A comparison of nine confidence intervals for a Poisson parameter when the expected number of events is ≤5
A comparison of nine confidence intervals for a Poisson parameter when the expected number of events is ≤5
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DOI：
10.1198/000313002317572736
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发表时间：
2002-05-01
影响因子：
1.8
通讯作者：
Barker, L
中科院分区：
文献类型：
--
作者：
Barker, L
设{X-i}（i=1）（n）是独立同分布Poisson theta随机变量的集合。theta的置信区间可以通过Wald方法、精确推理、方差稳定变换或许多其他技术来构建。当ntheta很小时，实际覆盖率和标称覆盖率可能相差很大。我们比较了9个置信区间的泊松平均覆盖范围和预期的置信限的宽度。我们表明，对于小的n θ：考虑的置信区间，只有确切的区间保持覆盖概率;而分数区间近似保持覆盖概率，其预期的宽度超过确切的区间;和修改后的版本的置信区间的方差稳定的置信区间的基础上，具有覆盖属性附近的标称和预期的宽度，不是特别大。因此，我们建议希望真实覆盖率不低于标称值的研究者使用精确区间，而愿意接受近似覆盖率的研究者使用方差稳定区间的修改形式。
Let {X-i}(i=1)(n) be a collection of independent, identically distributed Poisson theta random variables. Confidence intervals for theta can be constructed by the Wald method, by exact inference, from a variance stabilizing transformation, or by many other techniques. When ntheta is small, actual and nominal coverage can differ substantially. We compare nine confidence intervals for a Poisson mean with respect to coverage and expected width of confidence limits. We show that, for small ntheta: of the confidence intervals considered, only the exact interval maintains coverage probabilities; while the scores interval approximately maintains coverage probability, its expected width exceeds the exact interval's; and a modified version of the confidence interval based on the variance stabilized confidence interval has coverage properties near the nominal and an expected width that is not particularly large. Thus, we recommend that investigators desiring true cover not less than nominal use the exact interval and those willing to accept approximate coverage use a modified form of the variance stabilized interval.