Negative dependence and stochastic orderings

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Abstract

We explore negative dependence and stochastic orderings, showing that if an integer-valued random variable $W$ satisfies a certain negative dependence assumption, then $W$ is smaller (in the convex sense) than a Poisson variable of equal mean. Such $W$ include those which may be written as a sum of totally negatively dependent indicators. This is generalised to other stochastic orderings. Applications include entropy bounds, Poisson approximation and concentration. The proof uses thinning and size-biasing. We also show how these give a different Poisson approximation result, which is applied to mixed Poisson distributions. Analogous results for the binomial distribution are also presented.
Original languageEnglish
Pages (from-to)45-65
Number of pages21
JournalESAIM: Probability and Statistics
Volume20
DOIs
Publication statusPublished - 14 Jul 2016

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