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Confidence intervals for the ratio of two independent Poisson rates: Parametric bootstrap, modified asymptotic, and

Mahmood Kharrati-Kopaei¹, Raziye Dorosti-Motlagh¹

¹Department of Statistics, Shiraz University, Shiraz, Iran.

Statistical Methods in Medical Research

|November 12, 2019

Abstract:

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.

Keywords:

Confidence interval Poisson estimating probability mass function modified asymptotic parametric bootstrap ratio

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