One-sided confidence intervals in discrete distributions |
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| Institution: | 1. CNRS and I.M.J, Université Paris Diderot-Paris 7, Paris, France;2. Laboratoire de Mathématiques, Université de Cergy-Pontoise, 2 avenue Adolphe Chauvin, Cergy-Pontoise, France;1. Department of Statistics, Yunnan University, Kunming, Yunnan 650091, PR China;2. Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China;3. Department of Mathematics, South University of Science and Technology of China, Shenzhen, Guangdong 518055, PR China;1. DESP, University of Urbino, Urbino, Italy;2. IST, University of Stuttgart, Germany;3. LAAS, CNRS, INSA, Université de Toulouse, France;1. Centro de Estatística e Aplicações, Faculdade de Ciências, Universidade de Lisboa, Portugal;2. Centro de Estatística e Aplicações, Universidade de Lisboa, Portugal;3. Departamento de Matemática, Universidade dos Açores, Portugal;4. Centro de Matemática e Aplicações, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Portugal |
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| Abstract: | One-sided confidence intervals in the binomial, negative binomial, and Poisson distributions are considered. It is shown that the standard Wald interval suffers from a serious systematic bias in the coverage and so does the one-sided score interval. Alternative confidence intervals with better performance are considered. The coverage and length properties of the confidence intervals are compared through numerical and analytical calculations. Implications to hypothesis testing are also discussed. |
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