IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v85y2023i1d10.1007_s13171-022-00286-3.html
   My bibliography  Save this article

Jeffreys Prior for Negative Binomial and Zero Inflated Negative Binomial Distributions

Author

Listed:
  • Arnab Kumar Maity

    (Pfizer Inc.)

  • Erina Paul

    (Merck, Co., Inc.)

Abstract

The negative binomial distribution often fits many real datasets, for example, RNA sequence data, adequately. Furthermore, in the presence of many zeros in the data, it is customary to fit a zero inflated negative binomial distribution. In this note, we study the effect of assuming the Jeffreys prior on the parameters of these two distributions. Under this, we derive the closed form expression of the Bayes factor of the zero inflated negative binomial against negative binomial distribution. We demonstrate the effectiveness of our findings through simulations and real data analyses.

Suggested Citation

  • Arnab Kumar Maity & Erina Paul, 2023. "Jeffreys Prior for Negative Binomial and Zero Inflated Negative Binomial Distributions," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 999-1013, February.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-022-00286-3
    DOI: 10.1007/s13171-022-00286-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-022-00286-3
    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/s13171-022-00286-3?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. Gupta, Pushpa L. & Gupta, Ramesh C. & Tripathi, Ram C., 1996. "Analysis of zero-adjusted count data," Computational Statistics & Data Analysis, Elsevier, vol. 23(2), pages 207-218, December.
    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. Yip, Karen C.H. & Yau, Kelvin K.W., 2005. "On modeling claim frequency data in general insurance with extra zeros," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 153-163, April.
    2. Chen, Cathy W.S. & Chen, Chun-Shu & Hsiung, Mo-Hua, 2023. "Bayesian modeling of spatial integer-valued time series," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).
    3. Hossein Kavand & Marcel Voia, 2018. "Estimation of Health Care Demand and its Implication on Income Effects of Individuals," Springer Proceedings in Business and Economics, in: William H. Greene & Lynda Khalaf & Paul Makdissi & Robin C. Sickles & Michael Veall & Marcel-Cristia (ed.), Productivity and Inequality, pages 275-304, Springer.
    4. Angers, Jean-Francois & Biswas, Atanu, 2003. "A Bayesian analysis of zero-inflated generalized Poisson model," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 37-46, February.
    5. Baíllo, A. & Berrendero, J.R. & Cárcamo, J., 2009. "Tests for zero-inflation and overdispersion: A new approach based on the stochastic convex order," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2628-2639, May.
    6. Chen, Cathy W.S. & Lee, Sangyeol, 2016. "Generalized Poisson autoregressive models for time series of counts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 51-67.
    7. Constantinescu Corina D. & Kozubowski Tomasz J. & Qian Haoyu H., 2019. "Probability of ruin in discrete insurance risk model with dependent Pareto claims," Dependence Modeling, De Gruyter, vol. 7(1), pages 215-233, January.
    8. Costantino, Francesco & Di Gravio, Giulio & Patriarca, Riccardo & Petrella, Lea, 2018. "Spare parts management for irregular demand items," Omega, Elsevier, vol. 81(C), pages 57-66.
    9. Bae, S. & Famoye, F. & Wulu, J.T. & Bartolucci, A.A. & Singh, K.P., 2005. "A rich family of generalized Poisson regression models with applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 69(1), pages 4-11.
    10. Nobuaki Hoshino, 2005. "On a limiting quasi-multinomial distribution," CIRJE F-Series CIRJE-F-361, CIRJE, Faculty of Economics, University of Tokyo.
    11. Tanabe, Ryunosuke & Hamada, Etsuo, 2016. "Objective priors for the zero-modified model," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 92-97.
    12. E. Bahrami Samani & Y. Amirian & M. Ganjali, 2012. "Likelihood estimation for longitudinal zero-inflated power series regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(9), pages 1965-1974, May.
    13. Xie, M. & He, B. & Goh, T. N., 2001. "Zero-inflated Poisson model in statistical process control," Computational Statistics & Data Analysis, Elsevier, vol. 38(2), pages 191-201, December.
    14. Bedrick, Edward J. & Hossain, Anwar, 2013. "Conditional tests for homogeneity of zero-inflated Poisson and Poisson-hurdle distributions," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 99-106.
    15. Ramesh Gupta & S. Sim & S. Ong, 2014. "Analysis of discrete data by Conway–Maxwell Poisson distribution," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(4), pages 327-343, October.
    16. Martin Ridout & John Hinde & Clarice G. B. Demétrio, 2001. "A Score Test for Testing a Zero‐Inflated Poisson Regression Model Against Zero‐Inflated Negative Binomial Alternatives," Biometrics, The International Biometric Society, vol. 57(1), pages 219-223, March.

    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:sankha:v:85:y:2023:i:1:d:10.1007_s13171-022-00286-3. 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.