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A. Agresti and B. Coull, “Approximate Is Better than ‘Exact’ for Interval Estimation of Binomial Proportions,” The American Statistician, Vol. 52, No. 2, 1998, pp.119-126. doi:10.2307/2685469

has been cited by the following article:

• TITLE: Moved Score Confidence Intervals for Means of Discrete Distributions

  AUTHORS: Yu Guan

  KEYWORDS: Confidence Interval; Confidence Level; Coverage Probability; Discrete Distribution; Moved Score Confidence Interval

  JOURNAL NAME: Open Journal of Statistics, Vol.1 No.2, July 26, 2011

  ABSTRACT: Let X denote a discrete distribution as Poisson, binomial or negative binomial variable. The score confidence interval for the mean of X is obtained based on inverting the hypothesis test and the central limit theorem is discussed and recommended widely. But it has sharp downward spikes for small means. This paper proposes to move the score interval left a little (about 0.04 unit), called by moved score confidence interval. Numerical computation and Edgeworth expansion show that the moved score interval is analogous to the score interval completely and behaves better for moderate means; for small means the moved interval raises the infimum of the coverage probability and improves the sharp spikes significantly. Especially, it has unified explicit formulations to compute easily.