The compound Poisson distribution with gamm a claim sizes is a very common model for premium estimation in Property and Casualty insurance. Under this distributional assumption, generalised linear models (GLMs) are used to estimate the mean claim frequency and severity, then these estimators are simply multiplied to estimate the mean aggregate loss. The Tweedie distribution allows to parametrise the compound Poisson-gamma (CPG) distribution as a member of the exponential dispersion family and then fit a GLM with a CPG distribution for the response. Thus, with the Tweedie distribution it is possible to estimate the mean aggregate loss using GLMs directly, without the need to previously estimate the mean frequency and severity separately. The purpose of this educational note is to explore the differences between these two estimation methods, contrasting the advantages and disadvantages of each.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Bailey RA, Leroy S (1960) Two studies in automobile insurance ratemaking. ASTIN Bull 1(4):192–217
Briere-Giroux G, Huet J-F, Spaul R, Staudt A, Weinsier D (2010) Predictive modeling for life insurers. https://www.soa.org/files/pdf/research-pred-mod-life-huet.pdf
Czado C, Kastenmeier R, Brechmann EC, Min A (2012) A mixed copula model for insurance claims and claim sizes. Scand Actuarial J 4:278–305
Dunn PK (2014) Tweedie: Tweedie exponential family models. R package. Version 2.2.1
Dutang C (2015) Standard statistical inference. In: Charpentier A (eds) Computational actuarial science with R. CRC Press, New York, pp 75–125
Gilchrist R, Drinkwater D (1999) Fitting Tweedie models to data with probability of zero responses. In: Friedl H, Berghold A, Kauermann G (eds) Proceedings of the 14th international workshop on statistical modelling. Statistical Modelling Society, Hong Kong, pp 207–214
Jørgensen B (1992) The theory of exponential dispersion models and analysis of deviance. Instituto de Matemática Pura e Aplicada, (IMPA), Brazil
Jørgensen B (1997) The theory of dispersion models. Chapman & Hall, London
Jørgensen B, Paes de Souza MC (1994) Fitting Tweedie’s compound Poisson model to insurance claims data. Scand Actuarial J (1):69–93
Krämer N, Brechmann EC, Silvestrini D, Czado C (2013) Total loss estimation using copula-based regression models. Insur Math Econ 53(3):829–839
Ohlsson E, Johansson B (2010) Non-life insurance princing with generalized linear models. Springer, Berlin
Smyth GK, Jørgensen B (2002) Fitting Tweedie’s compound Poisson model to insurance claims data: dispersion modelling. ASTIN Bull 32(1):143–157
Smyth GK, Verbyla AP (1999) Adjusted likelihood methods for modelling dispersion in generalized linear models. Environmetrics 10(6):695–709
Song P (2000) Multivariate dispersion models generated from Gaussian copula. Scand J Stat 27(2):305–320
The authors are sincerely grateful to the Editor, Co-Editor and an anonymous referee for their constructive comments that helped improve this educational note.
The authors gratefully acknowledge the partial financial support of NSERC Grant 36860-2012.
About this article
Cite this article
Quijano Xacur, O.A., Garrido, J. Generalised linear models for aggregate claims: to Tweedie or not?. Eur. Actuar. J. 5, 181–202 (2015). https://doi.org/10.1007/s13385-015-0108-5
- Tweedie distribution
- Exponential dispersion family