Skip to main content
SpringerLink
Log in

Extreme values and meteorology

  • Published:
Theoretical and Applied Climatology Aims and scope Submit manuscript

Summary

The basic ideas of univariate extremes and some applications are described in the paper; some references are made to multivariate extremes and stochastic processes of extremes.

Zusammenfassung

Es werden einige grundlegende Ideen zu univariaten Extremen und ihren Anwendungen beschrieben. Multivariate Extreme und stochastische Prozesse von Extremen werden ebenfalls besprochen.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alexander GN (1970) Heavy rainfall as a stochastic process. Rev Int Stat Inst 38: 62–81

    Google Scholar 

  • Cehak K (1971) Der Jahresgang der monatlichen höchsten Windgeschwindigkeiten in der Darstellung durch Fisher-Tippett III Verteilungen. Arch Met Geoph Biokl B19: 165–192

    Google Scholar 

  • Cramer H, Leadbetter MR (1967) Stationary and related stochastic processes. Wiley, New York

    Google Scholar 

  • Dodd EL (1923) The greatest and least variable under general laws of error. Trans Amer Math Soc 25: 525–539

    Google Scholar 

  • Dwass M (1964) Extremal processes. Ann Math Stat 35: 1718–1725

    Google Scholar 

  • Fisher RA, Tippett LHC (1928) Limiting forms of the frequency distribution of the largest or smallest member of a sample. Proc Camb Phil Soc 24: 419–438

    Google Scholar 

  • Fraser DAS (1957) Non-parametric methods in statistics. Wiley, New York

    Google Scholar 

  • Fréchet M (1927) Sur la loi de probabilité de l'écart maximum. Ann Soc Polon Math (Krakow) 6: 93–116

    Google Scholar 

  • Galambos J (1978) The asymptotic theory of extreme order statistics. Wiley, New York

    Google Scholar 

  • Galambos J (1980) A statistical test for extreme value distributions. Non-parametric methods of statistics. Budapest, pp 221–230

    Google Scholar 

  • Gnedenko BV (1943) Sur la distribution limite du terme maximum d'une serie aléatoire. Ann Math 44: 423–453

    Google Scholar 

  • Gumbel EJ (1935) Les valeurs extrêmes des distributions statistiques. Ann Inst H Poincaré 4: 115–158

    Google Scholar 

  • Gumbel EJ (1958) Statistics of extremes. Columbia Univ Press, New York

    Google Scholar 

  • Gumbel EJ (1962) Statistical theory of extreme values. In: Sarhan and Greenberg (eds) Contributions to order statistics. Wiley, New York

    Google Scholar 

  • Gumbel EJ, Goldstein N (1964) Analysis of empirical bivariate extremal distributions. J Am Stat Assoc 59: 794–816

    Google Scholar 

  • Jenkinson AF (1955) The frequency distribution of the annual maximum (or minimum) values of meteorological elements. Quart J R Met Soc 81: 158–171

    Google Scholar 

  • Jenkinson AF (1969) Statistics of extremes. In: Estimation of maximum floods, Tech Note No 98, WMO, Genève, pp 183–227

    Google Scholar 

  • Johnson NL, Kotz S (1970) Distributions in statistics continuous univariate distributions-I. Houghton and Mifflin, New York, Atlanta

    Google Scholar 

  • Juncosa ML (1948) On the distribution of the minimum of a sequence of mutually independent random variables. Duke Math J 16: 609–618

    Google Scholar 

  • Lamperti J (1964) On extreme order statistics. Ann Math Stat 35: 1726–1737

    Google Scholar 

  • Leadbetter MR, Lindgren G, Rootzén H (1983) Extremes and related properties of random sequences and processes. Springer, Berlin, Heidelberg, New York

    Google Scholar 

  • Loynes RM (1965) Extreme values in uniformly mixing stationary stochastic processes. Ann Math Stat 36: 993–999

    Google Scholar 

  • Newell GF (1964) Asymptotic extremes form-dependent random variables. Ann Math Stat 35: 1322–1325

    Google Scholar 

  • Otten A, van Montfort MAJ (1980) Maximum likelihood estimation of the general extreme value distribution parameters. J Hydrol 47: 187–192

    Google Scholar 

  • Sevruk B, Geiger H (1981) Selection of distribution types for extremes of precipitation. Operational Hydrology Report No 15, WMO, Genève

