Advertisement

Study on the transform method of estimating discrete frequency from continuous variable: ratemaking for car repair insurance based on SAS system coding

  • Yuantao Xie
  • Huijuan Lv
  • Xiaoke Sun
  • Yu Mao
  • Juan Yang
Article
  • 18 Downloads

Abstract

Some discrete variable such as frequency cannot be estimated when a limited sample is drawn from the population which is not sufficient enough to represent the whole population. But the procedure records data from finite samples that can be converted to frequency estimates through computer intensive calculations. The aim of this paper is to develop an Accelerated Failure Time model for the continuous variables such as survival times or the first breakdown mileage by embedding Weibull distribution into a GLMs structure. Then we can derive the hazard ratio function and transform the continuous variable modeling into discrete variable inference. A numerical illustration based on a data derived from a Chinese auto dealer is performed with the statistical software SAS. The rate was made for different types of vehicles and their different parts based on the minimum repairing and the purchase of car repairing insurance for a certain time.

Keywords

Generalized linear models Hazard ratio function Frequency inference Accelerated failure time 

Notes

Acknowledgements

The paper was financially supported by the National Social Science Foundation of China “Individual Risk Assessment under the background of Risk Information Share” under Grant No. 71303045 and “the Fundamental Research Funds for the Central Universities” in UIBE (CXTD9-04), and the People’s Insurance Company of China Disaster Research Fund.

References

  1. 1.
    Antonio, K., Valdez, E.A.: Statistical concepts of a priori, and a posteriori, risk classification in insurance. AStA Adv. Stat. Anal. 96(2), 187–224 (2012)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Xie, Y.T., Yang, J.: Generalized linear mixed models based on generalized gamma distribution. Stat. Res. 27(10), 75–80 (2010). In Chinese Google Scholar
  3. 3.
    Xie, Y.T., Wang, W., Tan, Y.P., Yang, J.: Credibility analysis based on generalized linear mixed models. Stat. Inf. Forum 27(10), 3–8 (2012). In Chinese Google Scholar
  4. 4.
    Bermúdez, L., Karlis, D.: A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking. Comput. Stat. Data Anal. 56(12), 3988–3999 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bermúdez, L., Karlis, D.: A posteriori ratemaking using bivariate Poisson models. Scand. Actuar. J. 1–11 (2017)Google Scholar
  6. 6.
    Frees, E.W.: Regression Modeling with Actuarial and Financial Applications. Cambridge University Press, Cambridge (2010)zbMATHGoogle Scholar
  7. 7.
    Frees, E.W.J., Derrig, R.A., Meyers, G.: Predictive Modeling Applications in Actuarial Science: Predictive Modeling Techniques, vol. i. Cambridge Books, Cambridge (2014)CrossRefGoogle Scholar
  8. 8.
    Xie, Y.T., Mao, Y.: Hierarchical Bayesian models with gamma random effect in rating for vehicle extended warranty contract. Stat. Inf. Forum 33(1), 3–9 (2017). In Chinese Google Scholar
  9. 9.
    Klein, N., Denuit, M., Lang, S., Kneib, T.: Nonlife ratemaking and risk management with Bayesian generalized additive models for location, scale, and shape. Insur. Math. Econ. 55(1), 225–249 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Xie, Y.T., Li, Z.X.: Extension of Bonus-Malus factor based on joint pricing models. Stat. Inf. Forum 30(6), 33–39 (2015). In Chinese Google Scholar
  11. 11.
    Fischer, M.M., Wang, J.: Spatial data analysis. Annu. Rev. Public Health 37(1), 47 (2016)CrossRefGoogle Scholar
  12. 12.
    Balakrishnan, N., Kateri, M.: On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data. Stat. Probab. Lett. 78(17), 2971–2975 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Scitovski, R.: On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution. Comput. Stat. Data Anal. 52(9), 4502–4511 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Kantar, Y.M., Şenoğlu, B.: A comparative study for the location and scale parameters of the Weibull distribution with given shape parameter. Comput. Geosci. 34(12), 1900–1909 (2008)CrossRefGoogle Scholar
  15. 15.
    Dana, A.: Rate making for car repair insurance. Master Degree Thesis, University of International Business and Economics (2017)Google Scholar
  16. 16.
    Bebbington, M., Lai, C.D., Zitikis, R.: Reduction in mean residual life in the presence of a constant competing risk. Appl. Stoch. Models Bus. Ind. 24, 51–63 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Bebbington, M., Lai, C.D., Zitikis, R.: Estimating the turning point of a bathtub-shaped failure distribution. J. Stat. Plan. Inference 138, 1157–1166 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Bousquet, N., Bertholon, H., Celeux, G.: An alternative competing risk model to the Weibull distribution for modeling aging in lifetime data analysis. Lifetime Data Anal. 12, 481–504 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Ohlsson, Esbjörn, Johansson, Björn: Non-Life Insurance Pricing with Generalized Linear Models. Springer, Berlin (2010)CrossRefzbMATHGoogle Scholar
  20. 20.
    Gourieroux, C., Jasiak, J.: Heterogeneous in ar(1) model with application to car insurance. Insur. Math. Econ. 34(2), 177–192 (2004)CrossRefzbMATHGoogle Scholar
  21. 21.
    Pitrebois, S., Walhin, J.-F., Denuit, M., Mar´echal, X.: Actuarial Modeling of Claim Counts. Risk Classification, Credibility and Bonus-Malus Systems, pp. 2–14. Wiley, New York (2007)Google Scholar
  22. 22.
    Xie, Y.T., Li, Z.X., Parsa, R.: Extension and application of credibility models in predicting claim frequency. Math. Probl. Eng. (2018).  https://doi.org/10.1155/2018/6250686 MathSciNetGoogle Scholar
  23. 23.
    Li, H., Xie, Y., Yang, J.: Medical assessment based on generalized gamma distribution generalized linear mixed models. Stud. Ethno-Med. 11(2), 146–157 (2017).  https://doi.org/10.1080/09735070.2017.1316948 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Insurance and EconomicsUniversity of International Business and EconomicsBeijingChina
  2. 2.Institute of Comprehensive DevelopmentChinese Academy of Science and Technology for DevelopmentBeijingChina

Personalised recommendations