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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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    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.
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