Confidence intervals for average success probabilities
Słowa kluczowe:
Bernoulli convolution, binomial distribution inequality, Clopper–Pearson, hypergeometric distribution, inhomogeneous Bernoulli chain, Poisson-binomial distribution, robustnessAbstrakt
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.
