Skip to main content

Modelling of Insurance Claim Count with Hurdle Distribution for Panel Data

  • Chapter
  • First Online:
Advances in Mathematical and Statistical Modeling

Abstract

The aim of the paper is to propose a new model for panel data. In a recent paper, the authors showed that the hurdle model is an interesting alternative to Poisson and Negative Binomial for the analysis of the number of claims reported by an insured driver. We generalize the hurdle model to account for longitudinal data under the assumption that covariates are time independent. Predictive distributions are shown to be easily computed analytically, as well as future premiums that can be calculated using the classical credibility theory.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Boucher, J. P. and Denuit, M. (2006). Fixed versus random effects in Poisson regression models for claim counts: case study with motor insurance.Astin Bulletin, 36:285–301.

    Article  MathSciNet  Google Scholar 

  • Boucher, J. P., Denuit, M., and Guill’en, M. (2007). Risk classification for claim counts: a comparative analysis of various zero-inflated mixed Poisson and hurdle models.North American Actuarial Journal, in press.

    Google Scholar 

  • Bühlmann, H. (1967). Experience rating and credibility.Astin Bulletin, (4):199–207.

    Google Scholar 

  • Bühlmann, H. and Straub, E. (1970). Glaubwürdigkeit für Schadensätze.Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, 70:111.

    Google Scholar 

  • Dionne, G. and Vanasse, C. (1989). A generalization of automobile insurance rating models: the Negative Binomial distribution with regression component.Astin Bulletin, 19:199–212.

    Article  Google Scholar 

  • Grootendorst, P.V. (1995). A comparison of alternative models of prescription drug utilization.Health Economics, 4:183–198.

    Article  Google Scholar 

  • Gurmu, S. (1998). Generalized hurdle count data regression models.Economics Letters, 58:263–268.

    Article  MATH  Google Scholar 

  • Hachemeister, C.A. (1975). Credibility for regression models with applications to trend. InCredibility: Theory and Applications (Ed., P. M. Kahn), pp. 129–163, Academic Press, New York.

    Google Scholar 

  • Hausman, J.A., Hall, B.H., and Griliches, Z. (1984). Econometric models for count data with application to the patents-R and D relationship.Econometrica, 52:909–938.

    Article  Google Scholar 

  • Hsiao, C. (2003).Analysis of Panel Data. Cambridge University Press, Cambridge.

    Google Scholar 

  • Jewell, W.S. (1975). The use of collateral data in credibility theory: A hierarchical model.Giornale dell Istituto Italiano degli Attuari, 38:1–16.

    MATH  Google Scholar 

  • Johnson, N.L., Kotz, S., and Balakrishnan, N. (1996).Discrete Multivariate Distributions. Wiley, New York.

    Google Scholar 

  • Marshall, A.W. and Olkin, I. (1990). Multivariate distributions generated from mixtures of convolution and product families. InTopics in Statistical Dependence (Eds., H.W. Block, A.R. Sampson and T.H. Savits), 16:371–393, Lecture Notes-Monograph Series.

    Google Scholar 

  • Mullahy, J. (1986). MSpecification and testing in some modified count data models.Journal of Econometrics, 33:341–365.

    Article  MathSciNet  Google Scholar 

  • 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 

  • Mundlak, Y. (1978). On the pooling of time series and cross section data.Econometrica, 46:69–85.

    Article  MATH  MathSciNet  Google Scholar 

  • Pohlmeier, W. and Ulrich, V. (1995). An econometric model of the two-part decision making process in the demand for health care.Journal of Human Ressources, 30:339–361.

    Article  Google Scholar 

  • Santos Silva, J.M.C. (2003). A note on the estimation of mixture models under exogeneous sampling.Econometrics Journal, 6:46–52.

    Article  MATH  MathSciNet  Google Scholar 

  • Santos Silva, J.M.C. and Windmeijer, F. (2001). Two-part multiple spell models for health care demand.Journal of Econometrics, 104:67–89.

    Article  MATH  MathSciNet  Google Scholar 

  • Stoddart, G.L. and Barer, M.L. (1981). Analyses of the demand and utilization through episodes of medical care. InHealth, Economics and Health Economics (Eds.,van der Gaag, J. and Perlman, M.), Elsevier, Amsterdam.

    Google Scholar 

  • Vuong, Q.H. (1989). Likelihood ratio tests for model selection and non-nested hypotheses.Econometrica, 57:307–333.

    Article  MATH  MathSciNet  Google Scholar 

  • Winkelmann, R. (2000). Seemingly unrelated Negative Binomial distribution.Oxford Bulletin of Economics and Statistics, 62:553–560.

    Article  Google Scholar 

  • Winkelmann, R. (2003). Health care reform and the number of doctor visits—an econometric analysis.Journal of Applied Econometrics, 19:455–472.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Birkhäuser Boston

About this chapter

Cite this chapter

Boucher, JP., Denuit, M., Guillén, M. (2008). Modelling of Insurance Claim Count with Hurdle Distribution for Panel Data. In: Advances in Mathematical and Statistical Modeling. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4626-4_4

Download citation

Publish with us

Policies and ethics