed count data using a generalised Poisson-inverse Gaussian family," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1695-1703, August.
    6. Antonio Lijoi & Igor Prünster, 2014. "Discussion of “On simulation and properties of the stable law” by L. Devroye and L. James," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 371-377, August.
    7. Quentin L. Burrell, 2014. "The individual author’s publication–citation process: theory and practice," Scientometrics, Springer;Akadémiai Kiadó, vol. 98(1), pages 725-742, January.
    8. Pakes, Anthony G., 1995. "Characterization of discrete laws via mixed sums and Markov branching processes," Stochastic Processes and their Applications, Elsevier, vol. 55(2), pages 285-300, February.
    Full references (including those not matched with items on IDEAS)

    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. Pietro Battiston, 2014. "Citations are Forever: Modeling Constrained Network Formation," LEM Papers Series 2014/19, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    2. Ludwig Baringhaus & Rudolf Grübel, 1997. "On a Class of Characterization Problems for Random Convex Combinations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 555-567, September.
    3. Ajiferuke, Isola & Famoye, Felix, 2015. "Modelling count response variables in informetric studies: Comparison among count, linear, and lognormal regression models," Journal of Informetrics, Elsevier, vol. 9(3), pages 499-513.
    4. Jong-Hyun Kim & Yong-Gil Lee, 2021. "Factors of Collaboration Affecting the Performance of Alternative Energy Patents in South Korea from 2010 to 2017," Sustainability, MDPI, vol. 13(18), pages 1-25, September.
    5. Wu, Jiang & Ou, Guiyan & Liu, Xiaohui & Dong, Ke, 2022. "How does academic education background affect top researchers’ performance? Evidence from the field of artificial intelligence," Journal of Informetrics, Elsevier, vol. 16(2).
    6. Marco Pautasso, 2015. "The Italian University Habilitation and the Challenge of Increasing the Representation of Women in Academia," Challenges, MDPI, vol. 6(1), pages 1-16, March.
    7. Christoph, Gerd & Schreiber, Karina, 2000. "Scaled Sibuya distribution and discrete self-decomposability," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 181-187, June.
    8. 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.
    9. Gianluigi Pelloni & Marco Savioli, 2015. "Why Is Italy Doing So Badly?," Economic Affairs, Wiley Blackwell, vol. 35(3), pages 349-365, October.
    10. Cristiano Varin & Manuela Cattelan & David Firth, 2016. "Statistical modelling of citation exchange between statistics journals," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(1), pages 1-63, January.
    11. Frandsen, Tove Faber & Jacobsen, Rasmus Højbjerg & Wallin, Johan A. & Brixen, Kim & Ousager, Jakob, 2015. "Gender differences in scientific performance: A bibliometric matching analysis of Danish health sciences Graduates," Journal of Informetrics, Elsevier, vol. 9(4), pages 1007-1017.
    12. Zacchia, Giulia, 2016. "Segregation or homologation? Gender differences in recent Italian economic thought," MPRA Paper 72279, University Library of Munich, Germany.
    13. Klebanov, Lev B. & Slámová, Lenka, 2013. "Integer valued stable random variables," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1513-1519.
    14. Buddana Amrutha & Kozubowski Tomasz J., 2014. "Discrete Pareto Distributions," Stochastics and Quality Control, De Gruyter, vol. 29(2), pages 143-156, December.
    15. 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.
    16. Ana María Martínez-Rodríguez & Antonio Conde-Sánchez & María José Olmo-Jiménez, 2019. "A new approach to truncated regression for count data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(4), pages 503-526, December.
    17. Michael Grabchak, 2022. "Discrete Tempered Stable Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1877-1890, September.
    18. Joseph Gerald Hirschberg & Jeanette Ngaire Lye, 2020. "Grading Journals In Economics: The Abcs Of The Abdc," Journal of Economic Surveys, Wiley Blackwell, vol. 34(4), pages 876-921, September.
    19. Sapatinas, Theofanis, 1999. "A characterization of the negative binomial distribution via [alpha]-monotonicity," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 49-53, October.
    20. Paola Cerchiello & Paolo Giudici, 2014. "Financial big data analysis for the estimation of systemic risks," DEM Working Papers Series 086, University of Pavia, Department of Economics and Management.

    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:spr:stmapp:v:27:y:2018:i:1:d:10.1007_s10260-017-0386-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.