Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

A Short Consideration of Binomial Confidence Interval

이항신뢰구간에 대한 소고

  • Ryu, Jea-Bok (Division of Life Science.Genetic Engineering.Statistics, Cheongju University)
  • 류제복 (청주대학교 생명.유전.통계학부)
  • Published : 2009.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

The interval estimation for binomial proportion has been treated practically as well as theoretically for a long time. In this paper we compared the properties of major confidence intervals and summarized current issues for coverage probability and interval length which are the criteria of evaluation for confidence interval. Additionally, we examined the three topics which were considered in using the binomial confidence interval in the field. And finally we discussed the future studies for a low binomial proportion.

이항비율에 대한 구간추정의 문제는 오래전부터 많이 다루어져 왔다. 본 논문에서는 주요 신뢰구간들의 특성을 비교하고 신뢰구간의 평가기준인 포함확률과 신뢰구간의 길이에 대해 이제까지 다루어져온 문제들을 종합 정리해 보았다. 실제로 이항신뢰구간 문제를 다룰 때 고려해야 할 3가지 추가 사항들을 살펴보고, 이항비율 추정에 늘 문제가 되는 낮은 이항비율에 대한 향후 논의 사항들을 제시하였다.

Keywords

References

  1. 류제복, 이승주 (2006). 낮은 이항 비율에 대한 신뢰구간, <응용통계연구>, 19, 217-230 https://doi.org/10.5351/KJAS.2006.19.2.217
  2. 이승천 (2005). 이항비율의 가중 Polya Posterior 구간추정, <응용통계연구>, 18, 607-615 https://doi.org/10.5351/KJAS.2005.18.3.607
  3. Agresti, A. and Coull, B. A. (1998). Approximate is better than “Exact” for interval estimation of Binomial proportions, The American Statistician, 52, 119-126 https://doi.org/10.2307/2685469
  4. Angus, J. E. and Schafer, R. E. (1984). Improved confidence statements for the Binomial parameter, The American Statistician, 38, 189-191 https://doi.org/10.2307/2683650
  5. Berry, G. and Armitage, P. (1995). Mid-P confidence intervals: A brief review, The Statistician, 44, 417-423 https://doi.org/10.2307/2348891
  6. Blyth, C. R. and Still, H. A. (1983). Binomial confidence intervals, Journal of the American Statistical Association, 78, 108-116 https://doi.org/10.2307/2287116
  7. Borkowf, C. B. (2006). Constructing binomial confidence intervals with near nominal coverage by adding a single imaginary failure or success, Statistics in Medicine, 25, 3679-3695 https://doi.org/10.1002/sim.2469
  8. Brown, L. D., Cai, T. T. and DasGupta, A. (2001). Interval estimation for a binomial proportion (with discussion), Statistical Science, 16, 101-133 https://doi.org/10.1214/ss/1009213286
  9. Brown, L. D., Cai, T. T. and DasGupta, A. (2002). Confidence intervals for a binomial proportion and asymptotic expansions, The Annals of Statistics, 30, 160-201 https://doi.org/10.1214/aos/1015362189
  10. Brown, L. D., Cai, T. T. and DasGupta, A. (2003). Interval estimation in exponential families, Statistica Sinica, 13, 19-49
  11. Casella, G. (1986). Refining binomial confidence intervals, The Canadian Journal of Statistics, 14, 113-129 https://doi.org/10.2307/3314658
  12. Clopper, C. J. and Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial, Biometrika, 26, 403-413 https://doi.org/10.1093/biomet/26.4.404
  13. Crow, E. L. (1956). Confidence intervals for a proportion, Biometrika, 43, 423-435 https://doi.org/10.1093/biomet/43.3-4.423
  14. Ghosh, B. K. (1979). A comparison of some approximate confidence intervals for the Binomial parameter, Journal of the American Statistical Association, 74, 894-900 https://doi.org/10.2307/2286420
  15. Gray, A., Haslett, S. and Kuzmicich, G. (2004). Confidence intervals for proportions estimated from com-plex sample designs, Journal of Official Statistics, 20, 705-723
  16. Hanley, J. A. and Lippman-Hand, A. (1983). If nothing goes wrong, Is everything all right?, Journal of the American Medical Association, 249, 1743-1745 https://doi.org/10.1001/jama.249.13.1743
