Geodesic
Negative dependence and stochastic orderings
Daly, Fraser1
1 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.
ESAIM: Probability and Statistics, Tome 20 (2016), pp. 45-65

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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.

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Accepté le :
DOI : 10.1051/ps/2016002
Classification : 60E15, 62E17, 62E10, 94A17
Keywords: Thinning, size biasing, s-convex ordering, Poisson approximation, entropy

Daly, Fraser 1

1 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. 
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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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