Optimal mean-variance bounds on order statistics from families determined by star ordering

Volume 29 / 2002

Tomasz Rychlik Applicationes Mathematicae 29 (2002), 15-32 MSC: 60E15, 62G30, 62N05. DOI: 10.4064/am29-1-3


We present optimal upper bounds for expectations of order statistics from i.i.d. samples with a common distribution function belonging to the restricted family of probability measures that either precede or follow a given one in the star ordering. The bounds for families with monotone failure density and rate on the average are specified. The results are obtained by projecting functions onto convex cones of Hilbert spaces.


  • Tomasz RychlikInstitute of Mathematics
    Polish Academy of Sciences
    Chopina 12
    87-100 Toruń, Poland

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