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.
Ehm,Binomial approximation to the Poisson binomial distribution, Statistics & Probability Letters11(1) (1991) 7–16
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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.