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Comparison of location models of Weibull type samples and extreme value processes
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  • Published: June 1988

Comparison of location models of Weibull type samples and extreme value processes

  • A. Janssen1 &
  • R.-D. Reiss1 

Probability Theory and Related Fields volume 78, pages 273–292 (1988)Cite this article

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  • 7 Citations

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Summary

Four different location parameter models are compared within the sufficiency and deficiency concept. The starting is a location model of a Weibull type sample with shape parameter -1<a<1. Here our basic inequality concerns the approximate sufficiency of the k lower extremes. In addition, the lower extremes are approximately equal, in distribution, to \(\left( {S_m^{1/(1 + a)} + t} \right)_{m \leqq k} \) where S m is the sum of m i.i.d. standard exponential random variables and t is the location parameter. The final step leads us to the model of extreme value processes \(\left( {S_m^{1/(1 + a)} + t} \right)_{m = 1,2,3} \)...

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Siegen, Hölderlinstr. 3, D-5900, Siegen, Federal Republic of Germany

    A. Janssen & R.-D. Reiss

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  1. A. Janssen
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  2. R.-D. Reiss
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Janssen, A., Reiss, RD. Comparison of location models of Weibull type samples and extreme value processes. Probab. Th. Rel. Fields 78, 273–292 (1988). https://doi.org/10.1007/BF00322024

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  • Received: 03 November 1986

  • Revised: 22 December 1987

  • Issue Date: June 1988

  • DOI: https://doi.org/10.1007/BF00322024

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Keywords

  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Shape Parameter
  • Type Sample
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