Encyclopedia of Complexity and Systems Science

2009 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Extreme Value Statistics

  • Mario Nicodemi
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30440-3_197

Definition of the Subject

Extreme value theory is concerned with the statisticalproperties of the extreme events related to a random variable(see Fig. 1), and theunderstanding and applications of their probability distributions. Themethods and the practical use of such a theory have beendeveloped in the last 60 years, though, many complex real‐lifeproblems have only recently been tackled. Many disciplines use thetools of extreme value theory including meteorology, hydrology, oceanwave modeling, and finance to name just a few.

For example, in economics, extreme value theory is currently used by actuaries to evaluate and price insurance against the probability of rare but financially catastrophic events. An other application is for the estimation of Value at Risk. In hydrology, the theory is applied by environmental risk agencies to calculate, for example, the height of sea‐walls to prevent flooding. Similarly, extreme value theory is also used to set strength boundaries in engineering...

This is a preview of subscription content, log in to check access.

Bibliography

  1. 1.
    Antal T, Droz M, Gyrgyi G, Racz Z (2001) Phys Rev Lett 87:240601ADSGoogle Scholar
  2. 2.
    Berman SM (1964) Ann Math Stat 35:502zbMATHGoogle Scholar
  3. 3.
    Bouchaud J-P, Mézard M (1997) J Phys A 30:7997Google Scholar
  4. 4.
    Bramwell ST, Holdsworth PCW, Pinton J-F (1998) Nature (London) 396:552ADSGoogle Scholar
  5. 5.
    Bramwell ST, Christensen K, Fortin J-Y, Holdsworth PCW, Jensen HJ, Lise S, Lopez JM, Nicodemi M, Pinton J-F, Sellitto M (2000) Phys Rev Lett 84:3744ADSGoogle Scholar
  6. 6.
    Bunde A, Kropp J, Schellnhuber H-J (eds) (2002) The science of disasters‐climate disruptions, heart attacks, and market crashes. Springer, BerlinGoogle Scholar
  7. 7.
    Comtet A, Leboeuf P, Majumdar SN(2007) Phys Rev Lett 98:070404ADSGoogle Scholar
  8. 8.
    Dahlstedt K, Jensen HJ (2001) J Phys A 34:11193; [Inspec] [ISI]Google Scholar
  9. 9.
    Dean DS, Majumdar SN (2001) Phys Rev E 64:046121ADSGoogle Scholar
  10. 10.
    Eichner JF, Kantelhardt JW, Bunde A, Havlin S (2006) Phys Rev E 73:016130ADSGoogle Scholar
  11. 11.
    Embrechts P, Klüppelberg C, Mikosch T, Karatzas I, Yor M (eds) (1997) Modelling extremal events. Springer, BerlinGoogle Scholar
  12. 12.
    Finkenstadt B, Rootzen H (2004) Extreme values in finance, telecommunications, and the environment. Chapman and Hall/CRC Press, LondonGoogle Scholar
  13. 13.
    Galambos J (1978) The asymptotic theory of extreme order statistics. Wiley, New YorkzbMATHGoogle Scholar
  14. 14.
    Galambos J, Lechner J, Simin E (eds) (1994) Extreme value theory and applications. Kluwer, DordrechtzbMATHGoogle Scholar
  15. 15.
    Gnedenko BV (1998) Theory of probability. CRC, Boca Raton, FLGoogle Scholar
  16. 16.
    Guclu H, Korniss G (2004) Phys Rev E 69:065104(R)ADSGoogle Scholar
  17. 17.
    Gumbel EJ (1958) Statistics of extremes. Columbia University Press, New YorkzbMATHGoogle Scholar
  18. 18.
    Leadbetter MR, Lindgren G, Rootzen H (1983) Extremes and related properties of random sequences and processes. Springer, New YorkzbMATHGoogle Scholar
  19. 19.
    Majumdar SN, Comtet A (2004) Phys Rev Lett 92:225501; J Stat Phys 119, 777 (2005)Google Scholar
  20. 20.
    Raychaudhuri S, Cranston M, Przybyla C, Shapir Y (2001) Phys Rev Lett 87:136101ADSGoogle Scholar
  21. 21.
    Reiss RD, Thomas M (2001) Statistical analysis of extreme values: with applications to insurance, finance, hydrology, and other fields. Birkhäuser, BaselGoogle Scholar
  22. 22.
    Smith RL (2003) Statistics of extremes, with applications in environment, insurance and finance, chap 1. In: Statistical analysis of extreme values: with applications to insurance, finance, hydrology, and other fields. Birkhäuser, BaselGoogle Scholar
  23. 23.
    Smith RL, Tawn JA, Yuen HK (1990) Statistics of multivariate extremes. Int Stat Rev 58:47zbMATHGoogle Scholar
  24. 24.
    v. Storch H, Zwiers FW (2001) Statistical analysis in climate research. Cambridge University Press, CambridgeGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Mario Nicodemi
    • 1
  1. 1.Department of PhysicsUniversity of WarwickCoventryUK