Reverse Exchangeability and Extreme Order Statistics

Jiang, Yindeng, yindeng@uw.edu; Perlman, Michael D., michael@stat.washington.edu

doi:10.1214/12-IMSCOLL1005

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VOL. 10 | 2013 Reverse Exchangeability and Extreme Order Statistics

Yindeng Jiang, Michael D. Perlman

Editor(s) Galin Jones, Xiaotong Shen

Inst. Math. Stat. (IMS) Collect., 2013: 83-101 (2013) DOI: 10.1214/12-IMSCOLL1005

Abstract

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 $(X_{1},\ldots ,X_{n})$ are also given.