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General Linear Model: An Effective Tool For Analysis Of Claim Severity In Motor Third Party Liability Insurance

Author

Listed:
  • Šoltés Erik

    (University of Economics in Bratislava, Faculty of Economic Informatics, Department of Statistics, Bratislava, Slovakia .)

  • Zelinová Silvia

    (University of Economics in Bratislava, Faculty of Economic Informatics, Department of Mathematics and Actuarial Science, Bratislava, Slovakia .)

  • Bilíková Mária

    (University of Economics in Bratislava, Faculty of Economic Informatics, Department of Mathematics and Actuarial Science, Bratislava, Slovakia .)

Abstract

The paper focuses on the analysis of claim severity in motor third party liability insurance under the general linear model. The general linear model combines the analyses of variance and regression and makes it possible to measure the influence of categorical factors as well as the numerical explanatory variables on the target variable. In the paper, simple, main and interaction effects of relevant factors have been quantified using estimated regression coefficients and least squares means. Statistical inferences about least-squares means are essential in creating tariff classes and uncovering the impact of categorical factors, so the authors used the LSMEANS, CONTRAST and ESTIMATE statements in the GLM procedure of the Statistical Analysis Software (SAS). The study was based on a set of anonymised data of an insurance company operating in Slovakia; however, because each insurance company has its own portfolio subject to changes over time, the results of this research will not apply to all insurance companies. In this context, the authors feel that what is most valuable in their work, is the demonstration of practical applications that could be used by actuaries to estimate both the claim severity and the claim frequency, and, consequently, to determine net premiums for motor insurance (regardless of whether for motor third party liability insurance or casco insurance

Suggested Citation

  • Šoltés Erik & Zelinová Silvia & Bilíková Mária, 2019. "General Linear Model: An Effective Tool For Analysis Of Claim Severity In Motor Third Party Liability Insurance," Statistics in Transition New Series, Polish Statistical Association, vol. 20(4), pages 13-31, December.
    • Handle: RePEc:vrs:stintr:v:20:y:2019:i:4:p:13-31:n:4
    DOI: 10.21307/stattrans-2019-032
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    References listed on IDEAS

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    1. Lenth, Russell V., 2016. "Least-Squares Means: The R Package lsmeans," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i01).
    2. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149.
    3. James M. Graham, 2008. "The General Linear Model as Structural Equation Modeling," Journal of Educational and Behavioral Statistics, , vol. 33(4), pages 485-506, December.
    4. Zhengmin Duan & Yonglian Chang & Qi Wang & Tianyao Chen & Qing Zhao, 2018. "A Logistic Regression Based Auto Insurance Rate-Making Model Designed for the Insurance Rate Reform," IJFS, MDPI, vol. 6(1), pages 1-16, February.
    5. Shi, Peng & Feng, Xiaoping & Ivantsova, Anastasia, 2015. "Dependent frequency–severity modeling of insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 417-428.
    6. Edward W. Frees & Gee Lee & Lu Yang, 2016. "Multivariate Frequency-Severity Regression Models in Insurance," Risks, MDPI, vol. 4(1), pages 1-36, February.
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