CONFIDENCE INTERVALS FOR AVERAGE SUCCESS PROBABILITIES
Lutz Mattner
Christoph Tasto
Abstract: We provide Buehler-optimal one-sided and valid two-sided confidence intervals for the
average success probability of a possibly inhomogeneous fixed length Bernoulli
chain, based on the number of observed successes. Contrary to some claims in the
literature, the one-sided Clopper–Pearson intervals for the homogeneous case are not
completely robust here, not even if applied to hypergeometric estimation problems.
2000 AMS Mathematics Subject Classification: Primary: 62F25; Secondary:
62F35.
Keywords and phrases: Bernoulli convolution, binomial distribution inequality,
Clopper–Pearson, hypergeometric distribution, inhomogeneous Bernoulli chain,
Poisson-binomial distribution, robustness.