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.
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Barakat, H.M. The Asymptotic Distribution Theory of Bivariate Order Statistics. Annals of the Institute of Statistical Mathematics 53, 487–497 (2001). https://doi.org/10.1023/A:1014660811052
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DOI: https://doi.org/10.1023/A:1014660811052