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Projection Method for Moment Bounds on Order Statistics from Restricted Families, : II. Independent Case


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  • Gajek, Leslaw
  • Rychlik, Tomasz
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    The method of projection, proposed in Part I, is applied to derive sharp moment bounds for the expectations of order statistics based onindependentsamples from restricted families of distributions. Three families are considered: life distributions with decreasing failure density, decreasing failure rate, and symmetric unimodal ones. The respective bounds are also numerically compared with those for general populations in both the dependent and independent cases.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 64 (1998)
    Issue (Month): 2 (February)
    Pages: 156-182

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    Handle: RePEc:eee:jmvana:v:64:y:1998:i:2:p:156-182

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    Keywords: independent identically distributed random variables; decreasing failure rates; symmetric unimodal distribution; convex cone; Bernstein polynomial; variation diminishing property;


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    1. Gajek, Leslaw & Rychlik, Tomasz, 1996. "Projection Method for Moment Bounds on Order Statistics from Restricted Families: I. Dependent Case," Journal of Multivariate Analysis, Elsevier, vol. 57(1), pages 156-174, April.
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    Cited by:
    1. Tomasz Rychlik, 2014. "Non-positive upper bounds on expectations of small order statistics from DDA and DFRA populations," Metrika, Springer, vol. 77(4), pages 539-557, May.
    2. 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.
    3. Rychlik, Tomasz, 2009. "Tight evaluations for expectations of small order statistics from symmetric and symmetric unimodal populations," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1488-1493, June.
    4. Okolewski, Andrzej & Rychlik, Tomasz, 2001. "Sharp distribution-free bounds on the bias in estimating quantiles via order statistics," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 207-213, April.


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