IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i13p2021-d1425352.html
   My bibliography  Save this article

Generalized Linear Model (GLM) Applications for the Exponential Dispersion Model Generated by the Landau Distribution

Author

Listed:
  • Shaul K. Bar-Lev

    (Faculty of Industrial Engineering and Technology Management, Holon Institute of Technology, Holon 5810201, Israel)

  • Xu Liu

    (School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China
    Yunnan Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University, Kunming 650091, China)

  • Ad Ridder

    (School of Business and Economics, Vrije University of Amsterdam, 1081 HV Amsterdam, The Netherlands)

  • Ziyu Xiang

    (School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China)

Abstract

The exponential dispersion model (EDM) generated by the Landau distribution, denoted by EDM-EVF (exponential variance function), belongs to the Tweedie scale with power infinity. Its density function does not have an explicit form and, as of yet, has not been used for statistical aspects. Out of all EDMs belonging to the Tweedie scale, only two EDMs are steep and supported on the whole real line: the normal EDM with constant variance function and the EDM-EVF. All other absolutely continuous steep EDMs in the Tweedie scale are supported on the positive real line. This paper aims to accomplish an overall picture of all generalized linear model (GLM) applications belonging to the Tweedie scale by including the EDM-EVF. This paper introduces all GLM ingredients needed for its analysis, including the respective link function and total and scaled deviance. We study its analysis of deviance, derive the asymptotic properties of the maximum likelihood estimation (MLE) of the covariate parameters, and obtain the asymptotic distribution of deviance, using saddlepoint approximation. We provide numerical studies, which include estimation algorithm, simulation studies, and applications to three real datasets, and demonstrate that GLM using the EDM-EVF performs better than the linear model based on the normal EDM. An R package accompanies all of these.

Suggested Citation

  • Shaul K. Bar-Lev & Xu Liu & Ad Ridder & Ziyu Xiang, 2024. "Generalized Linear Model (GLM) Applications for the Exponential Dispersion Model Generated by the Landau Distribution," Mathematics, MDPI, vol. 12(13), pages 1-21, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2021-:d:1425352
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/13/2021/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/13/2021/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Shaul K. Bar-Lev, 2023. "The Exponential Dispersion Model Generated by the Landau Distribution—A Comprehensive Review and Further Developments," Mathematics, MDPI, vol. 11(20), pages 1-23, October.
    2. Ricci, Lila & Martinez, Raul, 2008. "Adjusted R2-type measures for Tweedie models," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1650-1660, January.
    3. Philip Hougaard, 1995. "Nonlinear regression and curved exponential families. Improvement of the approximation to the asymptotic distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 42(1), pages 191-202, 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. DJOKOTO, Justice Gameli & OWUSU, Victor & AWUNYO-VITOR, Dadson, 2020. "Is Organic Agriculture More Scale Efficient Than Conventional Agriculture? The Case Of Cocoa Cultivation In Ghana," Review of Agricultural and Applied Economics (RAAE), Faculty of Economics and Management, Slovak Agricultural University in Nitra, vol. 23(2), October.
    2. Ricci, Lila, 2010. "Adjusted R-squared type measure for exponential dispersion models," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1365-1368, September.

    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:gam:jmathe:v:12:y:2024:i:13:p:2021-:d:1425352. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.