Abstract
AbstractLet X1,…,Xn be exchangeable normal variables with a common correlation p, and let X(1) > … > X(n) denote their order statistics. The random variable σni=n—k+1xi, called the selection differential by geneticists, is of particular interest in genetic selection and related areas. In this paper we give results concerning a conjecture of Tong (1982) on the distribution of this random variable as a function of ρ. The same technique used can be applied to yield more general results for linear combinations of order statistics from elliptical distributions.
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