Exact confidence coefficients of confidence intervals for a binomial proportion

Hsiuying Wang*

*Corresponding author for this work

Research output: Contribution to journalArticle

20 Scopus citations

Abstract

Let X have a binomial distribution B(n,p). For a confidence interval (L(X),U(X)) of a binomial proportion p, the coverage probability is a variable function of p. The confidence coefficient of the confidence interval is the infimum of the coverage probabilities, inf0≤p≤1 Pp(p ε(L(X), U(X))). Usually, the exact confidence coefficient is unknown since the infimum of the coverage probabilities may occur at any point p ε (0, 1). In this paper, a methodology to compute the exact confidence coefficient is proposed. With this methodology, the point where the infimum of the coverage probabilities occurs, as well as the confidence coefficient, can be precisely derived.

Original languageEnglish
Pages (from-to)361-368
Number of pages8
JournalStatistica Sinica
Volume17
Issue number1
StatePublished - 1 Jan 2007

Keywords

  • Binomial distribution
  • Confidence coefficient
  • Confidence interval
  • Coverage probability

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