International Encyclopedia of Statistical Science

2011 Edition
| Editors: Miodrag Lovric

Extreme Value Distributions

  • Isabel Fraga Alves
  • Cláudia Neves
Reference work entry


Extreme Value distributions arise as limiting distributions for maximum or minimum (extreme value s) of a sample of independent and identically distributed random variables, as the sample size increases. Extreme Value Theory (EVT) is the theory of modelling and measuring events which occur with very small probability. This implies its usefulness in risk modelling as risky events per definition happen with low probability. Thus, these distributions are important in statistics. These models, along with the Generalized Extreme Value distribution, are widely used in risk management, finance, insurance, economics, hydrology, material sciences, telecommunications, and many other industries dealing with extreme events. The class of Extreme Value Distributions (EVD’s) essentially involves three types of extreme value distributions, types I, II and III, defined below.

Definition 1

(Extreme Value Distributions for maxima ). The following are the standard Extreme Value distribution...

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References and Further Reading

  1. Beirlant J, Goegebeur Y, Segers J, Teugels J (2004) Statistics of extremes: theory and applications. Wiley, EnglandGoogle Scholar
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  5. de Haan L, Ferreira A (2006) Extreme value theory: an introduction. Springer series in operations research and financial engineering, BostonGoogle Scholar
  6. Embrechts P, Klüppelberg C, Mikosch T (2001) Modelling extremal events for insurance and finance, 3rd edn. Springer, BerlinGoogle Scholar
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  12. Johnson NL, Balakrishnan N, Kotz S (1995) Continuous univariate distributions, vol 2., 2nd edn. Wiley, New YorkzbMATHGoogle Scholar
  13. Kotz S, Nadarajah S (2000). Extreme value distributions: theory and applications. Imperial College Press, LondonGoogle Scholar
  14. Neves C, Fraga MI, Alves MI (2008) Testing extreme value conditions – an overview and recent approaches. In: Statistics of extremes and related fields, Jan Beirlant, Isabel Frag Alves, Ross Leadbetter (eds INE), REVSTAT - Statistical Journal, special issue, vol. 6, 1, 83–100Google Scholar
  15. Reiss R-D, Thomas M (2001, 2007) Statistical analysis of extreme values, with application to insurance, finance, hydrology and other fields, 2nd and 3rd edn. Birkhuser Verlag, BaselGoogle Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Isabel Fraga Alves
    • 1
  • Cláudia Neves
    • 2
  1. 1.University of LisbonLisbonPortugal
  2. 2.University of AveiroAveiroPortugal