Beginnings of Extreme-Value Theory

Comments on Bortkiewicz (1922a) and von Mises (1923)
  • H. A. David
  • A. W. F. Edwards
Part of the Springer Series in Statistics book series (SSS)

Abstract

The distribution of the largest or the smallest of n iid variates naturally has a very long history and goes back at least to Nicholas Bernoulli in 1709. Bernoulli reduces a problem of the expected lifetime of the last survivor among n men to finding the expected value of the maximum of n iid uniform variates. Harter (1978) summarizes this and numerous other early papers that touch on the extremes and the range. Gumbel (1958) gives a brief historical account.

Keywords

Parent Distribution Prob Ability Extreme Order Statistics Biographical Note German Poet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bortkiewicz, L. von (1922a). Variationsbreite und mittlerer Fehler. Sitzungsberichte der Berliner Math. Gesellschaft, 21, 3–11.Google Scholar
  2. Bortkiewicz, L. von (1922b). Die Variationsbreite beim Gaussschen Fehlergesetz. Nordisk Statistisk Tidskrifl, 1, 11–38, 193–220.Google Scholar
  3. Cox, D.R. (1954). The mean and coefficient of variation of range in small samples from non-normal populations. Biometrika, 41, 469–481.MathSciNetMATHGoogle Scholar
  4. Cramer, H. (1953). Richard von Mises’ work in probability and statistics. Ann. Math. Statist, 24, 657–662.MathSciNetMATHCrossRefGoogle Scholar
  5. David, H.A. (1981). Order Statistics, 2nd edn. Wiley, New York.MATHGoogle Scholar
  6. Dodd, E.L. (1923). The greatest and the least variate under general laws of error. Trans. Amer. Math. Soc, 25, 525–539.MathSciNetCrossRefGoogle Scholar
  7. Fisher, R.A. and Tippett, L.H.C. (1928). Limiting forms of the frequency distribution of the largest or smallest member of a sample. Proc. Camb. Phil. Soc, 24, 180–190.MATHCrossRefGoogle Scholar
  8. Fréchet, M. (1927). Sur la loi de probabilité de l’écart maximum. Ann. Soc. Polonaise de Math. (Cracow), 6, 93–116.Google Scholar
  9. Galambos, J. (1987). The Asymptotic Theory of Extreme Order Statistics, 2nd edn. Krieger, Malabar, FL.MATHGoogle Scholar
  10. Gnedenko, B. (1943). Sur la distribution limite du terme maximum d’une série aléatoire. Ann. Math., 44, 423–453. [Introduced by R.L. Smith and translated by N.L. Johnson in Kotz and Johnson (1992)]MathSciNetMATHCrossRefGoogle Scholar
  11. Gumbel, E.J. (1935). Les valeurs extrêmes des distributions statistiques. Ann. Inst. Henri Poincaré, 5, 115–158.MathSciNetMATHGoogle Scholar
  12. Gumbel, E.J. (1958). Statistics of Extremes. Columbia University Press, New York.MATHGoogle Scholar
  13. Harter, H.L. (1978). A Chronological Annotated Bibliography of Order Statistics, 1. Pre-1950. U.S. Government Printing Office, Washington, DC. [Reprinted by American Sciences Press, Syracuse, NY (1983)]Google Scholar
  14. Johnson, N. L. and Kotz, S. (1997). Leading Personalities in Statistical Sciences. Wiley, New York.MATHGoogle Scholar
  15. Kotz, S. and Johnson, N.L. (1992). Breakthroughs in Statistics, Vol. I. Springer, New York.Google Scholar
  16. Mises, R. von (1919). Grundlagen der Wahrscheinlichkeitsrechnung. Math. Zeitschrift. [Reprinted in von Mises (1964), Vol. 2]Google Scholar
  17. Mises, R. von (1923). Über die Variationsbreite einer Beobachtungsreihe. Sitzungsberichte der Berliner Math. Gesellschaft, 22, 3–8. [Reprinted in von Mises (1964), Vol. 2]Google Scholar
  18. Mises, R. von (1936). La distribution de la plus grande de n valeurs. Rev. Math. Union Interbalkanique, 1, 141–160. [Reprinted in von Mises (1964), Vol. 2]Google Scholar
  19. Mises, R. von (1964). Selected Papers of Richard von Mises, Vol. 1 and 2. Amer. Math. Soc, Providence, RI.Google Scholar
  20. Pearson, K. (1902). Note on Francis Galton’s difference problem. Biometrika, 1, 390–399.Google Scholar
  21. Tippett, L.H.C. (1925). On the extreme individuals and the range of samples taken from a normal population. Biometrika, 17, 364–387.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • H. A. David
    • 1
  • A. W. F. Edwards
    • 2
  1. 1.Statistical Laboratory and Department of StatisticsIowa State UniversityAmesUSA
  2. 2.Gonville and Caius CollegeCambridgeUK

Personalised recommendations