Open Access
February 2017 Exact confidence intervals and hypothesis tests for parameters of discrete distributions
Måns Thulin, Silvelyn Zwanzig
Bernoulli 23(1): 479-502 (February 2017). DOI: 10.3150/15-BEJ750


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.


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Måns Thulin. Silvelyn Zwanzig. "Exact confidence intervals and hypothesis tests for parameters of discrete distributions." Bernoulli 23 (1) 479 - 502, February 2017.


Received: 1 December 2014; Revised: 1 March 2015; Published: February 2017
First available in Project Euclid: 27 September 2016

zbMATH: 06673485
MathSciNet: MR3556780
Digital Object Identifier: 10.3150/15-BEJ750

Keywords: Binomial distribution , Confidence interval , expected length , fiducial interval , hypothesis test , Poisson distribution

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 1 • February 2017
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