Skip to main content

Univariate and Multivariate Bonferroni-Type Inequalities: Methods for Proof and Questions of Optimality

  • Chapter
Probability Theory and Applications

Part of the book series: Mathematics and Its Applications ((MAIA,volume 80))

Abstract

For a sequence A 1,A 2,… ,A n of events, we denote by m n(A) the number of those which occur. The binomial moments of m n(A) are denoted by S k = S k,n(A), that is, (1).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Galambos J., Methods for proving Bonferroni-type inequalities, J. London Math.Soc., (2) 9 (1975), 561–564.

    Article  MathSciNet  MATH  Google Scholar 

  2. Galambos J., The Asymptotic Theory of Extreme Order Statistics, 2nd ed., Krieger, Melbourne, Florida, 1987.

    MATH  Google Scholar 

  3. Galambos J. and Lee M.-Y., Extensions of some univariate Bonferroni-type inequalities to multivariate setting, Probability Theory and Applications, eds.: J. Galambos and I. Kátai, Kluwer, Dordrecht, 1992, 143–154.

    Chapter  Google Scholar 

  4. Galambos J. and Mucci R., Inequalities for linear combinations of binomial moments, Publ.Math.Debrecen, 27 (1980), 263–268.

    MathSciNet  MATH  Google Scholar 

  5. Galambos J. and Xu Y., A new method for generating Bonferroni-type inequalities by iteration, Math.Proc. Cambridge Philos. Soc., 107 (1990), 601–607.

    Article  MathSciNet  MATH  Google Scholar 

  6. Galambos J. and Xu Y., Some optimal bivariate Bonferroni-type bounds, Proc.Amer.Math.Soc., to appear in 1992.

    Google Scholar 

  7. Hoppe F.M. and Seneta E., Bonferroni-type inequalities and the methods of indicators and polynomials, Adv.Appl.Probab., 22 (1990), 241–246.

    Article  MathSciNet  MATH  Google Scholar 

  8. Lee M.-Y., Bivariate Bonferroni inequalities, Aequationes Math., 1991, to appear.

    Google Scholar 

  9. Prékopa A., Sharp bounds on probabilities using linear programming, Operations Res., 38 (1990), 227–239.

    Article  MATH  Google Scholar 

  10. Rényi A., Egy általános módszer valoszűnségszámítási tételek bizonyítására, MTA III.Oszt.Közl, 11 (1961), 79–105.

    MATH  Google Scholar 

  11. Sibuya M., Bonferroni-type inequalities; Chebyshev-type inequalities for the distributions on [0,n], Ann.Inst.Statist.Math., 43 (1991), 261–285.

    Article  MathSciNet  MATH  Google Scholar 

  12. Xu Y., Bonferroni-type inequalities via interpolating polynomials, Proc. Amer.Math.Soc., 107 (1989), 825–831.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Galambos, J., Xu, Y. (1992). Univariate and Multivariate Bonferroni-Type Inequalities: Methods for Proof and Questions of Optimality. In: Galambos, J., Kátai, I. (eds) Probability Theory and Applications. Mathematics and Its Applications, vol 80. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2817-9_10

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-2817-9_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5252-8

  • Online ISBN: 978-94-011-2817-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics