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.
Publié le : 1988-01-14
Classification:
Arrangement increasing,
decreasing in transposition,
exchangeable random vector,
family of arrangement increasing densities,
inequalities,
moments,
Laplace transforms,
permutation,
60D05,
62H10
@article{1176991911,
author = {Boland, Philip J. and Proschan, Frank and Tong, Y. L.},
title = {Moment and Geometric Probability Inequalities Arising from Arrangement Increasing Functions},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 407-413},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991911}
}
Boland, Philip J.; Proschan, Frank; Tong, Y. L. Moment and Geometric Probability Inequalities Arising from Arrangement Increasing Functions. Ann. Probab., Tome 16 (1988) no. 4, pp. 407-413. http://gdmltest.u-ga.fr/item/1176991911/