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Journal of Mathematical Sciences

, Volume 147, Issue 4, pp 6932–6934 | Cite as

A generalization of the Chung-Erdös inequality for the probability of a union of events

  • V. V. Petrov
Article

Abstract

A generalization of the Chung-Erdös inequality for the probability of a union of arbitrary events is proved using some lower bounds for tail probabilities. We present a lower bound for the probability of appearance of at least m events from a set of events A1,..., An, where 1 ≤ m ≤ n. Bibliography: 6 titles.

Keywords

Positive Integer Lower Bound Limit Theorem Order Statistic Direct Proof 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    K. L. Chung and P. Erdös, “On the application of the Borel-Cantelli lemma,” Trans. Amer. Math. Soc., 72, 179–186 (1952).MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    V. V. Petrov, “On lower bounds for tail probabilities,” J. Statist. Planning and Inference, 137 (2007).Google Scholar
  3. 3.
    B. C. Arnold, “Some elementary variations of the Lyapunov inequality,” SIAM J. Appl. Math., 35, 117–118 (1978).MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    V. V. Petrov, “An inequality for moments of a random variable,” Teor. Veroyatn. Primen., 20, 391–392 (1975).MATHGoogle Scholar
  5. 5.
    V. V. Petrov, Limit Theorems of Probability Theory, Oxford University Press, New York (1995).MATHGoogle Scholar
  6. 6.
    W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, Wiley, New York (1970).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • V. V. Petrov
    • 1
  1. 1.St.Petersburg State UniversitySt.PetersburgRussia

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