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arXiv · 1408.0294

Large deviation upper bounds for sums of positively associated indicators

Matthias Löwe·Franck Vermet
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Abstract

We give exponential upper bounds for $P(S \le k)$, in particular $P(S=0)$, where $S$ is a sum of indicator random variables that are positively associated. These bounds allow, in particular, a comparison with the independent case. We give examples in which we compare with a famous exponential inequality for sums of correlated indicators, the Janson inequality. Here our bound sometimes proves to be superior to Janson's bound.

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Matthias Löwe, Franck Vermet. 2014-08-01. Large deviation upper bounds for sums of positively associated indicators. https://arxiv.org/abs/1408.0294

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