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However, the methods suffer from an inconsistency between the tests and the corresponding CIs: In some cases, a parameter value is rejected by the test, though it lies in the CI. The problem results from non-unimodality of the test <jats:italic>p<\/jats:italic> value functions. We propose a slight modification of the tests that avoids the inconsistency, while preserving nestedness and exactness. Fast and accurate algorithms for both the test modification and calculation of confidence bounds are presented together with their theoretical background.<\/jats:p>","DOI":"10.1007\/s00180-020-00986-0","type":"journal-article","created":{"date-parts":[[2020,4,18]],"date-time":"2020-04-18T15:02:25Z","timestamp":1587222145000},"page":"1775-1790","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["On matching confidence intervals and tests for some discrete distributions: methodological and computational aspects"],"prefix":"10.1007","volume":"36","author":[{"given":"Jan","family":"Klaschka","sequence":"first","affiliation":[]},{"given":"Jen\u0151","family":"Reiczigel","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,4,18]]},"reference":[{"key":"986_CR1","first-page":"119","volume":"52","author":"A Agresti","year":"1998","unstructured":"Agresti A, Coull A (1998) Approximate is better than \u201cexact\u201d for interval estimation of binomial proportions. 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