Inequalities for Multivariate Infinitely Divisible Processes
Lawrence D. Brown,Yosef Rinott +1 more
TLDR
In this article, a general class of multivariate infinitely divisible distributions and their related stochastic processes are described, and inequalities which are the analogs of Slepian's inequality for these distributions are applied to the distributions of $M/G/ ∞$ queues and of sample cumulative distribution functions for independent multivariate random variables.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 $M/G/\infty$ queues and of sample cumulative distribution functions for independent multivariate random variables.read more
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Bibliography on stable distributions, processes and related topics
TL;DR: The following sections are a start on organizing references on stable distributions by topic, and please provide all references in BibTeX form, especially if you have more than one or two additions.
Journal ArticleDOI
Criteria for the stochastic ordering of random sums, with actuarial applications
TL;DR: In this article, it was shown that vectors (S M 1, S Mn ) and (S' M'1, M n ) of random sums of positive random variables are stochastically ordered by upper orthant dependence, lower orthant dependency, concordance or by the supermodular ordering whenever their corresponding random numbers of terms (M 1, …, M n ), and (M' 1,...,..., M' n ) are themselves ordered in this fashion.
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Positive dependence orders: a survey
Marco Scarsini,Moshe Shaked +1 more
TL;DR: A survey of positive dependence orders can be found in this article, where some of these notions are based on some comparison of the joint distribution of X and Y with their distribution under the theoretical assumption that X and y are independent.
Journal ArticleDOI
A multivariate extension of poisson's theorem
TL;DR: For n ≥ 1, the convergence of the distribution of Sn to a Poisson distribution under general conditions was shown in this paper, where the authors extended this result to the multidimensional case.
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