THE ASYMPTOTIC DISTRIBUTION THEORY OF BIVARIATE ORDER STATISTICS

H. M. BARAKAT

Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt, e-mail: hbarakat2@hotmail.com

(Received July 30, 1998; revised February 28, 2000)

Abstract. In this paper the limit distribution function (d.f.) of general bivariate order statistics (o.s.) (extreme, intermediate and central) is studied by the notion of the exceedances of levels and characteristic function (c.f.) technique. The advantage of this approach is to give a simple and unified method to derive the limit d.f. of any bivariate o.s. The conditions under which the limit d.f. splits into the product of the limit marginals are obtained. Some illustrative examples are given.

Key words and phrases: Bivariate order statistics, exceedance of level, increasing rank.