Statistics Papers

Document Type

Journal Article

Date of this Version

1988

Publication Source

The Annals of Probability

Volume

16

Issue

2

Start Page

642

Last Page

657

DOI

10.1214/aop/1176991777

Abstract

We describe a general class of multivariate infinitely divisible distributions and their related stochastic processes. Then we prove inequalities which are the analogs of Slepian's inequality for these distributions. These inequalities are applied to the distributions of M/G/∞ queues and of sample cumulative distribution functions for independent multivariate random variables.

Keywords

Slepian's inequality, infinitely divisible distributions, multivariate Poisson distribution, queuing theory, multivariate sample cumulative distribution functions

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Date Posted: 27 November 2017

This document has been peer reviewed.