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Biometrika 1982 69(3):647-652; doi:10.1093/biomet/69.3.647
© 1982 by Biometrika Trust
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Improving the normal approximation when constructing one-sided confidence intervals for binomial or Poisson parameters

PETER HALL

Department of Statistics, Faculty of Economics, Australian National University Canberra, Australia

We show that the usual normal approximation used during the construction of onesided confidence intervals for binomial or Poisson parameters can be significantly in error due to skewness in the underlying distribution. We provide a simple method of correcting for skewness, and demonstrate that it is effective both in theory and in practice.

Key Words: Binomial distribution • Normal approximation • One-sided confidence interval • Poisson distribution • Rounding error • Skewness


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