Number of accidents or number of claims? An approach with zero-inflated poisson models for panel data

Journal of Risk and Insurance

Volumn 76, Issue 4, 2009, Pages 821-846

  Boucher, Jean Philippe ^a   Denuit, Michel ^b   Guillen, Montserrat ^c  

^a UNIVERSITÉ DU QUÉBEC À MONTRÉAL   (Canada)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^c UNIVERSITY OF BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70449396850     PISSN: 00224367     EISSN: 15396975     Source Type: Journal    
DOI: 10.1111/j.1539-6975.2009.01321.x     Document Type: Article

References (30)

1. Artis, M., M. Ayuso, and M. Guillén, 1999, Modelling Different Types of Automobile Insurance Fraud Behavior in the Spanish Market, Insurance Mathematics and Economics, 24 (1-2 67 81.
2. Boucher, J.-P., and M. Denuit, 2006, Fixed Versus Random Effects in Poisson Regression Models for Claim Counts: Case Study With Motor Insurance, ASTIN Bulletin, 36 : 285 301.
3. Boucher, J.-P., and M. Denuit, 2008, Credibility Premiums for the Zero-Inflated Model and New Hunger for Bonus Interpretation, Insurance: Mathematics and Economics, 42 : 727 735.
4. Boucher, J.-P., M. Denuit, and M. Guillén, 2007, Risk Classification for Claim Counts: A Comparative Analysis of Various Zero-Inflated Mixed Poisson and Hurdle Models, North American Actuarial Journal, 11 (4 110 131.
5. Boucher, J.-P., M. Denuit, and M. Guillén, 2008, Models of Insurance Claim Counts With Time Dependence Based on Generalisation of Poisson and Negative Binomial Distributions, Variance, 2 (1 135 162.
6. Cameron, A. C., and P. K. Trivedi, 1998, Regression Analysis of Count Data (New York : Cambridge University Press).
7. Chernoff, H., 1954, On the Distribution of the Log-Likelihood Ratio, Annual Mathematics Statistics, 25 : 573 578.
8. Denuit, M., X. Maréchal, S. Pitrebois, and J.-F. Walhin, 2007, Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Scales (New York : Wiley).
9. Dionne, G., and C. Vanasse, 1989, A Generalization of Automobile Insurance Rating Models: The Negative Binomial Distribution with Regression Component, ASTIN Bulletin, 19 : 199 212.
10. Dionne, G., and C. Vanasse, 1992, Automobile Insurance Ratemaking in the Presence of Asymmetrical Information, Journal of Applied Econometrics, 7 : 149 165.
11. Golden, R., 2003, Discrepancy Risk Model Selection Test for Comparing Possibly Misspecified or Nonnested Models, Psychometrika, 68 : 229 249.
12. Gourieroux, C., 1999, The Econometrics of Risk Classification in Insurance, The Geneva Papers on Risk and Insurance Theory, 24 : 119 137.
13. Hausman, J., B. Hall, and Z. Griliches, 1984, Econometric Models for Count Data With Application to the Patents-R and D Relationship, Econometrica, 52 : 909 938.
14. 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).
15. Holla, M., 1966, On a Poisson-Inverse Gaussian Distribution, Metrika, 11 : 115 121.
16. Hsiao, C., 2003, Analysis of Panel Data, 2nd edition (Cambridge : Cambridge University Press).
17. Lambert, D., 1992, Zero-Inflated Poisson Regression With an Application to Defects in Manufacturing, Technometrics, 34 : 1 14.
18. Lemaire, J., 1977, La Soif du Bonus, ASTIN Bulletin, 9 : 181 190.
19. Lemaire, J., 1995, Bonus-Malus Systems in Automobile Insurance (Boston : Kluwer Academic Publishers).
20. Lemaire, J., and H. Zi, 1994, A Comparative Analysis of 30 Bonus-Malus Systems, ASTIN Bulletin, 24 : 287 309.
21. Moran, P., 1971, Maximum Likelihood Estimation in Non-Standard Conditions, Proceeding of the Cambridge Philosophical Society, 70 : 441 450.
22. Mullahy, J., 1986, Specification and Testing in Some Modified Count Data Models, Journal of Econometrics, 33 : 341 365.
23. Mullahy, J., 1997, Heterogeneity, Excess Zeros, and the Structure of Count Data Models, Journal of Applied Econometrics, 12 (3 337 350.
24. Philipson, C., 1960, The Swedish System of Bonus, ASTIN Bulletin, 1 : 134 141.
25. Rivers, D., and Q. Vuong, 2002, Model Selection Tests for Nonlinear Dynamic Models, Econometrics Journal, 5 : 1 39.
26. Shoukri, M., M. Asyali, R. VanDorp, and D. Kelton, 2004, The Poisson Inverse Gaussian Regression Model in the Analysis of Clustered Counts Data, Journal of Data Science, 2 : 17 32.
27. Song, J., 2005, Zero-Inflated Poisson Regression to Analyze Lenghts of Hospital Stays Adjusting for Intra-Center Correlation, Communications in Statistics-Simulation and Computation, 11 : 59 67.
28. Vuong, Q., 1989, Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses, Econometrica, 57 : 307 333.
29. Walhin, J.-F., and J. Paris, 2000, The True Claim Amount and Frequency Distributions Within a Bonus-Malus System, ASTIN Bulletin, 30 : 391 403.
30. Young, V., and F. De Vylder, 2000, Credibility in Favor of Unlucky Insureds, North American Actuarial Journal, 4 : 107 113.