EXACT BOUNDS FOR THE EXPECTATIONS OF ORDER STATISTICS FROM NON-NEGATIVE POPULATIONS

NICKOS PAPADATOS

Department of Mathematics, Section of Statistics and Operations Research, University of Athens, Panepistemiopolis, 157 84 Athens, Greece

(Received March 22, 1995; revised November 21, 1996)

Abstract. Some new exact bounds for the expected values of order statistics, under the assumption that the parent population is non-negative, are obtained in terms of the population mean. Similar bounds for the differences of any two order statistics are also given. It is shown that the existing bounds for the general case can be improved considerably under the above assumption.

Key words and phrases: Exact bounds, expectations, order statistics, nonnegative populations.