The most commonly used estimator for a log-normal mean is the sample mean. In this paper, we show that this estimator can have a large mean square error, even for large samples. Then, we study three main alternative estimators: (i) a uniformly minimum variance unbiased (UMVU) estimator; (ii) a maxim
CONFIDENCE INTERVALS FOR THE LOG-NORMAL MEAN
โ Scribed by XIAO-HUA ZHOU; SUJUAN GAO
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 225 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0277-6715
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โฆ Synopsis
In this paper we conduct a simulation study to evaluate coverage error, interval width and relative bias of four main methods for the construction of confidence intervals of log-normal means: the naive method; Cox's method; a conservative method; and a parametric bootstrap method. The simulation study finds that the naive method is inappropriate, that Cox's method has the smallest coverage error for moderate and large sample sizes, and that the bootstrap method has the smallest coverage error for small sample sizes. In addition, Cox's method produces the smallest interval width among the three appropriate methods. We also apply the four methods to a real data set to contrast the differences.
1997 by
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The paper provides a comprehensive review of methodology for setting confidence intervals for the parameter of a Poisson distribution. The results are illustrated by a numerical example.