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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 35, Fasc. 2,
pages 301 - 312
 

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.

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