IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v33y2006i9p909-923.html
   My bibliography  Save this article

Bivariate Negative Binomial Generalized Linear Models for Environmental Count Data

Author

Listed:
  • Masakazu Iwasaki
  • Hiroe Tsubaki

Abstract

We propose a new bivariate negative binomial model with constant correlation structure, which was derived from a contagious bivariate distribution of two independent Poisson mass functions, by mixing the proposed bivariate gamma type density with constantly correlated covariance structure (Iwasaki & Tsubaki, 2005), which satisfies the integrability condition of McCullagh & Nelder (1989, p. 334). The proposed bivariate gamma type density comes from a natural exponential family. Joe (1997) points out the necessity of a multivariate gamma distribution to derive a multivariate distribution with negative binomial margins, and the luck of a convenient form of multivariate gamma distribution to get a model with greater flexibility in a dependent structure with indices of dispersion. In this paper we first derive a new bivariate negative binomial distribution as well as the first two cumulants, and, secondly, formulate bivariate generalized linear models with a constantly correlated negative binomial covariance structure in addition to the moment estimator of the components of the matrix. We finally fit the bivariate negative binomial models to two correlated environmental data sets.

Suggested Citation

  • Masakazu Iwasaki & Hiroe Tsubaki, 2006. "Bivariate Negative Binomial Generalized Linear Models for Environmental Count Data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(9), pages 909-923.
  • Handle: RePEc:taf:japsta:v:33:y:2006:i:9:p:909-923
    DOI: 10.1080/02664760600744157
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760600744157
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/02664760600744157?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. Masakazu Iwasaki & Hiroe Tsubaki, 2005. "A new bivariate distribution in natural exponential family," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(3), pages 323-336, 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. Nguyen, Truc T. & Chen, John T., 2009. "A connection between the double gamma model and Laplace sample mean," Statistics & Probability Letters, Elsevier, vol. 79(10), pages 1305-1310, May.
    2. Eufr�sio de A. Lima Neto & Ulisses U. dos Anjos, 2015. "Regression model for interval-valued variables based on copulas," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(9), pages 2010-2029, 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:taf:japsta:v:33:y:2006:i:9:p:909-923. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.