AISM 53, 487-497

© 2001 ISM

## 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.

**Source**
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