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A bivariate Sarmanov regression model for count data with generalised Poisson marginals

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  • Vera Hofer
  • Johannes Leitner

Abstract

We present a bivariate regression model for count data that allows for positive as well as negative correlation of the response variables. The covariance structure is based on the Sarmanov distribution and consists of a product of generalised Poisson marginals and a factor that depends on particular functions of the response variables. The closed form of the probability function is derived by means of the moment-generating function. The model is applied to a large real dataset on health care demand. Its performance is compared with alternative models presented in the literature. We find that our model is significantly better than or at least equivalent to the benchmark models. It gives insights into influences on the variance of the response variables.

Suggested Citation

  • Vera Hofer & Johannes Leitner, 2012. "A bivariate Sarmanov regression model for count data with generalised Poisson marginals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(12), pages 2599-2617, August.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:12:p:2599-2617
    DOI: 10.1080/02664763.2012.724661
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    Cited by:

    1. Vernic, Raluca, 2018. "On the evaluation of some multivariate compound distributions with Sarmanov’s counting distribution," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 184-193.
    2. Najla Qarmalah & Abdulhamid A. Alzaid, 2023. "Zero-Dependent Bivariate Poisson Distribution with Applications," Mathematics, MDPI, vol. 11(5), pages 1-16, February.
    3. Luiza S. C. Piancastelli & Wagner Barreto‐Souza & Hernando Ombao, 2023. "Flexible bivariate INGARCH process with a broad range of contemporaneous correlation," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(2), pages 206-222, March.
    4. Lluís Bermúdez & Dimitris Karlis, 2021. "Multivariate INAR(1) Regression Models Based on the Sarmanov Distribution," Mathematics, MDPI, vol. 9(5), pages 1-13, March.

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