This chapter looks at extreme value data analysis as an application of VGLMs/VGAMs. The two most important models (generalized extreme value or GEV distribution, and generalized Pareto distribution or GPD) are shown to be easily amenable to the VGLM/VGAM framework. Some real data examples are given.


  1. Beirlant, J., Y. Goegebeur, J. Segers, J. Teugels, D. De Waal, and C. Ferro 2004. Statistics of Extremes: Theory and Applications. Hoboken: Wiley.CrossRefGoogle Scholar
  2. Castillo, E., A. S. Hadi, N. Balakrishnan, and J. M. Sarabia 2005. Extreme Value and Related Models with Applications in Engineering and Science. Hoboken: Wiley.zbMATHGoogle Scholar
  3. Coles, S. 2001. An Introduction to Statistical Modeling of Extreme Values. London: Springer-Verlag.zbMATHCrossRefGoogle Scholar
  4. de Haan, L. and A. Ferreira 2006. Extreme Value Theory. New York: Springer.zbMATHCrossRefGoogle Scholar
  5. Embrechts, P., C. Klüppelberg, and T. Mikosch 1997. Modelling Extremal Events for Insurance and Finance. New York: Springer-Verlag.zbMATHCrossRefGoogle Scholar
  6. Finkenstadt, B. and H. Rootzén (Eds.) 2003. Extreme Values in Finance, Telecommunications and the Environment. Boca Raton: Chapman & Hall/CRC.Google Scholar
  7. Gilleland, E., M. Ribatet, and A. G. Stephenson 2013. A software review for extreme value analysis. Extremes 16(1):103–119.MathSciNetCrossRefGoogle Scholar
  8. Gomes, M.I., and A. Guillou. 2015. Extreme value theory and statistics of univariate extremes: a review. International Statistical Review 83(2):263–292.MathSciNetCrossRefGoogle Scholar
  9. Gumbel, E. J. 1958. Statistics of Extremes. New York, USA: Columbia University Press.zbMATHGoogle Scholar
  10. Kotz, S. and S. Nadarajah 2000. Extreme Value Distributions: Theory and Applications. London: Imperial College Press.CrossRefGoogle Scholar
  11. Leadbetter, M. R., G. Lindgren, and H. Rootzén 1983. Extremes and Related Properties of Random Sequences and Processes. New York, USA: Springer-Verlag.zbMATHCrossRefGoogle Scholar
  12. Novak, S. Y. 2012. Extreme Value Methods with Applications to Finance. Boca Raton, FL, USA: CRC Press.Google Scholar
  13. Pickands, J. 1975. Statistical inference using extreme order statistics. The Annals of Statistics 3(1):119–131.zbMATHMathSciNetCrossRefGoogle Scholar
  14. Prescott, P. and A. T. Walden 1980. Maximum likelihood estimation of the parameters of the generalized extreme-value distribution. Biometrika 67(3):723–724.MathSciNetCrossRefGoogle Scholar
  15. Reiss, R.-D. and M. Thomas 2007. Statistical Analysis of Extreme Values: with Applications to Insurance, Finance, Hydrology and Other Fields (Third ed.). Basel, Switzerland: Birkhäuser.Google Scholar
  16. Smith, R. L. 1985. Maximum likelihood estimation in a class of nonregular cases. Biometrika 72(1):67–90.zbMATHMathSciNetCrossRefGoogle Scholar
  17. Smith, R. L. 1986. Extreme value theory based on the r largest annual events. Journal of Hydrology 86(1–2):27–43.CrossRefGoogle Scholar
  18. Smith, R. L. 2003. Statistics of extremes, with applications in environment, insurance and finance. See Finkenstadt and Rootzén (2003), pp. 1–78.Google Scholar
  19. Tawn, J. A. 1988. An extreme-value theory model for dependent observations. Journal of Hydrology 101(1–4):227–250.CrossRefGoogle Scholar
  20. Withers, C. S. and S. Nadarajah 2009. The asymptotic behaviour of the maximum of a random sample subject to trends in location and scale. Random Operators and Stochastic Equations 17(1):55–60.zbMATHMathSciNetCrossRefGoogle Scholar
  21. Yee, T. W. and A. G. Stephenson 2007. Vector generalized linear and additive extreme value models. Extremes 10(1–2):1–19.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Thomas Yee 2015

Authors and Affiliations

  • Thomas W. Yee
    • 1
  1. 1.Department of StatisticsUniversity of AucklandAucklandNew Zealand

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