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Non-positive upper bounds on expectations of small order statistics from DDA and DFRA populations

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  • Tomasz Rychlik

Abstract

Rychlik [Appl Math (Warsaw) 29:15–32, 2002 ] presented positive sharp upper bounds on the expectations of order statistics with sufficiently large ranks, based on i.i.d. samples from the decreasing density and failure rate populations (DDA and DFRA, for short). They were expressed in terms of the population mean and standard deviation. Here we provide respective non-positive upper tight evaluations for expected small order statistics centered about the population mean, measured in various scale units. Copyright The Author(s) 2014

Suggested Citation

  • Tomasz Rychlik, 2014. "Non-positive upper bounds on expectations of small order statistics from DDA and DFRA populations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(4), pages 539-557, May.
    • Handle: RePEc:spr:metrik:v:77:y:2014:i:4:p:539-557
    DOI: 10.1007/s00184-013-0452-x
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    References listed on IDEAS

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    1. Danielak, Katarzyna & Rychlik, Tomasz, 2003. "Sharp bounds for expectations of spacings from DDA and DFRA families," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 303-316, December.
    2. Gajek, Leslaw & Rychlik, Tomasz, 1998. "Projection Method for Moment Bounds on Order Statistics from Restricted Families, : II. Independent Case," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 156-182, February.
    3. Arnold, Barry C., 1985. "p-Norm bounds on the expectation of the maximum of a possibly dependent sample," Journal of Multivariate Analysis, Elsevier, vol. 17(3), pages 316-332, December.
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