Sharp Bounds for the Probability of the Union of Events Under Unimodality Condition
Keywords:
Binomial moment problem, linear programming, bounding probabilities, discrete unimodality, reliabilityAbstract
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 withknown 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.
Downloads
Issue
Section
Mathematical Analysis
License
Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.
European Journal of Pure and Applied Mathematics will be Copyright Holder.
How to Cite
Sharp Bounds for the Probability of the Union of Events Under Unimodality Condition. (2007). European Journal of Pure and Applied Mathematics, 1(1), 60-81. https://www.ejpam.com/index.php/ejpam/article/view/87