• Bernoulli
  • Volume 23, Number 1 (2017), 479-502.

Exact confidence intervals and hypothesis tests for parameters of discrete distributions

Måns Thulin and Silvelyn Zwanzig

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We study exact confidence intervals and two-sided hypothesis tests for univariate parameters of stochastically increasing discrete distributions, such as the binomial and Poisson distributions. It is shown that several popular methods for constructing short intervals lack strict nestedness, meaning that accepting a lower confidence level not always will lead to a shorter confidence interval. These intervals correspond to a class of tests that are shown to assign differing $p$-values to indistinguishable models. Finally, we show that among strictly nested intervals, fiducial intervals, including the Clopper–Pearson interval for a binomial proportion and the Garwood interval for a Poisson mean, are optimal.

Article information

Bernoulli Volume 23, Number 1 (2017), 479-502.

Received: December 2014
Revised: March 2015
First available in Project Euclid: 27 September 2016

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binomial distribution confidence interval expected length fiducial interval hypothesis test Poisson distribution


Thulin, Måns; Zwanzig, Silvelyn. Exact confidence intervals and hypothesis tests for parameters of discrete distributions. Bernoulli 23 (2017), no. 1, 479--502. doi:10.3150/15-BEJ750.

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