Sharp Bounds for the Probability of the Union of Events Under Unimodality Condition

Andra's Pre'kopa, Mine Subasi, Ersoy Subasi

Abstract

Linear programming problem is formulated for bounding the probability of the union of events, where the probability distribution of the occurrences is supposed to be unimodal with
known mode and some of the binomial moments of the events are also known. Using a theorem on combinatorial determinants the dual feasible bases of a relaxed problem are fully described. The bounds for the probability of the union are presented in the form of formulas as well as the results of customized algorithmic solution of the LPs involved.

Keywords

Binomial moment problem, linear programming, bounding probabilities, discrete unimodality, reliability

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