1. Institute of Mathematics , Technical University of Lodz , Lodz, Poland kaluszka@p.lodz.pl;3. Institute of Mathematics , Technical University of Lodz , Lodz, Poland
Abstract:
ABSTRACT We present sharp bounds for expectations of generalized order statistics with random indices. The bounds are expressed in terms of logarithmic moments EXa (log max {1, X})b of the underlying observation X. They are attainable and provide characterizations of some non trivial distributions. No restrictions are imposed on the parameters of the generalized order statistics model.