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On Logarithmic Approximations for the One-Sided Binomial Confidence Interval

  • Lonnie TurpinJr.
  • William JensJr.
Article
  • 58 Downloads

Abstract

A one-sided binomial confidence interval occurs when all trials are successful or unsuccessful. This research considers the case when all trials are successful, and derives logarithmic approximations for the variable lower-bound under two common significance levels. We then establish ranges on the sample size for which the absolute differences between the approximations and the exact lower-bound are less than the chosen level.

Keywords

One-sided binomial confidence interval Logarithmic approximation Optimization 

Mathematics Subject Classification

62F25 90C30 

Notes

Acknowledgements

The authors would like to thank the Editor and the anonymous referees for their insightful comments, which greatly improved the presentation of this work.

References

  1. 1.
    Louis, T.: Confidence intervals for a binomial parameter after observing no successes. Am. Stat. 35, 154–154 (1981)Google Scholar
  2. 2.
    Bickel,.P., Doksum, K.: Mathematical Statistics: Basic Ideas and Selected Topics. CRC Press, Boca Raton (2015)zbMATHGoogle Scholar
  3. 3.
    Hall, P.: Improving the normal approximation when constructing one-sided confidence intervals for binomial or Poisson parameters. Biometrika 69, 647–652 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Hanley, J., Lippman-Hand, A.: If nothing goes wrong, is everything all right? Interpreting zero numerators. J. Am. Med. Assoc. 249, 1743–1745 (1983)CrossRefGoogle Scholar
  5. 5.
    Jovanovic, B., Levy, P.: A look at the rule of three. Am. Stat. 51, 137–139 (1997)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.McNeese State UniversityLake CharlesUSA

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