Optimal mean-variance bounds on order statistics from families determined by star ordering
Volume 29 / 2002
Applicationes Mathematicae 29 (2002), 15-32
MSC: 60E15, 62G30, 62N05.
DOI: 10.4064/am29-1-3
Abstract
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.
