2013 | 1(39) | 144-151
Article title

Zero-inflated claim count modeling and testing – a case study

Title variants
Languages of publication
In this paper the application of parametric count data models in claim counts modeling is investigated. Insurance portfolios have a very specific characteristic, i.e. for many policies there are no claims observed in the insurance history for a given period of time. As the zero-inflation and over-dispersion effects are a common situation in insurance portfolios, three models: zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB) and zeroinflated generalized Poisson regression (ZIGP) are tested against the classic Poisson model. The 4-step procedure for modeling zero-inflation effect is proposed. This procedure is applied in the case study. For all calculations the R CRAN software was used.
claim counts   ZIP   ZINB   ZIGP  
Physical description
  • Uniwersytet Ekonomiczny w Katowicach
  • De Jong P., Heller G.Z. (2008), Generalized Linear Models for Insurance Data, Cambridge University Press, Cambridge.
  • Denuit M., Marechal X., Pitrebois S., Walhin J. (2007), Actuarial Modelling of Claims Count, John Wiley&Sons.
  • Famoye F., Singh K.P. 2006, Zero-inflated generalized Poisson regression model with an application to domestic violence data, Journal of Data Science 4: 117–130.
  • Gamrot W. (2008), Representative sample selection via random search with application to surveying communication lines, [in:] P. Rehorova, K. Marsikova, Z. Hubinka (eds.), Proceedings of 26th International Conference on Mathematical Methods in Economics 2008, Technical University of Liberec, pp. 127–132.
  • Hall D.B. (2000), Zero-inflated Poisson and binomial regression with random effects: A case study, Biometrics 56: 1030–1039.
  • Lambert D. (1992), Zero-inflated Poisson regression, with an application to defects in manufacturing, Technometrics 34: 1–14.
  • Lawless J.F. (1987), Negative binomial and mixed Poisson regression, The Canadian Journal of Statistics 15 (3): 209–225.
  • Miller A. (1990), Subset Selection in Regression, Chapman and Hall, London.
  • Van den Broek J. (1995), A score test for zero inflation in a Poisson distribution, Biometrics 51: 738–743.
  • Vuong Q. (1989), Likelihood ratio tests for model selection and non-nested hypotheses, Econometrica 57: 307–33.
  • Wolny-Dominiak A. (2011), Zmodyfikowana regresja Poissona dla danych ubezpieczeniowych z dużą liczbą zer, [in:] Prognozowanie w zarządzaniu firmą, Prace Naukowe Uniwersytetu Ekonomicznego nr 185, pp. 21–30.
  • Yang Z., Hardin J.W., Addy Ch.L. (2009), Testing over-dispersion in the zero-inflated Poisson model, Journal of Statistical Planning and Inference 139: 3340–3353.
  • Yip K.C.H.,Yau K.K.W. (2005), On modeling claim frequency data in general insurance with extra zeros, Insurance: Mathematics and Economics 36: 153–163.
Document Type
Publication order reference
YADDA identifier
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.