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.
|Number of pages||21|
|Journal||ESAIM: Probability and Statistics|
|Publication status||Published - 14 Jul 2016|