ON MOMENTS OF BIVARIATE ORDER STATISTICS

H. M. BARAKAT

Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

(Received October 7, 1996; revised November 5, 1997)

Abstract. In the present paper, we give the exact explicit expression for the product moments (of any order) of bivariate order statistics (o.s.) from any arbitrary continuous bivariate distribution function (d.f.). Furthermore, for any arbitrary bivariate uniform d.f., universal distribution-free bounds for the differences of any two different product moments (of order (1, 1) or (−1, 1)) are given.

Key words and phrases: Bivariate order statistics, moments of order statistics, dependence function.