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Count copula regression model using generalized beta distribution of the second kind

Author

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  • Safari-Katesari Hadi

    (Department of Mathematics, Southern Illinois University, Carbondale, IL, 62901-4408, USA .)

  • Zaroudi Samira

    (Department of Mathematics, Southern Illinois University, Carbondale, IL, 62901-4408, USA .)

Abstract

Modelling claims severity for obtaining insurance premium is one of the major concerns of the insurance industry. There is a considerable amount of literature on the actuarial application of the copula model to calculate the pure premium. In this paper, we model claims severity for computing the pure premium in the collision market by means of the count copula model. Moreover, we apply a regression model using a generalized beta distribution of the second kind (GB2) to compute the premium for an average claim and the conditional computation for all coverage levels. Like many other researchers, we assume that the number of accidents is independent from the size of claims. For real data application, we use a portfolio of a major automobile insurer in Iran in 2007-2008, with a subsample of 59,547 policies available in their portfolio. We then proceed to compare the estimated premiums with the real premiums. The results demonstrate that there is strong positive dependency between the real premium and the estimated one.

Suggested Citation

  • Safari-Katesari Hadi & Zaroudi Samira, 2020. "Count copula regression model using generalized beta distribution of the second kind," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 1-12, June.
    • Handle: RePEc:vrs:stintr:v:21:y:2020:i:2:p:1-12:n:2
    DOI: 10.21307/stattrans-2020-011
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    References listed on IDEAS

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    1. Sun, Jiafeng & Frees, Edward W. & Rosenberg, Marjorie A., 2008. "Heavy-tailed longitudinal data modeling using copulas," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 817-830, April.
    2. Dickson,David C. M., 2016. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9781107154605.
    3. Shi, Peng & Valdez, Emiliano A., 2011. "A copula approach to test asymmetric information with applications to predictive modeling," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 226-239, September.
    4. McDonald, James B & Butler, Richard J, 1987. "Some Generalized Mixture Distributions with an Application to Unemployment Duration," The Review of Economics and Statistics, MIT Press, vol. 69(2), pages 232-240, May.
    5. Peng Shi & Lu Yang, 2018. "Pair Copula Constructions for Insurance Experience Rating," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 122-133, January.
    6. Frees, Edward W. & Valdez, Emiliano A., 2008. "Hierarchical Insurance Claims Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1457-1469.
    7. Frees, Edward W. & Jin, Xiaoli & Lin, Xiao, 2013. "Actuarial Applications of Multivariate Two-Part Regression Models," Annals of Actuarial Science, Cambridge University Press, vol. 7(2), pages 258-287, September.
    8. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
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