Mean and dispersion modelling for policy claims costs

A model for the statistical analysis of the total amount of insurance paid out on a policy is developed and applied. The model simultaneously deals with the number of claims (zero or more) and the amount of each claim. The number of claims is from a Poisson-based discrete distribution. Individual claim sizes are from a continuous right skewed distribution. The resulting distribution of total claim size is a mixed discrete-continuous model, with positive probability of a zero claim. The means and dispersions of the claim frequency and claim size distribution are modeled in terms of risk factors. The model is applied to a car insurance data set.

[1]  G A Whitmore,et al.  Analysis of overdispersed count data by mixtures of Poisson variables and Poisson processes. , 1997, Biometrics.

[2]  M. Kendall,et al.  Kendall's advanced theory of statistics , 1995 .

[3]  R. Rigby,et al.  Generalized additive models for location, scale and shape , 2005 .

[4]  Bent Jørgensen,et al.  Fitting Tweedie's compound poisson model to insurance claims data , 1994 .

[5]  Walter Zucchini,et al.  Parameter Estimation for the Sichel Distribution and its Multivariate Extension , 1987 .

[6]  R. C. V. Nostrand,et al.  Transformations and Weighting in Regression , 1990 .

[7]  J. Nelder,et al.  An extended quasi-likelihood function , 1987 .

[8]  John A. Nelder,et al.  Likelihood, Quasi-likelihood and Pseudolikelihood: Some Comparisons , 1992 .

[9]  Gordon K. Smyth,et al.  Generalized linear models with varying dispersion , 1989 .

[10]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[11]  A. Stuart,et al.  Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory , 1988 .

[12]  P. McCullagh,et al.  Generalized Linear Models, 2nd Edn. , 1990 .

[13]  Steven Haberman,et al.  Generalized linear models and actuarial science , 1996 .

[14]  R. Berk,et al.  Continuous Univariate Distributions, Volume 2 , 1995 .

[15]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[16]  G. Terrell.  Statistical theory and computational aspects of smoothing , 1997 .

[17]  G. Altmann,et al.  Thesaurus of univariate discrete probability distributions , 1999 .

[18]  Daiane Aparecida Zuanetti,et al.  A LOGNORMAL MODEL FOR INSURANCE CLAIMS DATA , 2006 .

[19]  Mikis D. Stasinopoulos,et al.  Mean and Dispersion Additive Models , 1996 .

[20]  Adrian Bowman,et al.  Generalized additive models for location, scale and shape - Discussion , 2005 .

[21]  Bent Jørgensen,et al.  Fitting Tweedie's Compound Poisson Model to Insurance Claims Data: Dispersion Modelling , 2002, ASTIN Bulletin.

[22]  M. Kendall,et al.  Kendall's Advanced Theory of Statistics: Volume 1 Distribution Theory , 1987 .

[23]  D. Ruppert,et al.  Transformation and Weighting in Regression , 1988 .

[24]  Diane Lambert,et al.  Zero-inflacted Poisson regression, with an application to defects in manufacturing , 1992 .

[25]  J. Nelder,et al.  Double hierarchical generalized linear models (with discussion) , 2006 .

[26]  J. H. Schuenemeyer,et al.  Generalized Linear Models (2nd ed.) , 1992 .

[27]  Célestin C. Kokonendji,et al.  Some discrete exponential dispersion models: poisson-Tweedie and Hinde-Demetrio classes , 2004 .