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A Longitudinal Analysis of the Impact of Distance Driven on the Probability of Car Accidents

Author

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  • Jean-Philippe Boucher

    (Département de Mathématiques, Université du Québec à Montréal (UQAM), Montréal, QC H3C 3P8, Canada)

  • Roxane Turcotte

    (Département de Mathématiques, Université du Québec à Montréal (UQAM), Montréal, QC H3C 3P8, Canada)

Abstract

Using telematics data, we study the relationship between claim frequency and distance driven through different models by observing smooth functions. We used Generalized Additive Models (GAM) for a Poisson distribution, and Generalized Additive Models for Location, Scale, and Shape (GAMLSS) that we generalize for panel count data. To correctly observe the relationship between distance driven and claim frequency, we show that a Poisson distribution with fixed effects should be used because it removes residual heterogeneity that was incorrectly captured by previous models based on GAM and GAMLSS theory. We show that an approximately linear relationship between distance driven and claim frequency can be derived. We argue that this approach can be used to compute the premium surcharge for additional kilometers the insured wants to drive, or as the basis to construct Pay-as-you-drive (PAYD) insurance for self-service vehicles. All models are illustrated using data from a major Canadian insurance company.

Suggested Citation

  • Jean-Philippe Boucher & Roxane Turcotte, 2020. "A Longitudinal Analysis of the Impact of Distance Driven on the Probability of Car Accidents," Risks, MDPI, vol. 8(3), pages 1-19, September.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:3:p:91-:d:407128
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    References listed on IDEAS

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    1. Roel Verbelen & Katrien Antonio & Gerda Claeskens, 2018. "Unravelling the predictive power of telematics data in car insurance pricing," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1275-1304, November.
    2. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273.
    3. 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).
    4. Boucher, Jean-Philippe & Denuit, Michel, 2006. "Fixed versus Random Effects in Poisson Regression Models for Claim Counts: A Case Study with Motor Insurance," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 285-301, May.
    5. 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.
    6. Mercedes Ayuso & Montserrat Guillen & Jens Perch Nielsen, 2019. "Improving automobile insurance ratemaking using telematics: incorporating mileage and driver behaviour data," Transportation, Springer, vol. 46(3), pages 735-752, June.
    7. Lemaire, Jean & Park, Sojung Carol & Wang, Kili C., 2016. "The Use Of Annual Mileage As A Rating Variable," ASTIN Bulletin, Cambridge University Press, vol. 46(1), pages 39-69, January.
    8. Ma, Yu-Luen & Zhu, Xiaoyu & Hu, Xianbiao & Chiu, Yi-Chang, 2018. "The use of context-sensitive insurance telematics data in auto insurance rate making," Transportation Research Part A: Policy and Practice, Elsevier, vol. 113(C), pages 243-258.
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    Cited by:

    1. Montserrat Guillen & Jens Perch Nielsen & Ana M. Pérez‐Marín, 2021. "Near‐miss telematics in motor insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(3), pages 569-589, September.
    2. Francis Duval & Jean‐Philippe Boucher & Mathieu Pigeon, 2023. "Enhancing claim classification with feature extraction from anomaly‐detection‐derived routine and peculiarity profiles," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 90(2), pages 421-458, June.
    3. Shengkun Xie & Kun Shi, 2023. "Generalised Additive Modelling of Auto Insurance Data with Territory Design: A Rate Regulation Perspective," Mathematics, MDPI, vol. 11(2), pages 1-24, January.
    4. Jonas Šiaulys & Rokas Puišys, 2022. "Survival with Random Effect," Mathematics, MDPI, vol. 10(7), pages 1-17, March.
    5. Jan Reig Torra & Montserrat Guillen & Ana M. Pérez-Marín & Lorena Rey Gámez & Giselle Aguer, 2023. "Weather Conditions and Telematics Panel Data in Monthly Motor Insurance Claim Frequency Models," Risks, MDPI, vol. 11(3), pages 1-18, March.

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