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Sharp bounds for expectations of spacings from DDA and DFRA families

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  • Danielak, Katarzyna
  • Rychlik, Tomasz

Abstract

We present sharp upper bounds for the expectations of spacings from i.i.d. samples coming from restricted families of distributions. Two families are considered: distributions with decreasing density on the average and with decreasing failure rate on the average. We also characterize the distributions attaining the bounds. The results are obtained by projecting functions onto convex cones in Hilbert spaces.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:65:y:2003:i:4:p:303-316
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    References listed on IDEAS

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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.
    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.
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    Cited by:

    1. Paweł Marcin Kozyra & Tomasz Rychlik, 2017. "Lower and upper bounds on the variances of spacings," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 417-428, April.
    2. 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.
    3. Agnieszka Goroncy & Tomasz Rychlik, 2016. "Evaluations of expectations of order statistics and spacings based on IFR distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(6), pages 635-657, August.

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