Table of Contents
ISRN Probability and Statistics
Volume 2013 (2013), Article ID 412958, 6 pages
http://dx.doi.org/10.1155/2013/412958
Research Article

Improved Inequalities for the Poisson and Binomial Distribution and Upper Tail Quantile Functions

Electronics & Control Group, Teesside University, Middlesbrough TS1 3BA, UK

Received 29 October 2013; Accepted 25 November 2013

Academic Editors: V. Makis and A. Volodin

Copyright © 2013 Michael Short. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. N. L. Johnson, A. W. Kemp, and S. Kotz, Univariate Discrete Distributions, Wiley-Interscience, New York, NY, USA, 3rd edition, 2005.
  2. N. Alon and A. J. Spencer, Probabilistic Method, John Wiley & Sons, New York, NY, USA, 2nd edition, 2000.
  3. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, 1992.
  4. W. Mollenaar, Normal Approximations to the Poisson, Binomial and Hypergeometric Functions, Tract 31, Amsterdam Mathematics Center, 1973.
  5. A. M. Zubkov and A. A. Serov, “A complete proof of universal inequalities for distribution function of binomial law,” Teoriya Veroyatnostei i ee Primeneniya, vol. 57, no. 3, pp. 597–602, 2012. View at Publisher · View at Google Scholar
  6. T. Hagerup and C. Rüb, “A guided tour of chernoff bounds,” Information Processing Letters, vol. 33, no. 6, pp. 305–308, 1990. View at Publisher · View at Google Scholar · View at Scopus
  7. W. Hoeffding, “Probability inequalities for sums of bounded random variables,” Journal of the American Statistical Association, vol. 58, no. 301, pp. 13–30, 1963. View at Publisher · View at Google Scholar
  8. M. Short and J. Proenza, “Towards efficient probabilistic scheduling guarantees for real-time systems subject to random errors and random bursts of errors,” in Proceedings of the 25th Euromicro Conference on Real-Time Systems (ECRTS '13), pp. 259–268, Paris, France, July 2013.
  9. Y. Li and L. Wang, “Testing for homogeneity in mixture using weighted relative entropy,” Communications in Statistics, vol. 37, no. 10, pp. 1981–1995, 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. S. Janson, “Large deviation inequalities for sums of indicator variables,” Tech. Rep., Department of Mathematics, Uppsala University, Uppsala, Sweden, 1994, http://www.math.uu.se/~svante/papers/index.html. View at Google Scholar
  11. M. J. Wichura, “Algorithm AS 241: the percentage points of the normal distribution,” Applied Statistics, vol. 37, no. 3, pp. 477–484, 1988. View at Publisher · View at Google Scholar
  12. R. D. Gordon, “Values of Mills' ratio of area bounding ordinate and of the normal probability integral for large values of the argument,” Annals of Mathematical Statistics, vol. 12, no. 3, pp. 364–366, 1941. View at Publisher · View at Google Scholar
  13. M. Chiani, D. Dardari, and M. K. Simon, “New exponential bounds and approximations for the computation of error probability in fading channels,” IEEE Transactions on Wireless Communications, vol. 2, no. 4, pp. 840–845, 2003. View at Publisher · View at Google Scholar · View at Scopus
  14. P. S. Bullen, A Dictionary of Inequalities, Addison Wesley/Longman, 1998.