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Statistische Hefte

, Volume 16, Issue 2, pp 105–114 | Cite as

Distribution of smallest log-normal and gamma extremes

  • K. V. Bury
Miszellen

Abstract

The asymptotic distribution of the first order statistic X(1) of log-Normal and Gamma samples is considered. The parameters of this extreme value asymptote (Weibull distribution) are approximated in terms of the initial sample size n and the parameters of the initial log-Normal and Gamma measurement models. The resulting asymptotic model of X(1) is found to be a reasonable and computationally convenient approximation to the exact model of X(1).

Keywords

Weibull Distribution Asymptotic Distribution Weibull Model Exact Model Gamma Model 
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.

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References

  1. [1]
    K.V. Bury, “Distributions of Weibull Extremes”, INFOR, Vol. 11, No. 2, June 1973, pp. 140–149.MathSciNetzbMATHGoogle Scholar
  2. [2]
    H. Cramér, “Mathematical Methods of Statistics”, Princeton University Press, Princeton, N.J., 1946.zbMATHGoogle Scholar
  3. [3]
    B. Gnedenko, “Sur la distribution limite du terme maximum d’une série aléatoire”, Ann. of Math., Vol. 44, 1943.Google Scholar
  4. [4]
    E.J. Gumbel, “Statistics of Extremes”, Columbia University Press, New York, 1958.zbMATHGoogle Scholar
  5. [5]
    S.S. Gupta, “Order Statistics from the Gamma Distribution”, Technometrics, Vol. 2, No. 1, May 1960, pp. 243–262.CrossRefMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • K. V. Bury
    • 1
  1. 1.Department of Mechanical EngineeringThe University of British ColumbiaVancouver 8Canada

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