DOI QR코드

DOI QR Code

The Influence of Extreme Value in Binomial Confidence Interval

이항 신뢰구간에서 극단값의 영향

  • Ryu, Jea-Bok (Division of Natural Science, Cheongju University)
  • Received : 20110700
  • Accepted : 20110800
  • Published : 2011.09.30

Abstract

Several methods are used in interval estimation for binomial proportion; however the coverage probabilities of most confidence intervals depart from the confidence level when the binomial population proportion closes to 0 or 1 due to the extreme value. Vollset (1993), Agresti and Coull (1998), Newcombe (1998), and Brown et al. (2001) suggested methods to adjust the extreme value. This paper discusses the influence of extreme value in a binomial confidence interval through the numerical comparison of 6 confidence intervals.

References

  1. 류제복 (2010). Wald 신뢰구간에서 극단값 조정의 효과, <산업과학연구>, 28, 29-34.
  2. 류제복, 이승주 (2006). 낮은 이항 비율에 대한 신뢰구간, <응용통계연구>, 19, 217-230. https://doi.org/10.5351/KJAS.2006.19.2.217
  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. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. Schader, M. and Schmid, F. (1990). Charting small sample characteristics of asymptotic confidence intervals for the binomial parameter, Statistical Papers, 31, 251-264. https://doi.org/10.1007/BF02924698
  13. Vollset, S. E. (1993). Confidence intervals for a binomial proportion, Statistics in Medicine, 12, 809-824. https://doi.org/10.1002/sim.4780120902
  14. 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

Cited by

  1. On Prediction Intervals for Binomial Data vol.26, pp.6, 2013, https://doi.org/10.5351/KJAS.2013.26.6.943
  2. 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