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Reverse exchangeability and extreme order statistics. (English) Zbl 1320.62110

Jones, Galin (ed.) et al., Advances in modern statistical theory and applications. A Festschrift in honor of Morris L. Eaton. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 978-0-940600-84-3). Institute of Mathematical Statistics Collections 10, 83-101 (2013).
Summary: For a bivariate random vector \((X,Y)\), symmetry conditions are presented that yield stochastic orderings among \(|X|\), \(|Y|\), \(|\max(X,Y)|\), and \(|\min(X,Y)|\). Partial extensions of these results for multivariate random vectors \((X_1,\dots,X_n)\) are also given.
For the entire collection see [Zbl 1319.62004].

MSC:

62G32 Statistics of extreme values; tail inference
62G30 Order statistics; empirical distribution functions
60E15 Inequalities; stochastic orderings
62H05 Characterization and structure theory for multivariate probability distributions; copulas
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