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Mixed poisson regression models with varying dispersion arising from non-conjugate mixing distributions

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  • Tzougas, George
  • Hong, Natalia
  • Ho, Ryan

Abstract

In this article we present a class of mixed Poisson regression models with varying dispersion arising from non-conjugate to the Poisson mixing distributions for modelling overdispersed claim counts in non-life insurance. The proposed family of models combined with the adopted modelling framework can provide sufficient flexibility for dealing with different levels of overdispersion. For illustrative purposes, the Poisson-lognormal regression model with regression structures on both its mean and dispersion parameters is employed for modelling claim count data from a motor insurance portfolio. Maximum likelihood estimation is carried out via an expectation-maximization type algorithm, which is developed for the proposed family of models and is demonstrated to perform satisfactorily.

Suggested Citation

  • Tzougas, George & Hong, Natalia & Ho, Ryan, 2022. "Mixed poisson regression models with varying dispersion arising from non-conjugate mixing distributions," LSE Research Online Documents on Economics 113616, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:113616
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    File URL: http://eprints.lse.ac.uk/113616/
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    References listed on IDEAS

    as
    1. Perline, Richard, 1998. "Mixed Poisson distributions tail equivalent to their mixing distributions," Statistics & Probability Letters, Elsevier, vol. 38(3), pages 229-233, June.
    2. Tzougas, George, 2020. "EM estimation for the Poisson-Inverse Gamma regression model with varying dispersion: an application to insurance ratemaking," LSE Research Online Documents on Economics 106539, London School of Economics and Political Science, LSE Library.
    3. Rigby, R.A. & Stasinopoulos, D.M. & Akantziliotou, C., 2008. "A framework for modelling overdispersed count data, including the Poisson-shifted generalized inverse Gaussian distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 381-393, December.
    4. George Tzougas, 2020. "EM Estimation for the Poisson-Inverse Gamma Regression Model with Varying Dispersion: An Application to Insurance Ratemaking," Risks, MDPI, vol. 8(3), pages 1-23, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    claim frequency; EM algorithm; non-life insurance; regression structures on the mean and dispersion parameters;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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