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Inequalities for the partial sums of elliptical order statistics related to genetic selection
Author(s) -
Fang KaiTai,
Liang JiaJuang
Publication year - 1989
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315483
Subject(s) - mathematics , selection (genetic algorithm) , random variable , statistics , order statistic , conjecture , order (exchange) , combinatorics , variable (mathematics) , distribution (mathematics) , mathematical analysis , computer science , artificial intelligence , finance , economics
Let X 1 ,…, X n be exchangeable normal variables with a common correlation p, and let X (1) > … > X ( n ) denote their order statistics. The random variable σ n i = n — k+1 x i , 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.