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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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)
Xie, Y.T., Yang, J.: Generalized linear mixed models based on generalized gamma distribution. Stat. Res. 27(10), 75–80 (2010). In Chinese
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
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)
Bermúdez, L., Karlis, D.: A posteriori ratemaking using bivariate Poisson models. Scand. Actuar. J. 1–11 (2017)
Frees, E.W.: Regression Modeling with Actuarial and Financial Applications. Cambridge University Press, Cambridge (2010)
Frees, E.W.J., Derrig, R.A., Meyers, G.: Predictive Modeling Applications in Actuarial Science: Predictive Modeling Techniques, vol. i. Cambridge Books, Cambridge (2014)
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
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)
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
Fischer, M.M., Wang, J.: Spatial data analysis. Annu. Rev. Public Health 37(1), 47 (2016)
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)
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)
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)
Dana, A.: Rate making for car repair insurance. Master Degree Thesis, University of International Business and Economics (2017)
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)
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)
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)
Ohlsson, Esbjörn, Johansson, Björn: Non-Life Insurance Pricing with Generalized Linear Models. Springer, Berlin (2010)
Gourieroux, C., Jasiak, J.: Heterogeneous in ar(1) model with application to car insurance. Insur. Math. Econ. 34(2), 177–192 (2004)
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)
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
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
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xie, Y., Lv, H., Sun, X. et al. Study on the transform method of estimating discrete frequency from continuous variable: ratemaking for car repair insurance based on SAS system coding. Cluster Comput 22 (Suppl 6), 15493–15503 (2019). https://doi.org/10.1007/s10586-018-2656-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10586-018-2656-3