We explore negative dependence and stochastic orderings, showing that if an integer-valued random variable satisfies a certain negative dependence assumption, then is smaller (in the convex sense) than a Poisson variable of equal mean. Such 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.
Accepté le :
DOI : 10.1051/ps/2016002
Mots-clés : Thinning, size biasing, s-convex ordering, Poisson approximation, entropy
@article{PS_2016__20__45_0, author = {Daly, Fraser}, title = {Negative dependence and stochastic orderings}, journal = {ESAIM: Probability and Statistics}, pages = {45--65}, publisher = {EDP-Sciences}, volume = {20}, year = {2016}, doi = {10.1051/ps/2016002}, mrnumber = {3528617}, zbl = {1384.60058}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps/2016002/} }
Daly, Fraser. Negative dependence and stochastic orderings. ESAIM: Probability and Statistics, Tome 20 (2016), pp. 45-65. doi : 10.1051/ps/2016002. http://www.numdam.org/articles/10.1051/ps/2016002/
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