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.
Pokrovskiy,A linear bound on the Manickam–Mikl´ os–Singhi conjecture, J
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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.