Lower bounds on the probability of a finite union of events
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In this paper, lower bounds on the probability of a finite union of events are considered, i.e., P(UNi=1Ai, in terms of the individual event probabilities {P(Ai), i = 1, ... ,N} and the sums of the pairwise event probabilities, i.e., {Σj:j≠i P(Ai ∩ Aj), i = 1, ... ,N}. The contribution of this paper includes the following: (i) in the class of all lower bounds that are established in terms of only the P(Ai)'s and σj:j≠ij P(Ai ≠ Aj)'s, the optimal lower bound is given numerically by solving a linear programming (LP) problem with N2 - N + 1 variables; (ii) a new analytical lower bound is proposed based on a relaxed LP problem, which is at least as good as the bound due to Kuai, Alajaji, and Takahara [Discrete Math., 215 (2000), pp. 147-158]; (iii) numerical examples are provided to illustrate the performance of the bounds.
Originalsprog | Engelsk |
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Tidsskrift | SIAM Journal on Discrete Mathematics |
Vol/bind | 30 |
Udgave nummer | 3 |
Sider (fra-til) | 1437-1452 |
Antal sider | 16 |
ISSN | 0895-4801 |
DOI | |
Status | Udgivet - 2016 |
Eksternt udgivet | Ja |
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