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EM Estimation for the Bivariate Mixed Exponential Regression Model

Author

Listed:
  • Zezhun Chen

    (Department of Statistics, London School of Economics and Political Science, London WC2A 2AE, UK)

  • Angelos Dassios

    (Department of Statistics, London School of Economics and Political Science, London WC2A 2AE, UK)

  • George Tzougas

    (Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH14 4AS, UK)

Abstract

In this paper, we present a new family of bivariate mixed exponential regression models for taking into account the positive correlation between the cost of claims from motor third party liability bodily injury and property damage in a versatile manner. Furthermore, we demonstrate how maximum likelihood estimation of the model parameters can be achieved via a novel Expectation-Maximization algorithm. The implementation of two members of this family, namely the bivariate Pareto or, Exponential-Inverse Gamma, and bivariate Exponential-Inverse Gaussian regression models is illustrated by a real data application which involves fitting motor insurance data from a European motor insurance company.

Suggested Citation

  • Zezhun Chen & Angelos Dassios & George Tzougas, 2022. "EM Estimation for the Bivariate Mixed Exponential Regression Model," Risks, MDPI, vol. 10(5), pages 1-13, May.
    • Handle: RePEc:gam:jrisks:v:10:y:2022:i:5:p:105-:d:817586
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    References listed on IDEAS

    as
    1. Denuit, Michel & Guillen, Montserrat & Trufin, Julien, 2019. "Multivariate credibility modelling for usage-based motor insurance pricing with behavioural data," LIDAM Reprints ISBA 2019039, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Denuit, Michel & Guillen, Montserrat & Trufin, Julien, 2019. "Multivariate credibility modelling for usage-based motor insurance pricing with behavioural data," Annals of Actuarial Science, Cambridge University Press, vol. 13(2), pages 378-399, September.
    3. Abu Bakar, S.A. & Hamzah, N.A. & Maghsoudi, M. & Nadarajah, S., 2015. "Modeling loss data using composite models," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 146-154.
    4. Bermúdez, Lluís & Karlis, Dimitris, 2012. "A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3988-3999.
    5. Abdallah, Anas & Boucher, Jean-Philippe & Cossette, Hélène, 2016. "Sarmanov family of multivariate distributions for bivariate dynamic claim counts model," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 120-133.
    6. Baumgartner, Carolin & Gruber, Lutz F. & Czado, Claudia, 2015. "Bayesian total loss estimation using shared random effects," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 194-201.
    Full references (including those not matched with items on IDEAS)

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