Abstracts
Abstract
The main objective of this paper is to model automobile claim frequency by using standard count regression and zero-inflated regression models. The use of the latter model is mainly motivated by its ability to handle the over dispersion and zero-inflation phenomenon. The sample data consist of claims data obtained from one randomly selected automobile insurance company in Tunisia for a single year, 2009, containing beginning drivers and drivers who have had a license for less than three years. Our estimation results show that many exogenous variables can explain the frequency of claims; they are not taken into account in calculating the basic insurance premium. Moreover, the ZI binomial negative regression outperforms the standard count models and the ZI Poisson model in handling zero-inflated and additional over dispersed claim count data.
Keywords:
- Claim frequency,
- over dispersion,
- zero inflated,
- Poisson,
- negative binomial
Download the article in PDF to read it.
Download
Appendices
Bibliography
- Benlagha, N., Charfeddine, L. and Karaa, I., (2012), Modelling claim occurrence in car insurance implementation on Tunisian data, Asian-African Journal of Economics and Econometrics, 12(2), 395-406.
- Benlagha, N. and Karaa, I., (2017), Evidence of adverse selection in automobile insurance market: A seemingly unrelated probit modelling, Cogent Economics and Finance, 5(1), 1330303.
- Boucher, J.P., Denuit, M. and Guillén, M., (2009), Number of claims or number of claims? An approach with zero-inflated Poisson models for panel data, The Journal of Risk and Insurance, 76,821-846.
- Boucher, J.P. and Guillén, M., (2011), A semi-non parametric approach to model panel count data, Communications in Statistics- Theory and Methods, 40, 622-634.
- Cameron, C. and Trivedi, P.K., (2015), Count panel data, Baltagi B.H.,The oxford handbook of Panel data, Oxford University Press USA, 233-256.
- Denuit, M.X., Marechal, S. Pitrebois, and Walhin JF., (2007), Actuarial modeling of claim counts: risk classification, credibility and bonus-malus systems, Wiley, New York.
- FTUSA, Fédération Tunisienne des Sociétés d’Assurance, (2013), Annual Report, December, Tunisia.
- Greene, W. H. (1994), Accounting for excess zeros and sample selection in Poisson and negative binomial regression models. Working paper, Stern School of Business, NYU EC-94-10.
- Hilbe, J.M. (2014), Modeling count data, Cambridge University Press.
- Karaa, I., and Benlagha, N. (2015), Testing for asymmetric information in Tunisian automobile insurance market, Mediterranean Journal of Social Sciences, 6, 455-464.
- Lambert, D. (1992), Zero-inflated Poisson regressions, with an application to defects in manufacturing, Technometrics, 34, 1-14.
- Lawless, J.F. (1987), Negative binomial and mixed Poisson regression, Canadian Journal of Statistics, 15(3), 209-225.
- Melgar, M. C., Ordaz Sanz, J.A. and Guerrero, M., (2005), Diverses alternatives pour déterminer les facteurs significatifs de la fréquence d’accidents dans l’assurance automobile, Insurance and Risk Management, 73(1), 31-54.
- Melgar, M. C., Ordaz Sanz, J.A. and Guerrero, M., (2006), Une étude économétrique du nombre d’accidents dans le secteur de l’assurance automobile, Brussels Economic Review, 49(2), 169-183.
- Mouatassim, Y., and Ezzahid, E., (2012), Poisson regression and zero- inflated Poisson regression: application to private health insurance data, European Actuarial Journal, 2, 187-204.
- Mouatassim, Y., Ezzahid E. and Belasri, Y. (2012), Operational Value-at-risk in case of zero-inflated frequency, International Journal of Economic and Finance, 4(6), 70-77.
- Stram, D.O., and Lee, J.W. (1994), Variance components testing in the longitudinal mixed effects model, Biometrics, 50, 1171-1177.
- Stram, D.O., and Lee, J.W. (1995), Correction to “Variance components testing in the longitudinal mixed effects model”, Biometrics, 51, 1196.
- Vasechko O.A., Grun-Rehomme M., and Benlagha N. (2009), Modélisation de la fréquence des sinistres en assurance automobile, Bulletin Français d’actuariat, 9(18), 41-63.
- Vuong, Q.H., (1989), Likelihood ratio tests for model selection and non-nested hypotheses, Econometrica, 57 (2), 307–333.
- Washington, S., karlaftis, M.G., and Mannering, F.L., (2003), Statistical and economic methods for transportation data analysis, Chapman and Hall/CRC Press.
- Yang, Z., Hardin, J. W., Addy, C. L. and Vuong, Q. H. (2007), Testing approaches for over dispersion in Poisson regression versus the generalized Poisson model, Biometrical Journal, 49, 565-584.
- Yau, K. K., Wang, K. and Lee, A. H. (2003), Zero-inflated negative binomial mixed regression modeling of over-dispersed count data with extra zeros, Biometrical Journal, 45, 437-452.
- Yip, K.C.H., and Yau, K.K.W. (2005), On modeling claim frequency data in general insurance with extra zeros, Insurance: Mathematics and Economic, 36, 153-163.
- Ismail, N., and Zamani H., (2013), Estimation of claim count data using negative binomial, generalized Poisson, zero-inflated negative binomial and zero-inflated generalized Poisson regression models, Casualty Actuarial Society E-Forum.
- Zhao, X., and Zhou, X., (2012), Copula models for insurance claim numbers with excess zeros and time-dependence, Insurance: Mathematics and Economics, 50, 191-199.