Department of Statistics, Shiraz University, Shiraz, Iran.
Stat Methods Med Res. 2020 Aug;29(8):2140-2150. doi: 10.1177/0962280219886889. Epub 2019 Nov 11.
We propose four confidence intervals for the ratio of two independent Poisson rates. We apply a parametric bootstrap approach, two modified asymptotic results, and we propose an ad-hoc approximate-estimate method to construct confidence intervals. We justify the correctness of the proposed methods asymptotically in the case of non-rare events (when the Poisson rates are large). We also compare the proposed confidence intervals with some recommended ones in the case of rare events (when the Poisson rates are small) via an extensive simulation study. The results show that the proposed modified asymptotic and the approximate-estimate confidence intervals perform reasonably well in terms of coverage probability and average length.
我们提出了四种用于估计两个独立泊松率之比的置信区间。我们应用参数bootstrap 方法、两种修正的渐近结果，并提出了一种特定的近似估计方法来构建置信区间。在非稀有事件（泊松率较大）的情况下，我们从渐近角度证明了所提出方法的正确性。我们还通过广泛的模拟研究，在稀有事件（泊松率较小）的情况下，将所提出的置信区间与一些推荐的置信区间进行了比较。结果表明，所提出的修正渐近和近似估计置信区间在覆盖概率和平均长度方面表现相当好。
