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Research Article

Efficient confidence intervals for the difference of two Bernoulli distributions’ success parameters

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Pages 76-93 | Received 10 Mar 2021, Accepted 07 Jul 2021, Published online: 13 Oct 2021

References

  • Agresti, A., & Coull, B. A. (1998). Approximate is better than “exact” for interval estimation of binomial proportions. American Statistician, 52, 119–126.
  • Armitage, P. (1958). Numerical studies in the sequential estimation of a binomial parameter. Biometrika, 45(1–2), 1–15. https://doi.org/10.1093/biomet/45.1–2.1
  • Bechhofer, R. E., Santner, T. J., & Goldsman, D. (1995). Design and analysis of experiments for statistical selection, screening and multiple comparisons. New York: John Wiley and Sons.
  • Brown, L. D., Cai, T., & Dasgupta, A. (2001). Interval estimation for a binomial proportion. Statistical Science, 16(2), 101–133. https://doi.org/10.1214/ss/1009213286
  • Brown, L. D., Cai, T., & Dasgupta, A. (2002). Interval estimation for a binomial proportion and asymptotic expansions. Annals of Statistics, 30(1), 160–201. https://doi.org/10.1214/aos/1015362189
  • Clopper, C. J., & Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika, 26(4), 404–413. https://doi.org/10.1093/biomet/26.4.404
  • Frey, J. (2010). Fixed-width sequential confidence intervals for a proportion. The American Statistician, 64(3), 242–249. https://doi.org/10.1198/tast.2010.09140
  • Goldsman, D. (2015). A practical guide to ranking and selection methods. In D. M. Aleman & A. C. Thiele Eds., The Operations Research revolution (pp. 89–110). Institute for Operations Research and the Management Sciences. TutORials in Operations Research series, ed. J. C. Smith. Cantonville, MD: INFORMS.
  • Huber, M. (2017). A Bernoulli mean estimate with known relative error distribution. Random Structures & Algorithms, 50(2), 173–182. https://doi.org/10.1002/rsa.20654
  • Khan, R. A. (1998). Fixed-width confidence sequences for the normal mean and the binomial probability. Sequential Analysis, 17(3–4), 205–217. https://doi.org/10.1080/07474949808836409
  • Malinovsky, Y., & Zacks, S. (2018). Proportional closeness estimation of probability of contamination under group testing. Sequential Analysis, 37(2), 145–157. https://doi.org/10.1080/07474946.2018.1466518
  • Mukhopadhyay, N., & Banerjee, S. (2015). Purely sequential and two-stage bounded-length confidence intervals for the Bernoulli parameter with illustrations from health studies and ecology. In P. Choudhary, C. Nagaraja, & H. K. T. Ng (Eds.), Ordered data analysis, modeling and health research methods. In Honor of H. N. Nagaraja’s 60th Birthday (pp. 211–234). New York: Springer.
  • Newcombe, R. G. (1998). Two-sided confidence intervals for the single proportion: comparison of seven methods. Statistics in Medicine, 17(8), 857–872. https://doi.org/10.1002/(SICI)1097-0258(19980430)17:8<857::AID-SIM777>3.0.CO;2-E“3.0.CO;2-E“https://doi.org/10.1002/(SICI)1097-0258(19980430)17:8<857::AID-SIM777>3.0.CO;2-E
  • Robbins, H., & Siegmund, D. (1974). Sequential estimation of p in Bernoulli trials. In E. J. G. Pitman & E. J. Williams (Eds.), Studies in probability and statistics (pp. 103–107). Jerusalem Academic Press.
  • Tanaka, M. (1961). On a confidence interval of given length for the parameter of the binomial and the Poisson distributions. Annals of the Institute of Statistical Mathematics, 13(1), 201–215. https://doi.org/10.1007/BF02868870
  • Turner, A. J., Balestrini-Robinson, S., & Mavris, D. (2013). Heuristics for the regression of stochastic simulations. Journal of Simulation, 7(4), 229–239. https://doi.org/10.1057/jos.2013.1
  • Wilson, E. B. (1927). Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association, 22(158), 209–212. https://doi.org/10.1080/01621459.1927.10502953
  • Yaacoub, T., Goldsman, D., Mei, Y., & Moustakides, G. V. (2019a). Tandem-width sequential confidence intervals for a Bernoulli proportion. Sequential Analysis, 38(2), 163–183. https://doi.org/10.1080/07474946.2019.1611315
  • Yaacoub, T., Moustakides, G. V., & Mei, Y. (2019b). Optimal stopping for interval estimation in Bernoulli trials. IEEE Transactions on Information Theory 65(5), 3022–3033. https://doi.org/10.1109/TIT.2018.2885405
  • Zacks, S., & Mukhopadhyay, N. (2007). Distributions of sequential and two-stage stopping times for fixed-width confidence intervals in Bernoulli trials: Application in reliability. Sequential Analysis, 26(4), 425–441. https://doi.org/10.1080/07474940701620907

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