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Sharp bounds for the probability of union of n events when m number of binomial moments are known

  • V. Kumaran
  • R. SwarnalathaEmail author
Research Article

Abstract

In this paper sharp bounds for the probability of union of n arbitrary events following unknown probability distribution are found, when only \(m(m < n)\) out of n binomial moments of the events are given. The bounds are found using a class of special matrices and their inverses. Generalized closed form probabilistic bounds are found for the probability of occurrence of at least r out of n events by using the same class of matrices and their inverses. In numerical examples section the parameter r is studied and tables are given to depict the effect of r over the sharp bounds. As an application, MAXSAT problem is also discussed and the effect of using relatively higher binomial moments over the chance of having the optimal upper bound less than 1 is discussed.

Keywords

Discrete moment problem Matrix inverse Binomial moment 

Mathematics Subject Classification

60E15 90C05 90C15 15A09 

Notes

Acknowledgements

The second author thanks MHRD and National Institute of Technology, Tiruchirappalli, India for financial support.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsNational Institute of TechnologyTiruchirappalliIndia

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