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The efficiency of Buehler confidence limits

✍ Scribed by Paul Kabaila; Chris J. Lloyd

Book ID
104302202
Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
224 KB
Volume
65
Category
Article
ISSN
0167-7152

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✦ Synopsis

The Buehler 1 -upper conÿdence limit is as small as possible, subject to the constraints that (a) its coverage probability never falls below 1 -and (b) it is a non-decreasing function of a designated statistic T . We provide two new results concerning the in uence of T on the e ciency of this conÿdence limit. Firstly, we extend the result of Kabaila (Statist. Probab. Lett. 52 (2001) 145) to prove that, for a wide class of Ts, the T which maximizes the large-sample e ciency of this conÿdence limit is itself an approximate 1upper conÿdence limit. Secondly, there may be ties among the possible values of T . We provide the result that breaking these ties by a su ciently small modiÿcation cannot decrease the ÿnite-sample e ciency of the Buehler conÿdence limit.

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✍ Paul Kabaila 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 142 KB

Consider the reliability problem of ÿnding a 1 -upper (lower) conÿdence limit for  the probability of system failure (non-failure), based on binomial data on the probability of failure of each component of the system. The Buehler 1conÿdence limit is usually based on an estimator of Â. This conÿdenc