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Bayesian quantile regression model for claim count data

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  • Fuzi, Mohd Fadzli Mohd
  • Jemain, Abdul Aziz
  • Ismail, Noriszura

Abstract

Quantile regression model estimates the relationship between the quantile of a response distribution and the regression parameters, and has been developed for linear models with continuous responses. In this paper, we apply Bayesian quantile regression model for the Malaysian motor insurance claim count data to study the effects of change in the estimates of regression parameters (or the rating factors) on the magnitude of the response variable (or the claim count). We also compare the results of quantile regression models from the Bayesian and frequentist approaches and the results of mean regression models from the Poisson and negative binomial. Comparison from Poisson and Bayesian quantile regression models shows that the effects of vehicle year decrease as the quantile increases, suggesting that the rating factor has lower risk for higher claim counts. On the other hand, the effects of vehicle type increase as the quantile increases, indicating that the rating factor has higher risk for higher claim counts.

Suggested Citation

  • Fuzi, Mohd Fadzli Mohd & Jemain, Abdul Aziz & Ismail, Noriszura, 2016. "Bayesian quantile regression model for claim count data," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 124-137.
    • Handle: RePEc:eee:insuma:v:66:y:2016:i:c:p:124-137
    DOI: 10.1016/j.insmatheco.2015.11.004
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    1. Duncan Lee & Tereza Neocleous, 2010. "Bayesian quantile regression for count data with application to environmental epidemiology," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(5), pages 905-920, November.
    2. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    3. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149, September.
    4. Machado, Jose A.F. & Silva, J. M. C. Santos, 2005. "Quantiles for Counts," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1226-1237, December.
    5. Klein, Nadja & Denuit, Michel & Lang, Stefan & Kneib, Thomas, 2014. "Nonlife ratemaking and risk management with Bayesian generalized additive models for location, scale, and shape," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 225-249.
    6. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
    7. Kudryavtsev, Andrey A., 2009. "Using quantile regression for rate-making," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 296-304, October.
    8. Pitt, D. G. W., 2006. "Regression Quantile Analysis of Claim Termination Rates for Income Protection Insurance," Annals of Actuarial Science, Cambridge University Press, vol. 1(2), pages 345-357, September.
    9. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    10. Rousseeuw, P. & Daniels, B. & Leroy, A., 1984. "Applying robust regression to insurance," Insurance: Mathematics and Economics, Elsevier, vol. 3(1), pages 67-72, January.
    11. Portnoy, Esther, 1997. "Regression-quantile graduation of Australian life tables, 1946-1992," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 163-172, November.
    12. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    13. Klein, Nadja & Denuit, Michel & Lang, Stefan & Kneib, Thomas, 2014. "Nonlife ratemaking and risk management with Bayesian generalized additive models for location, scale, and shape," LIDAM Reprints ISBA 2014006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
    15. Hossein Zamani & Noriszura Ismail, 2013. "Score test for testing zero-inflated Poisson regression against zero-inflated generalized Poisson alternatives," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(9), pages 2056-2068, September.
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    3. Chawarat Rotejanaprasert & Andrew B. Lawson, 2018. "A Bayesian Quantile Modeling for Spatiotemporal Relative Risk: An Application to Adverse Risk Detection of Respiratory Diseases in South Carolina, USA," IJERPH, MDPI, vol. 15(9), pages 1-15, September.
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    7. Ganguly, Boudhayan & Sengupta, Pooja & Biswas, Baidyanath, 2024. "What are the significant determinants of helpfulness of online review? An exploration across product-types," Journal of Retailing and Consumer Services, Elsevier, vol. 78(C).

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