FREQUENTIST AND BAYESIAN ZERO-INFLATED REGRESSION MODELS ON INSURANCE CLAIM FREQUENCY: A COMPARISON STUDY USING MALAYSIA’S MOTOR INSURANCE DATA

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Razik Ridzuan Mohd Tajuddin
Noriszura Ismail

Abstract

A no-claim event is a common scenario in insurance and the abundance of no-claim events can be described adequately by zero-inflated models. The zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) regression models from frequentist and Bayesian approaches are considered for fitting to Malaysia’s motor insurance data. The results from the fittings are compared using mean absolute deviation and mean squared prediction error. The data is categorized into three claim types and the factors considered for regression modelling are coverage type, vehicle age, vehicle cubic capacity and vehicle make. The results from the fittings showed that the ZIP model from both approaches provide better fit than the ZINB model. Also, both ZIP and ZINB models from the Bayesian approach provide better fitting than the frequentist models. Therefore, Bayesian ZIP is the best model in explaining motor insurance claim frequency in Malaysia for all three claim types. From the best regression models, vehicle age, coverage type and vehicle make are the most influential factors in determining the frequency of claim for each claim type. Vehicle age and coverage type have positive effect on the frequency of claim whereas the vehicle make has negative effect on the frequency of claim.

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How to Cite
Tajuddin, R. R. M., & Ismail, N. (2022). FREQUENTIST AND BAYESIAN ZERO-INFLATED REGRESSION MODELS ON INSURANCE CLAIM FREQUENCY: A COMPARISON STUDY USING MALAYSIA’S MOTOR INSURANCE DATA. Malaysian Journal of Science, 41(2), 16–29. https://doi.org/10.22452/mjs.vol41no2.2
Section
Original Articles

References

Garrido, J., Genest, C. & Schulz, J. (2016). Generalized linear models for dependentfrequency and severity of insurance claims, Insurance: Mathematics and Economics 70: 205-215.

Ghosh, S.K., Mukhopadhyay, P. & Lu, J.C. (2006). Bayesian analysis of zero-inflatedregression models, Journal of Statistical Planning and Inference 136: 1360-1375.

Gilenko, E.V. & Miranova, E.A. (2017). Modern claim frequency and claim severity models: An application to the Russian motor own damage insurance market, Cogent Economics & Finance 5: 1311097.

Ismail, N. & 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, Spring.

Jackman, S., Tahk, A., Zeileis, A., Maimone, C., Fearon, J. & Meers, Z. (2017). Package ‘pscl’.

Liu, H. & Powers, D.A. (2012). Bayesian inference for zero-inflated Poisson regression models, Journal of Statistics: Advances in Theory and Applications 7: 155-188.

Puig, P. & Valero, J. (2006). Count data distributions: Some characterizations with applications, Journal of the American Statistical Association 101: 332-340.

Rodrigues, J. (2003). Bayesian analysis of zero-inflated distributions, Communication in Statistics – Theory and Methods 32: 281-289.

Roohi, S., Baneshi, M.R., Norrozi, A. Hajebi, A. & Bahrampour, A. (2016). Comparing Bayesian regression and classic zero-inflated negative binomial on size estimation of people who use alcohol, Journal of Biostatistics and Epidemiology 2: 173-179.

Su, Y.S. & Yajima, M. (2015). Package ‘R2jags’.

Tzougas, G., Vrontos, S.D. & Frangos, N.E. 2015. Risk classification for claim counts and losses using regression models for location, scale and shape, Variance 9: 140-157.

Wagh, Y.S. & Kamalja, K.K. (2017). Modeling auto insurance claims in Singapore, Sri Lankan Journal of Applied Statistics 18: 105-118.

Wagh, Y.S. & Kamalja, K.K. (2018). Zero-inflated models and estimation in zero-inflated Poisson distribution, Communications in Statistics – Simulation and Computation 47: 2248-2265.

Xie, F.C., Lin, J.G. & Wei, B.C. (2014). Bayesian zero-inflated generalized Poisson regression model: estimation and case influence diagnostic, Journal of Applied Statistics 41: 1382-1392.

Zamani, H. & Ismail, N. (2014). Functional form for the zero-inflated generalized Poisson regression model, Communications in Statistics – Theory and Methods 43: 515-529.