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January, 1988 Moment and Geometric Probability Inequalities Arising from Arrangement Increasing Functions
Philip J. Boland, Frank Proschan, Y. L. Tong
Ann. Probab. 16(1): 407-413 (January, 1988). DOI: 10.1214/aop/1176991911


A real-valued function $g$ of two vector arguments $\mathbf{x}$ and $\mathbf{y} \in R^n$ is said to be arrangement increasing if it increases in value as the arrangement of components in $\mathbf{x}$ becomes increasingly similar to the arrangement of components in $\mathbf{y}$. Hollander, Proschan and Sethuraman (1977) show that the convolution of arrangement increasing functions is arrangement increasing. This result is used to generate some interesting probability inequalities of a geometric nature for exchangeable random vectors. Other geometric inequalities for families of arrangement increasing multivariate densities are also given, and some moment inequalities are obtained.


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Philip J. Boland. Frank Proschan. Y. L. Tong. "Moment and Geometric Probability Inequalities Arising from Arrangement Increasing Functions." Ann. Probab. 16 (1) 407 - 413, January, 1988.


Published: January, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0638.60013
MathSciNet: MR920281
Digital Object Identifier: 10.1214/aop/1176991911

Primary: 60D05
Secondary: 62H10

Keywords: arrangement increasing , decreasing in transposition , exchangeable random vector , family of arrangement increasing densities , Inequalities‎ , Laplace transforms , moments , permutation

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 1 • January, 1988
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