The Annals of Probability

Moment and Geometric Probability Inequalities Arising from Arrangement Increasing Functions

Philip J. Boland, Frank Proschan, and Y. L. Tong

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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.

Article information

Ann. Probab., Volume 16, Number 1 (1988), 407-413.

First available in Project Euclid: 19 April 2007

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Zentralblatt MATH identifier


Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 62H10: Distribution of statistics

Arrangement increasing decreasing in transposition exchangeable random vector family of arrangement increasing densities inequalities moments Laplace transforms permutation


Boland, Philip J.; Proschan, Frank; Tong, Y. L. Moment and Geometric Probability Inequalities Arising from Arrangement Increasing Functions. Ann. Probab. 16 (1988), no. 1, 407--413. doi:10.1214/aop/1176991911.

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