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A survey on models for panel count data with applications to insurance

Una revisión de los modelos para paneles de datos de enumeración con aplicaciones a seguros

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Abstract

In insurance the expected number of claims per year given the observed characteristics of the covered risk is the basis for setting the price of a policy. Companies accumulate information of clients along several years, but in practice the panel data structure is not exploited. We review panel count data models that are useful in this context and present a new alternative based on the generalization of a compound sum.

Resumen

En seguros, el número esperado de reclamaciones por año dadas las características del riesgo cubierto es la base para establecer el precio de una póliza. Las compañías de seguros acumulan informaci ón de clientes a lo largo de varias anualidades, pero en la práctica la estructura de panel de los datos no se explota. Revisamos los modelos para paneles de datos de enumeración que son útiles en este contexto y presentamos una nueva alternativa basada en la generalización de una suma compuesta.

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References

  1. Boucher, J.-P. andDenuit, M., (2006). Fixed versus Random Effects in Poisson Regression Models for Claim Counts: Case Study with Motor Insurance,ASTIN Bull.,36, 285–301.

    Article  MATH  MathSciNet  Google Scholar 

  2. Boucher, J.-P. andDenuit, M., (2007). Duration Dependence Models for Claim Counts,Deutsche Gesellschaft fur Versicherungsmathematik (German Actuarial Bulletin),28, 29–45.

    MATH  MathSciNet  Google Scholar 

  3. Boucher, J.-P., Denuit, M. andGuillén, M., (2007). Risk Classification for Claim Counts: A Comparative Analysis of Various Zero-Inflated Mixed Poisson and Hurdle Models,N. Am. Actuar. J.,11–4, 110–131.

    Google Scholar 

  4. Boucher, J.-P., Denuit, M. and Guillén, M., (2008). Correlated Random Effects for Hurdle Models Applied to Panel Data Count,Université du Québec à Montréal, working paper.

  5. Boucher, J.-P., Denuit, M. and Guillén, M., (2008). Modeling of Insurance Claim Count with Hurdle Distribution for Panel Data, inAdvances in mathematical and Statistical Modeling, Statistics for Industry and Technology (SIT), Birkhäuser Boston, Inc..

  6. Boucher, J.-P., Denuit, M. andGuillén, M., (2008). Models of Insurance Claim Counts with Time Dependence Based on Generalisation of Poisson and Negative Binomial Distributions,Variance,2(1), 135–162.

    Google Scholar 

  7. Boucher, J.-P., Denuit, M. and Guillén, M., (2008). Number of Accidents or Number of Claims? An Approach with Zero-inflated Poisson Models for Panel Data,Journal of Risk and Insurance, to appear.

  8. Boucher, J.-P. and Guillé N, M., (2008). A Semi-Nonparametric Approach to Model Panel Count Data,Université du Québec à Montréal, working paper.

  9. Bradlow, E., Fader, P., Adrian, M. andMcshane, B., (2008). Count Models Based on Weibull Interarrival Times,J. Bus. Econom. Statist.,26(3), 369–378.

    MathSciNet  Google Scholar 

  10. Cameron, A. C. andTrivedi, P. K., (1998).Regression Analysis of Count Data, New York, Cambridge University Press.

    MATH  Google Scholar 

  11. Cragg, J., (1971). Some statistical models for limited dependent variables with application to the demand for durable goods,Econometrica,39(5), 829–844.

    Article  MATH  Google Scholar 

  12. Denuit, M., Maré Chal, X., Pitrebois, S. andWalhin, J.-F., (2007).Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Scales, Wiley, New York.

    MATH  Google Scholar 

  13. Frees, E., V. R., Y. andYu, L., (2001). Case Studies Using Panel DataModels,N. Am. Actuar. J.,5(4), 24–42.

    MATH  MathSciNet  Google Scholar 

  14. Frees, E. W. andValdez, E. A., (2008). Hierarchical Insurance Claims Modeling,J. Amer. Statist. Assoc.,103, 484, 1457–1469.

    Article  Google Scholar 

  15. Gó Mez-Déniz, E., Sarabia, J. andCalderón Ojeda, E., (2008). Univariate and multivariate versions of the negative binomial-inverse Gaussian distributions with applications,Insurance Math. Econom.,42(1), 39–49.

    MathSciNet  Google Scholar 

  16. Golden, R., (2003). Discrepancy RiskModel Selection Test for Comparing PossiblyMisspecified or Nonnested Models,Psychometrika,68, 229–249.

