Chapter 12: Tweedie GLMs

  • Peter K. Dunn
  • Gordon K. Smyth
Part of the Springer Texts in Statistics book series (STS)


This chapter introduces glms based on Tweedie edms. Tweedie edms are distributions that generalize many of the edms already seen (the normal, Poisson, gamma and inverse Gaussian distributions are special cases) and include other distributions also.


  1. [1]
    Andrew, D.F., Herzberg, A.M.: Data: A Collection of Problems from Many Fields for the Student and Research Worker. Springer, New York (1985)CrossRefGoogle Scholar
  2. [2]
    Aoki, R., Achcar, J.A., Bolfarine, H., Singer, J.M.: Bayesian analysis of null-intercept errors-in-variables regression for pretest/post-test data. Journal of Applied Statistics 31(1), 3–12 (2003)CrossRefGoogle Scholar
  3. [3]
    Bailey, R.C., Summe, J.P., Hommer, L.D., McCracken, L.E.: A model for the analysis of the anesthetic response. Biometrics 34(2), 223–232 (1978)CrossRefGoogle Scholar
  4. [4]
    Bax, N.J., Williams, A.: Habitat and fisheries production in the South East fishery ecosystem. Final Report 1994/040, Fisheries Research and Development Corporation (2000)Google Scholar
  5. [5]
    Box, G.E.P.: Science and statistics. Journal of the American Statistical Association 71, 791–799 (1976)MathSciNetCrossRefGoogle Scholar
  6. [6]
    Box, G.E.P., Cox, D.R.: An analysis of transformations (with discussion). Journal of the Royal Statistical Society, Series B 26, 211–252 (1964)Google Scholar
  7. [7]
    Brown, J.E., Dunn, P.K.: Comparisons of Tobit, linear, and Poisson-gamma regression models: an application of time use data. Sociological Methods & Research 40(3), 511–535 (2011)MathSciNetCrossRefGoogle Scholar
  8. [8]
    Browning, L.E., Patrick, S.C., Rollins, L.A., Griffith, S.C., Russell, A.F.: Kin selection, not group augmentation, predicts helping in an obligate cooperatively breeding bird. Proceedings of the Royal Society B 279, 3861–3869 (2012)CrossRefGoogle Scholar
  9. [9]
    Carr, L.J., Dunsiger, S.I., Marcus, B.H.: Validation of Walk Score for estimating access to walkable amenities. British Journal of Sports Medicine 45(14), 1144–1148 (2011)CrossRefGoogle Scholar
  10. [10]
    Cole, R., Dunn, P., Hunter, I., Owen, N., Sugiyama, T.: Walk score and Australian adults’ home-based walking for transport. Health & Place 35, 60–65 (2015)CrossRefGoogle Scholar
  11. [11]
    Connolly, R.D., Schirmer, J., Dunn, P.K.: A daily rainfall disaggregation model. Agricultural and Forest Meteorology 92(2), 105–117 (1998)CrossRefGoogle Scholar
  12. [12]
    Dunn, P.K.: Precipitation occurrence and amount can be modelled simultaneously. International Journal of Climatology 24, 1231–1239 (2004)CrossRefGoogle Scholar
  13. [13]
    Dunn, P.K.: tweedie: Tweedie exponential family models (2017). URL R package version 2.3.0
  14. [14]
    Dunn, P.K., Smyth, G.K.: Randomized quantile residuals. Journal of Computational and Graphical Statistics 5(3), 236–244 (1996)Google Scholar
  15. [15]
    Dunn, P.K., Smyth, G.K.: Series evaluation of Tweedie exponential dispersion models. Statistics and Computing 15(4), 267–280 (2005)MathSciNetCrossRefGoogle Scholar
  16. [16]
    Dunn, P.K., Smyth, G.K.: Evaluation of Tweedie exponential dispersion models using Fourier inversion. Statistics and Computing 18(1), 73–86 (2008)MathSciNetCrossRefGoogle Scholar
  17. [17]
    Foster, S.D., Bravington, M.V.: A Poisson–gamma model for analysis of ecological data. Environmental and Ecological Statistics 20(4), 533–552 (2013)MathSciNetCrossRefGoogle Scholar
  18. [18]
    Garby, L., Garrow, J.S., Jørgensen, B., Lammert, O., Madsen, K., Sørensen, P., Webster, J.: Relation between energy expenditure and body composition in man: Specific energy expenditure in vivo of fat and fat-free tissue. European Journal of Clinical Nutrition 42(4), 301–305 (1988)Google Scholar
  19. [19]
