Volume 20, 2016
|Page(s)||45 - 65|
|Published online||14 July 2016|
Negative dependence and stochastic orderings
Department of Actuarial Mathematics and Statistics and the Maxwell Institute
for Mathematical Sciences, School of Mathematical and Computer Sciences, Heriot-Watt
University, Edinburgh EH14 4AS, UK.
Revised: 17 June 2015
Accepted: 19 January 2016
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.
Mathematics Subject Classification: 60E15 / 62E17 / 62E10 / 94A17
Key words: Thinning / size biasing / s-convex ordering / Poisson approximation / entropy
© EDP Sciences, SMAI 2016
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