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Negative dependence and stochastic ordering
Fri 17 May 2013, 15:40
Fraser Daly
Bristol
Organisers: Nick Whiteley, Feng Yu
ABSTRACT
We let $W$ be a non-negative, integer-valued random variable. We consider those $W$ which satisfy a certain stochastic ordering inequality which is closely related to several well-known concepts of negative dependence. This class of random variables includes sums of negatively related or totally negatively dependent indicators, and also includes ultra-log concave random variables. Within this class of negatively dependent random variables, we may find a straightforward upper bound on the total variation distance between $W$ and a Poisson distribution with the same mean. We also have an upper bound on the Poincar\'e (inverse spectral gap) constant of $W$. Finally, such $W$ are smaller (in the convex sense) than a Poisson distribution of the same mean.