FREQUENTIST AND BAYESIAN ZERO-INFLATED REGRESSION MODELS ON INSURANCE CLAIM FREQUENCY: A COMPARISON STUDY USING MALAYSIA’S MOTOR INSURANCE DATA
Article Sidebar
Main Article Content
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.
Downloads
Article Details
Transfer of Copyrights
- In the event of publication of the manuscript entitled [INSERT MANUSCRIPT TITLE AND REF NO.] in the Malaysian Journal of Science, I hereby transfer copyrights of the manuscript title, abstract and contents to the Malaysian Journal of Science and the Faculty of Science, University of Malaya (as the publisher) for the full legal term of copyright and any renewals thereof throughout the world in any format, and any media for communication.
Conditions of Publication
- I hereby state that this manuscript to be published is an original work, unpublished in any form prior and I have obtained the necessary permission for the reproduction (or am the owner) of any images, illustrations, tables, charts, figures, maps, photographs and other visual materials of whom the copyrights is owned by a third party.
- This manuscript contains no statements that are contradictory to the relevant local and international laws or that infringes on the rights of others.
- I agree to indemnify the Malaysian Journal of Science and the Faculty of Science, University of Malaya (as the publisher) in the event of any claims that arise in regards to the above conditions and assume full liability on the published manuscript.
Reviewer’s Responsibilities
- Reviewers must treat the manuscripts received for reviewing process as confidential. It must not be shown or discussed with others without the authorization from the editor of MJS.
- Reviewers assigned must not have conflicts of interest with respect to the original work, the authors of the article or the research funding.
- Reviewers should judge or evaluate the manuscripts objective as possible. The feedback from the reviewers should be express clearly with supporting arguments.
- If the assigned reviewer considers themselves not able to complete the review of the manuscript, they must communicate with the editor, so that the manuscript could be sent to another suitable reviewer.
Copyright: Rights of the Author(s)
- Effective 2007, it will become the policy of the Malaysian Journal of Science (published by the Faculty of Science, University of Malaya) to obtain copyrights of all manuscripts published. This is to facilitate:
(a) Protection against copyright infringement of the manuscript through copyright breaches or piracy.
(b) Timely handling of reproduction requests from authorized third parties that are addressed directly to the Faculty of Science, University of Malaya. - As the author, you may publish the fore-mentioned manuscript, whole or any part thereof, provided acknowledgement regarding copyright notice and reference to first publication in the Malaysian Journal of Science and Faculty of Science, University of Malaya (as the publishers) are given.
You may produce copies of your manuscript, whole or any part thereof, for teaching purposes or to be provided, on individual basis, to fellow researchers. - You may include the fore-mentioned manuscript, whole or any part thereof, electronically on a secure network at your affiliated institution, provided acknowledgement regarding copyright notice and reference to first publication in the Malaysian Journal of Science and Faculty of Science, University of Malaya (as the publishers) are given.
- You may include the fore-mentioned manuscript, whole or any part thereof, on the World Wide Web, provided acknowledgement regarding copyright notice and reference to first publication in the Malaysian Journal of Science and Faculty of Science, University of Malaya (as the publishers) are given.
- In the event that your manuscript, whole or any part thereof, has been requested to be reproduced, for any purpose or in any form approved by the Malaysian Journal of Science and Faculty of Science, University of Malaya (as the publishers), you will be informed. It is requested that any changes to your contact details (especially e-mail addresses) are made known.
Copyright: Role and responsibility of the Author(s)
- In the event of the manuscript to be published in the Malaysian Journal of Science contains materials copyrighted to others prior, it is the responsibility of current author(s) to obtain written permission from the copyright owner or owners.
- This written permission should be submitted with the proof-copy of the manuscript to be published in the Malaysian Journal of Science
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.