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Supermodular ordering of Poisson and binomial random vectors by tree-based correlations

Kızıldemir B., Privault N.

Probability and Mathematical Statistics

2018

Vol. 38, Fasc. 2

385--405

We construct a dependence structure for binomial, Poisson and Gaussian random vectors, based on partially ordered binary trees and sums of independent random variables. Using this construction, we characterize the supermodular ordering of such random vectors via the componentwise ordering of their covariance matrices. For this, we apply Möbius inversion techniques on partially ordered trees, which allow us to connect the Lévy measures of Poisson random vectors on the discrete d-dimensional hypercube to their covariance matrices.

A study on the performance measures of a system operated in random environment

Cha J. H., Mi J.

Journal of Polish Safety and Reliability Association

2007

Vol. 1

55--58

Most devices (systems) are operated under different environmental conditions. The failure process of a system not only depends on the intrinsic characteristic of the system itself but also on the external environmental conditions under which the system is being operated. In this article we study a stochastic failure model in random environment and investigate the effect of the environmental factors on the failure process of the system. Some stochastic orderings will also be briefly discussed.