Tolerance Intervals for Hypergeometric and Negative Hypergeometric Variables

Brown, L.D., Cai, T.T. and DasGupta, A. (2001). Interval estimation for a binomial proportion. Statist. Sci. 16, 101–133.

Cai, T.T. and Wang, H. (2009). Tolerance intervals for discrete distributions in exponential families. Statist. Sinica 19, 905–923.

Eichenberger, P., Hulliger, B. and Potterat, J. (2011). Two measures for sample size determination. Survey Research Methods 5, 27–37.

Guenther, W.C. (1975). The inverse hypergeometric - a useful model. Stat. Neerl. 29, 129–144.

Hahn, G.J. and Chandra, R. (1981). Tolerance intervals for Poisson and binomial random variables. Journal of Quality Technology 13, 100–110.

Hahn, G.J. and Meeker, W.Q. (1991). Statistical Intervals: A Guide for Practitioners. Wiley-Interscience, New York.

Johnson, N.L., Kemp, A.W. and Kotz, S. (2005). Univariate Discrete Distributions, 3rd edn. Wiley, Hoboken.

Jolliffe, I.T. and Jolliffe, A.R. (1997). Modelling memory in coal tits: An illustration of the EM algorithm. Biometrics 53, 1136–1142.

Krishnamoorthy, K. and Mathew, T. (2009). Statistical Tolerance Regions: Theory, Applications, and Computation. Wiley, Hoboken.

Krishnamoorthy, K., Xia, Y. and Xie, F. (2011). A simple approximate procedure for constructing binomial and Poisson tolerance intervals. Comm. Statist. Theory Methods,40, 2443–2458.

Lehmann, E.L. and Romano, J.P. (2005). Testing Statistical Hypotheses. Springer.

Mathew, T. and Young, D.S. (2013). Fiducial-based tolerance intervals for some discrete distributions. Comput. Statist. Data Anal. 61, 38–49.

Miller, G.K. and Fridell, S.L. (2007). A forgotten discrete distribution? Reviving the negative hypergeometric model. Amer. Statist. 61, 347–350.

Montgomery, D.C. (2013). Introduction to Statistical Quality Control, 7th edn. Wiley, New Jersey.

Newcombe, R.G. (1998). Two-sided confidence intervals for the single proportion: Comparison of seven methods. Stat. Med. 17, 857–872.

R Development Core Team 2013 R: A Language and Environment for Statistical Computing, Vienna. ISBN 3-900051-07-0. http://www.R-project.org/ .

Ridiout, M.S. (1999). Memory in coal tits: An alternative model. Biometrics 55, 660–662.

Tian, M., Tang, M.L., Ng, H.K.T. and Chen, P.S. (2009). A comparative study of confidence intervals for negative binomial proportions. J. Stat. Comput. Simul. 79, 241–249.

Vener, K.J., Feuer, E.J. and Gorelic, L. (1993). A statistical model validating triage for the peer review process: Keeping the competitive applications in the review pipeline. The Federation of American Societies for Experimental Biology Journal 7, 1312–1319.

Wang, H. and Tsung, F. (2009). Tolerance intervals with improved coverage probabilities for binomial and Poisson variables. Technometrics 51, 25–33.

Wilks, S.S. (1941). Determination of sample sizes for setting tolerance limits. The Annals of Mathematical Statistics 12, 91–96.

Wilks, S.S. (1942). Statistical prediction with special reference to the problem of tolerance limits. The Annals of Mathematical Statistics 13, 400–409.

Wright, T. (1997). A simple algorithm for tighter exact upper confidence bounds with rare attributes in finite universes. Statist. Probab. Lett. 36, 59–67.

Young, D.S. (2010). tolerance: An R package for estimating tolerance intervals. Journal of Statistical Software 36, 1–39.

Young, D.S. (2014). A procedure for approximate negative binomial tolerance intervals. J. Stat. Comput. Simul. 84, 438–450.

Zacks, S. (1970). Uniformly most accurate upper tolerance limits for monotone likelihood ratio families of discrete distributions. J. Amer. Statist. Assoc. 65, 307–316.

Zaslavsky, B.G. (2007). Calculation of tolerance limits and sample size determination for clinical trials with dichotomous outcomes. J. Biopharm. Statist. 17, 481–491.

Zhang, L. and Johnson, W.D. (2011) Approximate confidence intervals for a parameter of the negative hypergeometric distribution. In Proceedings of the Section on Survey Research Methods, pages 1753–1767. American Statistical Association.