Decreasing in transposition property of overlapping sums, and applications

In this paper a large class of multivariate densities and frequency functions, including the multivariate Poisson distribution and the compound multivariate Poisson distribution, are shown to have the decreasing in transposition property introduced by [4], Ann. Statist. 5, 722-733). Sample applications in ecology and reliability are given; other applications to cumulation of damage and component down times are mentioned, but are not presented in detail.