New lower bounds are proven for P(H ≥ E[H]) in the hypergeometric distribution, including a simple bound of k/n when n ≥ 8k and a variance-based bound under additional conditions.
Siegel,Median bounds and their application, Journal of Algorithms38(1) (2001) 184–236
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On lower bounds for hypergeometric tails
New lower bounds are proven for P(H ≥ E[H]) in the hypergeometric distribution, including a simple bound of k/n when n ≥ 8k and a variance-based bound under additional conditions.