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Abstract

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.

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Notes

  1. 1.

    Also known as the extreme value trinity theorem or three types theorem.

References

  • Beirlant, J., Y. Goegebeur, J. Segers, J. Teugels, D. De Waal, and C. Ferro 2004. Statistics of Extremes: Theory and Applications. Hoboken: Wiley.

    Book  Google Scholar 

  • 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.

    MATH  Google Scholar 

  • Coles, S. 2001. An Introduction to Statistical Modeling of Extreme Values. London: Springer-Verlag.

    Book  MATH  Google Scholar 

  • de Haan, L. and A. Ferreira 2006. Extreme Value Theory. New York: Springer.

    Book  MATH  Google Scholar 

  • Embrechts, P., C. Klüppelberg, and T. Mikosch 1997. Modelling Extremal Events for Insurance and Finance. New York: Springer-Verlag.

    Book  MATH  Google Scholar 

  • Finkenstadt, B. and H. Rootzén (Eds.) 2003. Extreme Values in Finance, Telecommunications and the Environment. Boca Raton: Chapman & Hall/CRC.

    Google Scholar 

  • Gilleland, E., M. Ribatet, and A. G. Stephenson 2013. A software review for extreme value analysis. Extremes 16(1):103–119.

    Article  MathSciNet  Google Scholar 

  • Gomes, M.I., and A. Guillou. 2015. Extreme value theory and statistics of univariate extremes: a review. International Statistical Review 83(2):263–292.

    Article  MathSciNet  Google Scholar 

  • Gumbel, E. J. 1958. Statistics of Extremes. New York, USA: Columbia University Press.

    MATH  Google Scholar 

  • Kotz, S. and S. Nadarajah 2000. Extreme Value Distributions: Theory and Applications. London: Imperial College Press.

    Book  Google Scholar 

  • Leadbetter, M. R., G. Lindgren, and H. Rootzén 1983. Extremes and Related Properties of Random Sequences and Processes. New York, USA: Springer-Verlag.

    Book  MATH  Google Scholar 

  • Novak, S. Y. 2012. Extreme Value Methods with Applications to Finance. Boca Raton, FL, USA: CRC Press.

    Google Scholar 

  • Pickands, J. 1975. Statistical inference using extreme order statistics. The Annals of Statistics 3(1):119–131.

    Article  MATH  MathSciNet  Google Scholar 

  • Prescott, P. and A. T. Walden 1980. Maximum likelihood estimation of the parameters of the generalized extreme-value distribution. Biometrika 67(3):723–724.

    Article  MathSciNet  Google Scholar 

  • 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 

  • Smith, R. L. 1985. Maximum likelihood estimation in a class of nonregular cases. Biometrika 72(1):67–90.

    Article  MATH  MathSciNet  Google Scholar 

  • Smith, R. L. 1986. Extreme value theory based on the r largest annual events. Journal of Hydrology 86(1–2):27–43.

    Article  Google Scholar 

  • Smith, R. L. 2003. Statistics of extremes, with applications in environment, insurance and finance. See Finkenstadt and Rootzén (2003), pp. 1–78.

    Google Scholar 

  • Tawn, J. A. 1988. An extreme-value theory model for dependent observations. Journal of Hydrology 101(1–4):227–250.

    Article  Google Scholar 

  • 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.

    Article  MATH  MathSciNet  Google Scholar 

  • Yee, T. W. and A. G. Stephenson 2007. Vector generalized linear and additive extreme value models. Extremes 10(1–2):1–19.

    Article  MATH  MathSciNet  Google Scholar 

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© 2015 Thomas Yee

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Yee, T.W. (2015). Extremes. In: Vector Generalized Linear and Additive Models. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2818-7_16

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