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The Modelling of Auto Insurance Claim-Frequency Counts by the Inverse Trinomial Distribution

Author

Listed:
  • Seng Huat Ong

    (Institute of Actuarial Science and Data Analytics, UCSI University, Kuala Lumpur 56000, Malaysia
    Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603, Malaysia)

  • Shin Zhu Sim

    (School of Mathematical Sciences, University of Nottingham Malaysia, Semenyih 43500, Malaysia)

  • Shuangzhe Liu

    (Faculty of Science and Technology, University of Canberra, Canberra 2600, Australia)

Abstract

In the transportation services industry, the proper assessment of insurance claim count distribution is an important step to determine insurance premiums based on policyholders’ risk profiles. Risk factors are identified through regression analysis. In this paper, the inverse trinomial distribution is proposed as a count data model for insurance claims characterised by having long tails and a high index of dispersion. Two regression models are developed to identify associated risk factors. Other popular models, such as the negative binomial and COM-Poisson, are fitted and compared to information criteria. The risk profiles of policyholders are determined based on the selected model. To illustrate the application of the inverse trinomial regression models, the ausprivautolong dataset of automobile claims in Australia has been fitted with identification of risk factors.

Suggested Citation

  • Seng Huat Ong & Shin Zhu Sim & Shuangzhe Liu, 2024. "The Modelling of Auto Insurance Claim-Frequency Counts by the Inverse Trinomial Distribution," JRFM, MDPI, vol. 18(1), pages 1-12, December.
    • Handle: RePEc:gam:jjrfmx:v:18:y:2024:i:1:p:7-:d:1554513
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    References listed on IDEAS

    as
    1. Kazuki Aoyama & Kunio Shimizu & S. Ong, 2008. "A first–passage time random walk distribution with five transition probabilities: a generalization of the shifted inverse trinomial," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(1), pages 1-20, March.
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