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Unimodality of uniform generalized order statistics, with applications to mean bounds

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Abstract

We prove that uniform generalized order statistics are unimodal for an arbitrary choice of model parameters. The result is applied to establish optimal lower and upper bounds on the expectations of generalized order statistics based on nonnegative samples in the population mean unit of measurement. The bounds are attained by two-point distributions.

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Authors and Affiliations

  1. Institute of Mathematics, University of Oldenburg, PO Box 2503, D-26111, Oldenburg, Germany

    Erhard Cramer & Udo Kamps

  2. Institute of Mathematics, Polish Academy of Sciences, Chopina 12, 87100, Toruń, Poland

    Tomasz Rychlik

Authors
  1. Erhard Cramer
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  2. Udo Kamps
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  3. Tomasz Rychlik
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Cramer, E., Kamps, U. & Rychlik, T. Unimodality of uniform generalized order statistics, with applications to mean bounds. Ann Inst Stat Math 56, 183–192 (2004). https://doi.org/10.1007/BF02530531

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  • DOI: https://doi.org/10.1007/BF02530531

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