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Confidence interval

A confidence interval is a set of parameter values produced by a procedure with a stated repeated-sampling coverage under specified model and sampling assumptions.

A 95% confidence procedure targets coverage of the fixed parameter in 95% of repeated samples under its assumptions; an exact discrete procedure can have coverage above that nominal level. The observed interval either contains the parameter or does not. Its confidence level is not a posterior probability assigned to that parameter. [1]

A one-sided upper bound and the upper endpoint of an equal-tailed two-sided interval use different tail probabilities. For 95% confidence these are 0.05 and 0.025 respectively. State the interval method, the parameter being bounded, the observation horizon or exposure, and the assumptions. Sampling uncertainty does not include unmodelled selection bias, dependence or systematic measurement error. [2] [3]

Relations

related
binomial-proportion, poisson-rate-model, afr, right-censoring

Citations

  1. NIST e-Handbook: Confidence limits and repeated-sampling interpretation (accessed 2026-10-17)
  2. NIST e-Handbook: Exact binomial confidence intervals (accessed 2026-10-17)
  3. Hesela: AFR is a rate, not a one-year failure probability (accessed 2026-10-17)

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