Abstract
Probability that exactly k-out-of-n events occur, where the underlying probability distribution is known to be unimodal, is formulated as binomial moment problems. Dual feasible basis structures of the corresponding linear programs are fully described. Closed form bounds based on the first two binomial moments are presented. A dual simplex method based algorithm is developed to obtain robust and efficiently computable bounds for the probability that exactly k-out-of-n events occur based on the first m binomial moments, where the underlying probability distribution is assumed to be unimodal with known mode.
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