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Extreme Value Theory pp 125–131Cite as

A Characterization of the Uniform Distribution via Maximum Likelihood Estimation of its Location Parameter

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Part of the book series: Lecture Notes in Statistics ((LNS,volume 51))

Abstract

Let F(x--θ) be a family of probability density functions with location parameter θ. If for every ordered sample x1 ≦ x2 ≦ ≦ ⋯ ≦xn the midrange (x1+xn)/2 is a maximum likelihood estimation of θ then f(x) is the density function of a symmetric uniform distribution. (The converse statement is obvious and well known.)

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References

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Author information

Authors and Affiliations

  1. Mathematical Institute, Eötvös University, Budapest, Muzeum krt. 6-8, H-1088, Hungary

    Z. Buczolich & G. J. Székely

Authors
  1. Z. Buczolich
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  2. G. J. Székely
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Editor information

Editors and Affiliations

  1. Institut für mathematische Statistik, Universität Bern, Sidlerstrasse 5, 3012, Bern, Switzerland

    Jürg Hüsler

  2. Universität Gesamthochschule Siegen, Hölderlinstr. 3, 5900, Siegen, Federal Republic of Germany

    Rolf-Dieter Reiss

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© 1989 Springer-Verlag Berlin Heidelberg

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Buczolich, Z., Székely, G.J. (1989). A Characterization of the Uniform Distribution via Maximum Likelihood Estimation of its Location Parameter. In: Hüsler, J., Reiss, RD. (eds) Extreme Value Theory. Lecture Notes in Statistics, vol 51. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3634-4_11

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  • DOI: https://doi.org/10.1007/978-1-4612-3634-4_11

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96954-1

  • Online ISBN: 978-1-4612-3634-4

  • eBook Packages: Springer Book Archive

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