  17. Jovanovic, B. D. and Levy, P. S. (1997). A look at the rule of three, The American Statistician, 51, 137-139 https://doi.org/10.2307/2685405
  18. Koit, P. S., Andersson, P. G. and Nerman, O. (2001). Two-sided coverage intervals for small proportions based on survey data, Federal Committee on Statistical Methodology Research Conference, 2001
  19. Leemis, L. M. and Trivedi, K. S. (1996). A comparison of approximate interval estimators for the bernoulli parameters, The Amnerican Statistician, 50, 63-68 https://doi.org/10.2307/2685046
  20. Miao, W. and Gastwirth, J. L. (2004). The effect of dependence on confidence intervals for a population proportion, The American Statistician, 58, 124-130 https://doi.org/10.1198/0003130043303
  21. Newcombe, R. G. (1998). Two-sided confidence intervals for the single proportion: Comparison of seven methods, Statistics in Medicine, 17, 857-872 https://doi.org/10.1002/(SICI)1097-0258(19980430)17:8<857::AID-SIM777>3.0.CO;2-E
  22. Reiczigel, J. (2003). Confidence intervals for a binomial parameter: Some new considerations, Statistics in Medicine, 22, 611-621 https://doi.org/10.1002/sim.1320
  23. Santner, T. J. (1998). Teaching large-sample Binomial confidence intervals, Teaching Statistics, 20, 20-23 https://doi.org/10.1111/j.1467-9639.1998.tb00753.x
  24. Schader, M. and Schmid, F. (1990). Charting small sample characteristics of asymptotic confidence inter-vals for the binomial parameter p, Statistical Papers, 31, 251-264 https://doi.org/10.1007/BF02924698
  25. Stein, C. (1985). On the coverage probability of confidence sets based on a prior distribution, Sequential Methods in Statistics, 16, 485-514
  26. Sterne, T. E. (1954). Some remarks on confidence or fiducial limits, Biometrika, 41, 275-278 https://doi.org/10.1093/biomet/41.1-2.275
  27. Tuyl, R., Gerlach, R. and Mengersen, K. (2008). A comparison of Bayes-Laplace, Jeffreys, and other priors: The case of zero events, The American Statistician, 62, 40-44 https://doi.org/10.1198/000313008X267839
  28. Vollset, S. E. (1993). Confidence intervals for a binomial proportion, Statistics in Medicine, 12, 809-824 https://doi.org/10.1002/sim.4780120902
  29. Wang, H. (2007). Exact confidence coefficients of confidence intervals for a binomial proportion, Statistica Sinica, 17, 361-368
  30. Wang, H. (2009). Exact average coverage probabilities and confidence coefficients of confidence intervals for discrete distributions, Statistic and Computing, 19, 139-148 https://doi.org/10.1007/s11222-008-9077-8
  31. Wilson, E. B. (1927). Probable inference, the law of succession, and statistical inference, Journal of the American Statistical Association, 22, 209-212 https://doi.org/10.2307/2276774
  32. Winkler, R. L., Smith, J. E. and Fryback, D. G. (2002). The role of informative priors in zero-numerator problems: Being conservative versus being candid, The American Statistician, 56, 1-4 https://doi.org/10.1198/000313002753631295
  33. Woodroofe, M. (1986). Very weak expansions for sequential confidence levels, The Annals of Statistics, 14, 1049-1067 https://doi.org/10.1214/aos/1176350049

Cited by

  1. Confidence Interval for Sensitive Binomial Attribute : Direct Question Method and Indirect Question Method vol.28, pp.1, 2015, https://doi.org/10.5351/KJAS.2015.28.1.075
  2. On Prediction Intervals for Binomial Data vol.26, pp.6, 2013, https://doi.org/10.5351/KJAS.2013.26.6.943
  3. An Interval Estimation Method of Patent Keyword Data for Sustainable Technology Forecasting vol.9, pp.11, 2017, https://doi.org/10.3390/su9112025