    Article  MathSciNet  Google Scholar 

  17. Hausman, J., Hall, B. andGriliches, Z., (1984). Econometric Models for Count Data with Application to the Patents-R and D Relationship,Econometrica,52, 909–938.

    Article  Google Scholar 

  18. Hinde, J., (1982). Compound Poisson Regression Models, in R. Gilchrist, ed.,GLIM 82: Proceeding of the International Conference on Generalised Linear Models, New York, Springer-Verlag.

    Google Scholar 

  19. Holgate,, P., (1964). Estimation for the Bivariate Poisson distribution,Biometrika,51, 241–245.

    MATH  MathSciNet  Google Scholar 

  20. Hsiao, C., (2003).Analysis of Panel Data, Cambridge, Cambridge University Press, 2nd ed.

    Book  Google Scholar 

  21. Johnson, N., Kotz, S. andBalakrishnan, N., (1996).Discrete Multivariate Distributions, New York, Wiley, 2nd ed.

    Google Scholar 

  22. Lambert, D., (1992). Zero-Inflated Poisson Regression with an Application to Defects in Manufacturing,Technometrics,34, 1–14.

    Article  MATH  Google Scholar 

  23. Marshall, A. and Olkin, I., (1990). Multivariate Distributions Generated fromMixtures of Convolution and Product Families, inTopics in Statistical Dependence, H.W. Block, A. R. Sampson and T. H. Savits, eds. Lecture Notes-Monograph Series, Vol.16, 371–393.

  24. Molenberghs, G. and Verbeke, G., (2005).Models for Discrete Longitudinal Data, Springer.

  25. Mullahy, J., (1986). Specification and Testing in some Modified Count Data Models,J. Econometrics,33, 341–365.

    Article  MathSciNet  Google Scholar 

  26. Mullahy, J., (1997). Instrumental Variable Estimation of Count Data Models: Applications to Models of Cigarette Smoking Behavior,Review of Economics and Statistics,79, 586–593.

    Article  Google Scholar 

  27. Mundlak, Y., (1978). On the Pooling of Time Series and Cross Section Data,Econometrica,46, 69–85.

    Article  MATH  MathSciNet  Google Scholar 

  28. Pinquet, J., Guillén, M. andBolance, C., (2001). Allowance for the Age of Claims in Bonus-Malus Systems,ASTIN Bull.,31, 337–348.

    Article  MATH  MathSciNet  Google Scholar 

  29. Purcaru, O., Guillen, M. andDenuit, M., (2004). Linear Credibility Models Based on Time Series for Claim Counts,Belgian Actuarial Bulletin,4, 62–74.

    Google Scholar 

  30. Rivers, D. andVuong, Q., (2002). Model Selection Tests for Nonlinear Dynamic Models,Econom. J.,5, 1–39.

    Article  MATH  MathSciNet  Google Scholar 

  31. Santos Silva, J. andWindmeijer, F., (2001). Two-part Multiple Spell Models for Health Care Demand,J. Econometrics,104, 67–89.

    Article  MATH  MathSciNet  Google Scholar 

  32. Vuong, Q., (1989). Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses,Econometrica,57, 307–333.

    Article  MATH  MathSciNet  Google Scholar 

  33. Willmot, G., (1987). The Poisson-Inverse Gaussian Distribution as an Alternative to the Negative Binomial,Scand. Actuar. J.,87, 113–127.

    MathSciNet  Google Scholar 

  34. Winkelmann, R., (1995). Duration Dependence and Dispersion in Count Data Models,J. Bus. Econom. Statist.,13, 467–474.

    Article  MathSciNet  Google Scholar 

  35. Winkelmann, R., (2008).Econometric Analysis of Count Data, Springer-Verlag, Berlin, 5th ed.

    Google Scholar 

  36. Xu, S., Jones, R. andGrunwald, G., (2007). Analysis of Longitudinal Count Data with Serial Correlation,Biom. J.,49(3), 416–428.

    Article  MathSciNet  Google Scholar 

  37. Young, V. andDe Vylder, F., (2000). Credibility in Favor of Unlucky Insureds,N. Am. Actuar. J.,4, 107–113.

    MATH  MathSciNet  Google Scholar 

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Boucher, JP., Guillén, M. A survey on models for panel count data with applications to insurance. Rev. R. Acad. Cien. Serie A. Mat. 103, 277–294 (2009). https://doi.org/10.1007/BF03191908

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  • DOI: https://doi.org/10.1007/BF03191908

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