COMPUTING THE MOMENTS OF BIVARIATE AND TRIVARIATE ORDER STATISTICS

摘要

The most of the material of this article is an overview of principle results in and related to the computing of the product moments (of any order) of bivariate (and trivariate) order statistics arisen from any arbitrary bivariate (and trivariate) distribution function. The exact explicit expression, as well as formulae to compute easily these moments are presented. Some recent analytic bootstrap-type methods for estimating these moments are exhibited. In addition, universal distribution -free bounds for the differences of any two different product moments and general recurrence relations satisfied by the product moments (of any order) are discussed. Finally, a recent general bivariate and trivariate versions of the basic triangle rule for order statistics arisen from univariate distribution function is presented.