IDEAS home Printed from https://ideas.repec.org/a/spr/sankhb/v84y2022i2d10.1007_s13571-022-00284-3.html
   My bibliography  Save this article

On Improving the Posterior Predictive Distribution of the Difference Between two Independent Poisson Distribution

Author

Listed:
  • Abdolnasser Sadeghkhani

    (Ohio State University)

Abstract

This paper addresses the exact Bayesian analysis of the difference between two independent Poisson distributions with means μ1 and μ2 respectively, known as the Skellam distribution with parameters (μ1, μ2). We develop a closed form for the posterior predictive distribution of the future distribution under the order constraint of μ1 > μ2. This kind of constraint is quite common and useful in applications specially in sports data analysis. We show that the proposed distribution estimator outperforms other types of distribution estimators in the literature. We use a simulation study with an example regarding the prediction in soccer games to show the performance of the proposed method.

Suggested Citation

  • Abdolnasser Sadeghkhani, 2022. "On Improving the Posterior Predictive Distribution of the Difference Between two Independent Poisson Distribution," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 765-777, November.
    • Handle: RePEc:spr:sankhb:v:84:y:2022:i:2:d:10.1007_s13571-022-00284-3
    DOI: 10.1007/s13571-022-00284-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13571-022-00284-3
    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/s13571-022-00284-3?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. Abdolnasser Sadeghkhani & Seyed Ejaz Ahmed, 2019. "A Bayesian Approach to Predict the Number of Goals in Hockey," Stats, MDPI, vol. 2(2), pages 1-11, April.
    2. José Manuel Corcuera & Federica Giummolè, 1999. "A Generalized Bayes Rule for Prediction," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 265-279, June.
    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. Essam Al-Hussaini & Abd Ahmad, 2003. "On Bayesian interval prediction of future records," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 79-99, June.
    2. Tatsuya Kubokawa & Éric Marchand & William E. Strawderman & Jean-Philippe Turcotte, 2012. "Minimaxity in Predictive Density Estimation with Parametric Constraints," CIRJE F-Series CIRJE-F-843, CIRJE, Faculty of Economics, University of Tokyo.
    3. Malay Ghosh & Tatsuya Kubokawa & Gauri Sankar Datta, 2020. "Density Prediction and the Stein Phenomenon," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 330-352, August.
    4. Takemi Yanagimoto & Toshio Ohnishi, 2014. "Permissible boundary prior function as a virtually proper prior density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 789-809, August.
    5. Zhang, Fode & Shi, Yimin & Wang, Ruibing, 2017. "Geometry of the q-exponential distribution with dependent competing risks and accelerated life testing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 552-565.
    6. Ghosh, Malay & Mergel, Victor & Datta, Gauri Sankar, 2008. "Estimation, prediction and the Stein phenomenon under divergence loss," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1941-1961, October.
    7. Chang, In Hong & Mukerjee, Rahul, 2004. "Asymptotic results on the frequentist mean squared error of generalized Bayes point predictors," Statistics & Probability Letters, Elsevier, vol. 67(1), pages 65-71, March.
    8. Kubokawa, Tatsuya & Marchand, Éric & Strawderman, William E. & Turcotte, Jean-Philippe, 2013. "Minimaxity in predictive density estimation with parametric constraints," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 382-397.

    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:sankhb:v:84:y:2022:i:2:d:10.1007_s13571-022-00284-3. 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.