Generalised linear models for aggregate claims: to Tweedie or not?


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.

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  1. 1.

    Bailey RA, Leroy S (1960) Two studies in automobile insurance ratemaking. ASTIN Bull 1(4):192–217

    Google Scholar 

  2. 2.

    Briere-Giroux G, Huet J-F, Spaul R, Staudt A, Weinsier D (2010) Predictive modeling for life insurers.

  3. 3.

    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

    MathSciNet  Article  Google Scholar 

  4. 4.

    Dunn PK (2014) Tweedie: Tweedie exponential family models. R package. Version 2.2.1

  5. 5.

    Dutang C (2015) Standard statistical inference. In: Charpentier A (eds) Computational actuarial science with R. CRC Press, New York, pp 75–125

  6. 6.

    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

  7. 7.

    Jørgensen B (1992) The theory of exponential dispersion models and analysis of deviance. Instituto de Matemática Pura e Aplicada, (IMPA), Brazil

  8. 8.

    Jørgensen B (1997) The theory of dispersion models. Chapman & Hall, London

  9. 9.

    Jørgensen B, Paes de Souza MC (1994) Fitting Tweedie’s compound Poisson model to insurance claims data. Scand Actuarial J (1):69–93

  10. 10.

    Krämer N, Brechmann EC, Silvestrini D, Czado C (2013) Total loss estimation using copula-based regression models. Insur Math Econ 53(3):829–839

    MATH  Article  Google Scholar 

  11. 11.

    Ohlsson E, Johansson B (2010) Non-life insurance princing with generalized linear models. Springer, Berlin

    Google Scholar 

  12. 12.

    Smyth GK, Jørgensen B (2002) Fitting Tweedie’s compound Poisson model to insurance claims data: dispersion modelling. ASTIN Bull 32(1):143–157

    MATH  MathSciNet  Article  Google Scholar 

  13. 13.

    Smyth GK, Verbyla AP (1999) Adjusted likelihood methods for modelling dispersion in generalized linear models. Environmetrics 10(6):695–709

    Article  Google Scholar 

  14. 14.

    Song P (2000) Multivariate dispersion models generated from Gaussian copula. Scand J Stat 27(2):305–320

    MATH  Article  Google Scholar 

Download references


The authors are sincerely grateful to the Editor, Co-Editor and an anonymous referee for their constructive comments that helped improve this educational note.

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Correspondence to Oscar Alberto Quijano Xacur.

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The authors gratefully acknowledge the partial financial support of NSERC Grant 36860-2012.

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Quijano Xacur, O.A., Garrido, J. Generalised linear models for aggregate claims: to Tweedie or not?. Eur. Actuar. J. 5, 181–202 (2015).

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  • Tweedie distribution
  • GLMs
  • Exponential dispersion family