Modeling insurance data using generalized gamma regression

Document Type : Original Scientific Paper

Authors

Department of Statistics, University of Hormozgan, Hormozgan, Iran

Abstract

The generalized gamma (GG) is a flexible distribution in statistical literature with the special cases of exponential, gamma, Weibull and lognormal distributions. This paper investigates the GG additive model for modeling hospital claim costs. In comparison to other models, the GG is more flexible and has a better performance in modeling positively skewed data. The proposed model was fitted to the hospital costs data from the nationwide inpatient sample of the health care cost and utilization project, a nationwide survey of hospital costs conducted by the U.S. Agency for healthcare research and quality. The results indicate that the claim cost is affected by the given explanatory variables and based on the AIC and BIC criteria, the GG has a better performance for the given data compared to the alternatives.

Keywords

Main Subjects


Czado, C. (2005). Spatial modelling of claim frequency and claim size in insurance. Insurance for Statistics. Sonderforschungsbereich 386, Paper 461.
Frees, E.W. (2010). Regression Modeling with Actuarial and Financial Applications. Cambridge University Press.
Jorgensen, B. and Souza, M.C.P.D. (1994). Fitting Tweedie's compound Poisson model to insurance claims data. Scandinavian Actuarial Journal, 1, 69–93.
McCullagh, P. and Nelder, J.A. (1989). Generalized Linear Models, 2nd Edn. Chapman and Hall, Boca Raton.
Smyth, G.K. and Jorgensen, B. (2002). Fitting Tweedie's compound Poisson model to insurance claims data: dispersion modeling. ASTIN Bulletin: The Journal of the IAA, 32, 143–157.
Brockman, M.J. and Wright, T.S. (1992). Statistical motor rating: Making effective use of your data. Journal of the Institute of Actuaries, 119, 457–543.
Hogg, R.V. and Klugman, S.A. (2009). Loss Distributions. First Edn. John Wiley and Sons, New York.
Tong, E.N., Mues, C. and Thomas, L. (2013). A zero-adjusted gamma model for mortgage loan loss given default. International Journal of Forecasting, 29, 548–562.
Rigby, R.A. and Stasinopoulos, D.M. (2007). Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, 23, 1–46.