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
Keywords: Thinning, size biasing, s-convex ordering, Poisson approximation, entropy
Daly, Fraser 1
@article{PS_2016__20__45_0,
author = {Daly, Fraser},
title = {Negative dependence and stochastic orderings},
journal = {ESAIM: Probability and Statistics},
pages = {45--65},
year = {2016},
publisher = {EDP Sciences},
volume = {20},
doi = {10.1051/ps/2016002},
mrnumber = {3528617},
zbl = {1384.60058},
language = {en},
url = {https://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
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