A generalized confidence limit for the reliability function of a two-parameter exponential distribution |
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| Institution: | 1. Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, Keelung 20224, Taiwan, ROC;2. Department of Civil Engineering, National Taiwan University, Taipei 10617, Taiwan, ROC;1. Department of Mathematics and Statistics, Concordia University, Montréal, QC H3G 1M8, Canada;2. Department of Mathematical Sciences, Central Connecticut State University, 1615 Stanley Street, New Britain, CT 06050, USA;1. Department of Informatics, Karlsruhe Institute of Technology, Germany;2. Siemens Corporation, Corporate Technology, Princeton, NJ, USA;3. Federal University of Rio de Janeiro (UFRJ), PO BOX 68.530, 21941-590 Rio de Janeiro/RJ, Brazil;4. Federal University of the State of Rio de Janeiro, RJ, Brazil;5. Duke University, Durham, NC, USA;1. Stanford Neuroscience Program, Stanford University School of Medicine, Stanford, CA 94305, USA;2. Department of Neurology and Neurological Sciences, Stanford University School of Medicine, Stanford, CA 94305, USA;1. Lublin University of Technology, Nadbystrzycka 40, 20-618 Lublin, Poland;2. University “A.I. Cuza” of Iasi, Department of Mathematics, 700506 Iasi, Romania;3. University Duisburg-Essen, Faculty of Mathematics, 45127 Essen, Germany;1. Departamento de Bioquímica, Genética e Inmunología, Facultad de Biología, Universidad de Vigo, Vigo, Pontevedra, España;2. Instituto de Investigación Biomédica de Vigo (IBIV), Vigo, Pontevedra, España;3. Servicio de Neumología, Complexo Hospitalario de Pontevedra, Pontevedra, España;4. Servicio de Neumología, Hospital Xeral de Vigo, Vigo, Pontevedra, España |
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| Abstract: | Based on type II censored data, an exact lower confidence limit is constructed for the reliability function of a two-parameter exponential distribution, using the concept of a generalized confidence interval due to Weerahandi (J. Amer. Statist. Assoc. 88 (1993) 899). It is shown that the interval is exact, i.e., it provides the intended coverage. The confidence limit has to be numerically obtained; however, the required computations are simple and straightforward. An approximation is also developed for the confidence limit and its performance is numerically investigated. The numerical results show that compared to what is currently available, our approximation is more satisfactory in terms of providing the intended coverage, especially for small samples. |
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