Exact average coverage probabilities and confidence coefficients of confidence intervals for discrete distributions

Hsiuying Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

For a confidence interval (L(X),U(X)) of a parameter θ in one-parameter discrete distributions, the coverage probability is a variable function of θ. The confidence coefficient is the infimum of the coverage probabilities, inf∈ θ P θ (θ (L(X),U(X))). Since we do not know which point in the parameter space the infimum coverage probability occurs at, the exact confidence coefficients are unknown. Beside confidence coefficients, evaluation of a confidence intervals can be based on the average coverage probability. Usually, the exact average probability is also unknown and it was approximated by taking the mean of the coverage probabilities at some randomly chosen points in the parameter space. In this article, methodologies for computing the exact average coverage probabilities as well as the exact confidence coefficients of confidence intervals for one-parameter discrete distributions are proposed. With these methodologies, both exact values can be derived.

Original languageEnglish
Pages (from-to)139-148
Number of pages10
JournalStatistics and Computing
Volume19
Issue number2
DOIs
StatePublished - 1 Jun 2009

Keywords

  • Confidence coefficient
  • Confidence interval
  • Coverage probability
  • Discrete distribution

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