## 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, inf_{0≤p≤1} P_{p}(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 language | English |
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Pages (from-to) | 361-368 |

Number of pages | 8 |

Journal | Statistica Sinica |

Volume | 17 |

Issue number | 1 |

State | Published - 1 Jan 2007 |

## Keywords

- Binomial distribution
- Confidence coefficient
- Confidence interval
- Coverage probability