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Maximal Expectations of Extreme Order Statistics from Increasing Density and Failure Rate Populations

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  • Tomasz Rychlik

Abstract

We determine sharp bounds for the expectations of the first and second and last order statistics for the i.i.d. samples from the increasing density and failure rate populations. These bounds are expressed by means of the population mean and standard deviation. The results are determined by use of the projections of elements of Hilbert spaces onto convex cones.

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  • Tomasz Rychlik, 2014. "Maximal Expectations of Extreme Order Statistics from Increasing Density and Failure Rate Populations," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(10-12), pages 2199-2213, May.
    • Handle: RePEc:taf:lstaxx:v:43:y:2014:i:10-12:p:2199-2213
    DOI: 10.1080/03610926.2013.783071
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    Cited by:

    1. Agnieszka Goroncy & Tomasz Rychlik, 2015. "Optimal bounds on expectations of order statistics and spacings from nonparametric families of distributions generated by convex transform order," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(2), pages 175-204, February.
    2. 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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