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.
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.
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.
Coles, S. 2001. An Introduction to Statistical Modeling of Extreme Values. London: Springer-Verlag.
de Haan, L. and A. Ferreira 2006. Extreme Value Theory. New York: Springer.
Embrechts, P., C. Klüppelberg, and T. Mikosch 1997. Modelling Extremal Events for Insurance and Finance. New York: Springer-Verlag.
Finkenstadt, B. and H. Rootzén (Eds.) 2003. Extreme Values in Finance, Telecommunications and the Environment. Boca Raton: Chapman & Hall/CRC.
Gilleland, E., M. Ribatet, and A. G. Stephenson 2013. A software review for extreme value analysis. Extremes 16(1):103–119.
Gomes, M.I., and A. Guillou. 2015. Extreme value theory and statistics of univariate extremes: a review. International Statistical Review 83(2):263–292.
Gumbel, E. J. 1958. Statistics of Extremes. New York, USA: Columbia University Press.
Kotz, S. and S. Nadarajah 2000. Extreme Value Distributions: Theory and Applications. London: Imperial College Press.
Leadbetter, M. R., G. Lindgren, and H. Rootzén 1983. Extremes and Related Properties of Random Sequences and Processes. New York, USA: Springer-Verlag.
Novak, S. Y. 2012. Extreme Value Methods with Applications to Finance. Boca Raton, FL, USA: CRC Press.
Pickands, J. 1975. Statistical inference using extreme order statistics. The Annals of Statistics 3(1):119–131.
Prescott, P. and A. T. Walden 1980. Maximum likelihood estimation of the parameters of the generalized extreme-value distribution. Biometrika 67(3):723–724.
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.
Smith, R. L. 1985. Maximum likelihood estimation in a class of nonregular cases. Biometrika 72(1):67–90.
Smith, R. L. 1986. Extreme value theory based on the r largest annual events. Journal of Hydrology 86(1–2):27–43.
Smith, R. L. 2003. Statistics of extremes, with applications in environment, insurance and finance. See Finkenstadt and Rootzén (2003), pp. 1–78.
Tawn, J. A. 1988. An extreme-value theory model for dependent observations. Journal of Hydrology 101(1–4):227–250.
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.
Yee, T. W. and A. G. Stephenson 2007. Vector generalized linear and additive extreme value models. Extremes 10(1–2):1–19.
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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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