    Gilchrist, R.: Regression models for data with a non-zero probability of a zero response. Communications in Statistics—Theory and Methods 29, 1987–2003 (2000)CrossRefGoogle Scholar
  20. [20]
    Gilchrist, R., Drinkwater, D.: Fitting Tweedie models to data with probability of zero responses. In: H. Friedl, A. Berghold, G. Kauermann (eds.) Statistical Modelling: Proceedings of the 14th International Workshop on Statistical Modelling, pp. 207–214. International Workshop on Statistical Modelling, Gräz (1999)Google Scholar
  21. [21]
    Hallin, M., François Ingenbleek, J.: The Swedish automobile portfolio in 1997. Scandinavian Actuarial Journal pp. 49–64 (1983)CrossRefGoogle Scholar
  22. [22]
    Hasan, M.M., Dunn, P.K.: A simple Poisson–gamma model for modelling rainfall occurrence and amount simultaneously. Agricultural and Forest Meteorology 150, 1319–1330 (2010)CrossRefGoogle Scholar
  23. [23]
    Jørgensen, B.: Exponential dispersion models (with discussion). Journal of the Royal Statistical Society, Series B 49, 127–162 (1987)Google Scholar
  24. [24]
    Jørgensen, B.: Exponential dispersion models and extensions: A review. International Statistical Review 60(1), 5–20 (1992)CrossRefGoogle Scholar
  25. [25]
    Jørgensen, B.: The Theory of Dispersion Models. Monographs on Statistics and Applied Probability. Chapman and Hall, London (1997)Google Scholar
  26. [26]
    Jørgensen, B., de Souza, M.C.P.: Fitting Tweedie’s compound Poisson model to insurance claims data. Scandinavian Actuarial Journal 1, 69–93 (1994)MathSciNetCrossRefGoogle Scholar
  27. [27]
    McBride, J.L., Nicholls, N.: Seasonal relationships between Australian rainfall and the southern oscillation. Monthly Weather Review 111(10), 1998–2004 (1983)CrossRefGoogle Scholar
  28. [28]
    National Institute of Standards and Technology: Statistical reference datasets (2016). URL
  29. [29]
    Nelson, W.: Analysis of performance-degradation data from accelerated tests. IEEE Transactions on Reliability 30(2), 149–155 (1981)CrossRefGoogle Scholar
  30. [30]
    Singer, J.M., Andrade, D.F.: Regression models for the analysis of pretest/posttest data. Biometrics 53, 729–725 (1997)CrossRefGoogle Scholar
  31. [31]
    Smyth, G.K.: Regression analysis of quantity data with exact zeros. In: Proceedings of the Second Australia–Japan Workshop on Stochastic Models in Engineering, Technology and Management, pp. 572–580. Technology Management Centre, University of Queensland, Brisbane (1996)Google Scholar
  32. [32]
    Smyth, G.K.: Australasian data and story library (Ozdasl) (2011). URL
  33. [33]
    Smyth, G.K.: statmod: Statistical Modeling (2017). URL R package version 1.4.30. With contributions from Yifang Hu, Peter Dunn, Belinda Phipson and Yunshun Chen.
  34. [34]
    Smyth, G.K., Jørgensen, B.: Fitting Tweedie’s compound Poisson model to insurance claims data: Dispersion modelling. In: Proceedings of the 52nd Session of the International Statistical Institute. Helsinki, Finland (1999). Paper Meeting 68: Statistics and InsuranceGoogle Scholar
  35. [35]
    Stone, R.C., Auliciems, A.: soi phase relationships with rainfall in eastern Australia. International Journal of Climatology 12, 625–636 (1992)CrossRefGoogle Scholar
  36. [36]
    Taylor, L.R.: Aggregation, variance and the mean. Nature 189, 732–735 (1961)CrossRefGoogle Scholar
  37. [37]
    Tweedie, M.C.K.: The regression of the sample variance on the sample mean. Journal of the London Mathematical Society 21, 22–28 (1946)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Peter K. Dunn
    • 1
  • Gordon K. Smyth
    • 2
  1. 1.Faculty of Science, Health, Education and EngineeringSchool of Health of Sport Science, University of the Sunshine CoastQueenslandAustralia
  2. 2.Bioinformatics DivisionWalter and Eliza Hall Institute of Medical ResearchParkvilleAustralia

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