Fuzzy and randomized confidence intervals and P-values

Research output: Contribution to journalReview article

44 Scopus citations


The optimal hypothesis tests for the binomial distribution and some other discrete distributions are uniformly most powerful (UMP) onetailed and UMP unbiased (UMPU) two-tailed randomized tests. Conventional confidence intervals are not dual to randomized tests and perform badly on discrete data at small and moderate sample sizes. We introduce a new confidence interval notion, called fuzzy confidence intervals, that is dual to and inherits the exactness and optimality of UMP and UMPU tests. We also introduce a new P-value notion, called fuzzy P-values or abstract randomized P-values, that also inherits the same exactness and optimality.

Original languageEnglish (US)
Pages (from-to)358-366
Number of pages9
JournalStatistical Science
Issue number4
StatePublished - Nov 1 2005



  • Confidence interval
  • Fuzzy set theory
  • Hypothesis test
  • P-value
  • Randomized test
  • Uniformly most powerful unbiased (UMP and UMPU)

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