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Optimal evaluations for the bias of trimmed means of $$k$$ k th record values

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  • Mariusz Bieniek

Abstract

We provide sharp upper and lower mean-variance bounds on the expectations of trimmed means of $$k$$ k th record values from general family of distributions. Also we improve these bounds in the case of non-trimmed means for parent distributions with decreasing density or decreasing failure rate. They can be viewed as bounds on the bias of approximation of expectation of the parent population by mean or trimmed mean of record values. The results are illustrated with numerical examples. Copyright The Author(s) 2015

Suggested Citation

  • Mariusz Bieniek, 2015. "Optimal evaluations for the bias of trimmed means of $$k$$ k th record values," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(4), pages 437-460, May.
    • Handle: RePEc:spr:metrik:v:78:y:2015:i:4:p:437-460
    DOI: 10.1007/s00184-014-0511-y
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    References listed on IDEAS

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    1. 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.
    2. Raqab, Mohammad Z., 1997. "Bounds based on greatest convex minorants for moments of record values," Statistics & Probability Letters, Elsevier, vol. 36(1), pages 35-41, November.
    3. Katarzyna Danielak & Tomasz Rychlik, 2003. "Theory & Methods: Exact Bounds for the Bias of Trimmed Means," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 45(1), pages 83-96, March.
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