, Volume 28, Issue 2, pp 522–542 | Cite as

Prior-free probabilistic interval estimation for binomial proportion

  • Hezhi Lu
  • Hua JinEmail author
  • Zhining Wang
  • Chao Chen
  • Ying Lu
Original Paper


The interval estimation of a binomial proportion has been one of the most important problems in statistical inference. The modified Wilson interval, Agresti–Coull interval, and modified Jeffreys interval have good coverage probabilities among the existing methods. However, as approximation approaches, they still behave poorly under some circumstances. In this paper, we propose an exact and efficient randomized plausible interval based on the inference model and suggest the practical use of its non-randomized approximation. The randomized plausible interval is proven to have the exact coverage probability. Moreover, our non-randomized approximation is competitive with the existing approaches confirmed by the simulation studies. Three examples including a real data analysis are illustrated to portray the usefulness of our method.


Inferential model Binomial proportion Interval estimation Coverage probability Expected length 

Mathematics Subject Classification

62F25 62P10 



We thank the referees for the constructive comments that much improved the paper. The study is supported by grants from Guangdong Engineering Research Center for Data Science, Natural Science Foundation of Guangdong Province, China (2017A030313018), the Innovation Project of Graduate School of South China Normal University (2016lkwm73) and the National Institutes of Health (5UL1TR00108505 and P30 CA124435).


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2018

Authors and Affiliations

  • Hezhi Lu
    • 1
  • Hua Jin
    • 1
    • 2
    Email author
  • Zhining Wang
    • 1
  • Chao Chen
    • 1
  • Ying Lu
    • 2
    • 3
    • 4
  1. 1.School of Mathematical ScienceSouth China Normal UniversityGuangzhouPeople’s Republic of China
  2. 2.Department of Biomedical Data ScienceStanford UniversityStanfordUSA
  3. 3.Center for Innovative Study DesignStanford UniversityStanfordUSA
  4. 4.Stanford Cancer InstituteStanford UniversityStanfordUSA

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