    Google Scholar 

  • Sneyers R (1977) L'intensité maximale des precipitations en Belgique. Publ Ser B, no 86, Inst Roy Met Belgique

  • Sneyers R (1979) L'intensité et le durée maximales des precipitation en Belgique. Publ Ser B, no 99, Inst Roy Met Belgique

  • Thom HCS (1968) Toward a universal climatological extreme wind distribution. Proc Sem Extreme Wind Distr, Nat Res Comc Proc, preprint

  • Thom HCS (1971) Asymptotic extreme-value distributions of wave heights in the open Ocean. J Mar Res 29: 19–27

    Google Scholar 

  • Tiago de Oliveira J (1968) Extremal processes; definition and properties. Publ Inst Stat Univ Paris XVIII: 25–36

    Google Scholar 

  • Tiago de Oliveira J (1972) Statistics for Gumbel and Fréchet distributions. In: Freudenthal (ed) Structural safety and reliability. Pergamon Press, Oxford, New York, pp 91–105

    Google Scholar 

  • Tiago de Oliveira J (1973) An extreme-markovian-stationary process. Proc 4th Conf Probab Theory, Romenia, Braşov, pp 217–225

    Google Scholar 

  • Tiago de Oliveira J (1975a) Bivariate and multivariate extreme distributions. In: Patil, Kotz and Ord (eds) Statistical distributions in scientific work. Reidel, The Netherlands, pp 355–361

    Google Scholar 

  • Tiago de Oliveira J (1975b) Statistical decision for extremes. Trab Inv Oper y Estad (Madrid) XXVI: 433–471

    Google Scholar 

  • Tiago de Oliveira J (1975c) Bivariate extremes; extensions. Proc 40th Session I.S.I. (Warsow), book 2, pp 241–251

  • Tiago de Oliveria J (1977a) Statistical methodology for large claims. The Astin Bull IX: 1–9

    Google Scholar 

  • Tiago de Oliveira J (1977b) Asymptotic distributions for univariate and bivariatem-th extremes. In: Barra et al. (ed) Recent developments in statistics, North Holland, Amsterdam, pp 613–617

  • Tiago de Oliveira J (1978) Approximate distributions for sequences of maxima. Metron (Roma) XXXVI: 3–21

    Google Scholar 

  • Tiago de Oliveira J (1981) Statistical choice of univariate extreme models. In: Taillie C et al (ed), Statistical distributions in scientific work, vol 6. Reidel, The Netherlands, pp 367–387

    Google Scholar 

  • Tiago de Oliveira J (1982a) Decision and modelling for extremes. In: Tiago de Oliveira J, Epstein B (eds) Some recent advances in statistics. Academic Press, London, New York, pp 101–110

    Google Scholar 

  • Tiago de Oliveira J (1982b) The δ-method for the obtention of asymptotic distributions; applications. Publ Inst Stat Univ Paris XXVII: 49–70

    Google Scholar 

  • Tiago de Oliveira J (1984a) Probability paper and plotting positions — a new approach. XIV Congr Nac Estad, Inv Oper e Infor, vol I, Granada, pp 275–286

  • Tiago de Oliveira J (ed) (1984b) Statistical extremes and applications, NATO ASI series. Reidel, The Netherlands

    Google Scholar 

  • van Montfort MAJ, Otten A (1973) An asymmetric test of the type of distribution of extremes. Meded Landbouwhogeschool Wogeniagen, 73-18, pp 1–15

    Google Scholar 

  • von Mises R (1936) La distribution de la plus grande den valeurs. Rev Math de l'Union Interbalkanique, vol 1; Selected Papers, vol 2, A.M.S., Providence, R.I., pp 271–294

  • Watson GS (1954) Extreme values in samples form-dependent stationary stochastic processes. Ann Math Stat 25: 798–800

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Academy of Sciences of Lisbon; Department of Statistics, Faculty of Sciences of Lisbon, Center for Statistics and Applications (I.N.I.C.), Portugal

    J. Tiago de Oliveira

Authors
  1. J. Tiago de Oliveira
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

With 4 Figures

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tiago de Oliveira, J. Extreme values and meteorology. Theor Appl Climatol 37, 184–193 (1986). https://doi.org/10.1007/BF00867576

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00867576

Keywords

Search

Navigation