Skip to main content

Extreme Value Models

  • Chapter
  • 880 Accesses

Abstract

This chapter is devoted to statistical procedures in parametric extreme value (EV) models which are especially designed for maxima. It is worth recalling that minima can be dealt with by changing the sign of the data.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Benjamin, J.R. and Cornell, C.A. (1970). Probability, Statistics and Decisions for Civil Engineers. McGraw-Hill, New York.

    Google Scholar 

  2. Pericchi, L.R. and Rodriguez-Iturbe, I. (1985). On the statistical analysis of floods. In: A Celebration of Statistics. The ISI Centenary Volume, A.C. Atkinson and S.E. Fienberg (eds.), 511–541.

    Google Scholar 

  3. Greenwood, J.A., Landwehr, J.M., Matalas, N.C. and Wallis, J.R. (1979). Probability weighted moments: definition and relation to parameters of several distributions expressable in inverse form. Wat. Resour. Res. 15, 1049–1054.

    Google Scholar 

  4. Hosking, J.R.M. (1990). Lmoments: analysis and estimation od distributions using linear combinations of order statistics. J. R. Statist. Soc. B 52, 105–124.

    Google Scholar 

  5. Also see [26] and Buishand, T.A. (1989). Statistics of extremes in climatology. Statist. Neerlandica 43, 1–30.

    Google Scholar 

  6. cf. also Stoyan, D., Stoyan, H. and Jansen, U. (1997). Umweltstatistik. Teubner, Stuttgart.

    Google Scholar 

  7. Coles, S.G. and Walshaw, D. (1994). Directional modelling of extreme wind speeds. Appl. Statist. 43, 139–157.

    Google Scholar 

  8. Zwiers, F.W. (1995). An extreme-value analysis of wind speeds at five Canadian locations. In [14], pp. 124–134.

    Google Scholar 

  9. Ross, W.H. (1995). A peaks-over-threshold analysis of extreme wind speeds. In [14], pp. 135–142.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  11. Pfeifer, D. (1989). Einführung in die Extremwertstatistik. Teubner, Stuttgart.

    Book  MATH  Google Scholar 

  12. Castillo, E., Galambos, J. and Sarabia, J.M. (1989). The selection of the domain of attraction of extreme value distribution from the set of data. In [10], pp. 181–190.

    Google Scholar 

  13. Hosking, J.R.M. (1984). Testing whether the shape is zero in the generalized extreme—value distribution. Biometrika 71, 367–374.

    MathSciNet  Google Scholar 

  14. See, e.g, Barndorff—Nielsen, O.E. and Cox, D.R. (1994). Inference and Asymptotics. Chapmann & Hall, London.

    Google Scholar 

  15. Otten, A. and van Montfort, M.A.J. (1978). The power of two tests on the type of the distributions of extremes. J. Hydrology 37, 195–199.

    Article  Google Scholar 

  16. Stephens, M.A. (1977). Goodness of fit for the extreme value distribution. Biometrika 64, 583–588.

    Article  MathSciNet  MATH  Google Scholar 

  17. Houghton, J.C. (1978). Birth of a parent: The Wakeby distribution for modeling flows. Water Resour. Res. 14, 1105–1110, and Hosking, J.R.M., Wallis, J.R. and Wood, E.F. (1985). An appraisal of the regional flood frequency procedure in the UK Flood Studies Report. Hydrol. Sci. J. 30, 85–109.

    Google Scholar 

  18. Todorovic, P. and Rousselle, J. (1971). Some problems of flood analysis. Water Re-sour. Res. 7, 1144–1150

    Google Scholar 

  19. Changery, M.J. (1982). Historical extreme winds for the United States—Atlantic and Gulf of Mexico coastlines. U.S. Nuclear Regulatory Commission, NUREG/CR-2639.

    Google Scholar 

  20. Rossi, F., Fiorenti, M. and Versace, P. (1984). Two—component extreme value distribution for flood frequency analysis. Water Resour. Res. 20, 847–856.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Basel AG

About this chapter

Cite this chapter

Reiss, RD., Thomas, M. (1997). Extreme Value Models. In: Statistical Analysis of Extreme Values. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6336-0_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-6336-0_4

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-5768-9

  • Online ISBN: 978-3-0348-6336-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics