IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v79y2009i15p1695-1703.html

Modelling heavy-tailed count data using a generalised Poisson-inverse Gaussian family

Author

Listed:
  • Zhu, Rong
  • Joe, Harry

Abstract

We generalise the Poisson-inverse Gaussian distribution to a three-parameter family, which includes the Poisson and discrete stable distributions as boundary cases. It is flexible in modelling count data sets with different tail heaviness. Although the family only has a closed-form probability generating function, a recursive method is developed for statistical inferences based on the likelihood. As an example, this new family is applied to data sets of citation counts of published articles.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:15:p:1695-1703
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(09)00157-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    for a different version of it.

    References listed on IDEAS

    as
    1. Christoph, Gerd & Schreiber, Karina, 1998. "Discrete stable random variables," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 243-247, March.
    2. Christoph, Gerd & Schreiber, Karina, 2000. "Scaled Sibuya distribution and discrete self-decomposability," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 181-187, June.
    3. M. Holla, 1967. "On a poisson-inverse gaussian distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 11(1), pages 115-121, December.
    4. Tremblay, Luc, 1992. "Using the Poisson Inverse Gaussian in Bonus-Malus Systems," ASTIN Bulletin, Cambridge University Press, vol. 22(1), pages 97-106, May.
    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. Ping Li & Feilong Lu, 2025. "Bayesian estimation of first-order integer generalized autoregressive models based on the negative binomial thinning operator," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 34(4), pages 865-894, September.
    2. Di Noia, Antonio & Marcheselli, Marzia & Pisani, Caterina & Pratelli, Luca, 2023. "Censoring heavy-tail count distributions for parameter estimation with an application to stable distributions," Statistics & Probability Letters, Elsevier, vol. 202(C).
    3. Baccini, A. & Barabesi, L. & Marcheselli, M. & Pratelli, L., 2012. "Statistical inference on the h-index with an application to top-scientist performance," Journal of Informetrics, Elsevier, vol. 6(4), pages 721-728.
    4. Klebanov, Lev B. & Slámová, Lenka, 2013. "Integer valued stable random variables," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1513-1519.
    5. 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.
    6. Mahsa Nadifar & Hossein Baghishani & Afshin Fallah, 2023. "A Flexible Generalized Poisson Likelihood for Spatial Counts Constructed by Renewal Theory, Motivated by Groundwater Quality Assessment," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(4), pages 726-748, December.
    7. 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.
    8. Yang Lu, 2021. "The predictive distributions of thinning‐based count processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 42-67, March.
    9. Rahma Abid & Célestin C. Kokonendji & Afif Masmoudi, 2021. "On Poisson-exponential-Tweedie models for ultra-overdispersed count data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 1-23, March.
    10. Michael Grabchak, 2022. "Discrete Tempered Stable Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1877-1890, September.
    11. Jiménez-Gamero, M.D. & Alba-Fernández, M.V., 2019. "Testing for the Poisson–Tweedie distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 164(C), pages 146-162.

    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. Tomasz J. Kozubowski & Krzysztof Podgórski, 2018. "A generalized Sibuya distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 855-887, August.
    2. Nadjib Bouzar & K. Jayakumar, 2008. "Time series with discrete semistable marginals," Statistical Papers, Springer, vol. 49(4), pages 619-635, October.
    3. Christoph, Gerd & Schreiber, Karina, 2000. "Scaled Sibuya distribution and discrete self-decomposability," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 181-187, June.
    4. Nadjib Bouzar, 2024. "On the Convolution of Scaled Sibuya Distributions," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 699-720, August.
    5. Buddana Amrutha & Kozubowski Tomasz J., 2014. "Discrete Pareto Distributions," Stochastics and Quality Control, De Gruyter, vol. 29(2), pages 143-156, December.
    6. Kukla, Jonas & Möhle, Martin, 2018. "On the block counting process and the fixation line of the Bolthausen–Sznitman coalescent," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 939-962.
    7. Michael Grabchak, 2022. "Discrete Tempered Stable Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1877-1890, September.
    8. Nadjib Bouzar, 2008. "The semi-Sibuya distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 459-464, June.
    9. Rodrigues, Josemar & Balakrishnan, N. & Cordeiro, Gauss M. & de Castro, Mário, 2011. "A unified view on lifetime distributions arising from selection mechanisms," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3311-3319, December.
    10. N. Bouzar & S. Satheesh, 2008. "Comments on a-decomposability," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 243-252.
    11. Rémillard Bruno & Theodorescu Radu, 2000. "Inference Based On The Empirical Probability Generating Function For Mixtures Of Poisson Distributions," Statistics & Risk Modeling, De Gruyter, vol. 18(4), pages 349-366, April.
    12. Matthew A. Ohemeng & Tomasz J. Kozubowski, 2025. "Discrete-Continuous Dual Families, Reciprocal Laws, Random Summation, and Mixtures of Gaussian Distributions," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 87(2), pages 741-789, August.
    13. Lev B Klebanov, 2023. "On Sibuya-Like Distributions in Branching and Birthand-Death Processes," Biomedical Journal of Scientific & Technical Research, Biomedical Research Network+, LLC, vol. 48(5), pages 40037-40046, February.
    14. Di Noia, Antonio & Marcheselli, Marzia & Pisani, Caterina & Pratelli, Luca, 2023. "Censoring heavy-tail count distributions for parameter estimation with an application to stable distributions," Statistics & Probability Letters, Elsevier, vol. 202(C).
    15. Soltani, A.R. & Shirvani, A. & Alqallaf, F., 2009. "A class of discrete distributions induced by stable laws," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1608-1614, July.
    16. Emilio Gomez-Deniz & Enrique Calderin-Ojeda, 2010. "A study of Bayesian local robustness with applications in actuarial statistics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1537-1546.
    17. Azaare Jacob & Zhao Wu, 2020. "An Alternative Pricing System through Bayesian Estimates and Method of Moments in a Bonus-Malus Framework for the Ghanaian Auto Insurance Market," JRFM, MDPI, vol. 13(7), pages 1-15, July.
    18. Farouk Mselmi, 2022. "Generalized linear model for subordinated Lévy processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 772-801, June.
    19. Yang Lu, 2018. "Dynamic Frailty Count Process in Insurance: A Unified Framework for Estimation, Pricing, and Forecasting," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(4), pages 1083-1102, December.
    20. Klebanov, Lev B. & Slámová, Lenka, 2013. "Integer valued stable random variables," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1513-1519.

    More about this item

    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:stapro:v:79:y:2009:i:15:p:1695-1703. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.