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Design and analysis of shortest two-sided confidence intervals for a probability under prior information

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  • Rainer Göb
  • Kristina Lurz

Abstract

Two-sided confidence intervals for a probability $$p$$ p under a prescribed confidence level $$\gamma $$ γ are an elementary tool of statistical data analysis. A confidence interval has two basic quality characteristics: i) exactness, i. e., whether the actual coverage probability equals or exceeds the prescribed level $$\gamma $$ γ ; ii) inferential precision, measured by the length of the confidence interval. The interval provided by Clopper and Pearson (Biometrika 26:404–413, 1934 ) is the only exact interval actually used in statistical data analysis. Various authors have suggested shorter, i. e., more precise exact intervals. The present paper makes two contributions. i) We provide a general design scheme for minimum volume confidence regions under prior knowledge on the target parameter. ii) We apply the scheme to the problem of confidence intervals for a probability $$p$$ p where prior knowledge is expressed in a flexible way by a beta distribution on a subset of the unit interval. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Rainer Göb & Kristina Lurz, 2014. "Design and analysis of shortest two-sided confidence intervals for a probability under prior information," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(3), pages 389-413, April.
    • Handle: RePEc:spr:metrik:v:77:y:2014:i:3:p:389-413
    DOI: 10.1007/s00184-013-0445-9
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