Journal of Applied Probability

Improved Chen‒Stein bounds on the probability of a union

Sheldon M. Ross

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We improve the Chen‒Stein bounds when applied to the probability of a union. When the probability is small, the improvement in the distance from the lower to the upper bound is roughly a factor of 2. Further improvements are determined when the events of the union are either negatively or positively dependent.

Article information

Source
J. Appl. Probab., Volume 53, Number 4 (2016), 1265-1270.

Dates
First available in Project Euclid: 7 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.jap/1481132851

Mathematical Reviews number (MathSciNet)
MR3581256

Zentralblatt MATH identifier
1358.60040

Subjects
Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60E99: None of the above, but in this section

Keywords
Chen‒Stein Poisson approximation improved bounds on unions negative and positive dependencies

Citation

Ross, Sheldon M. Improved Chen‒Stein bounds on the probability of a union. J. Appl. Probab. 53 (2016), no. 4, 1265--1270. https://projecteuclid.org/euclid.jap/1481132851


Export citation

References

  • Barbour, A. D., Holst, L. and Janson, S. (1992). Poisson Approximations. Oxford University Press.
  • Block, H. W., Savits, T. H. and Shaked, M. (1982). Some concepts of negative dependence. Ann. Prob. 10, 765–772.
  • Chen, L. H. Y. (1975). Poisson approximations for dependent trials. Ann. Prob. 3, 534–545.
  • Cohen, A. and Sackrowitz, H. B. (1994). Association and unbiased tests in statistics. In Stochastic Orders and Their Applications, Academic Press, Boston, MA, pp. 251–274.
  • Janson, S. (1998). New versions of Suen's correlation inequality. Random Structures Algorithms 13, 467–483.
  • Mallows, C. (1968). An inequality involving multinomial probabilities. Biometrika 55, 422–424.
  • Ross, S. M. (2002). Probability Models for Computer Science. Academic Press, San Diego, CA.
  • Suen, W.-C. S. (1990). A correlation inequality and a Poisson limit theorem for nonoverlapping balanced subgraphs of a random graph. Random Structures Algorithms 1, 231–242.