×

Exact short Poisson confidence intervals. (English) Zbl 1013.62027

Summary: The authors propose a new method for constructing a confidence interval for the expectation \(\theta\) of a Poisson random variable. The interval they obtain cannot be shortened without the infimum over \(\theta\) of the coverage probability falling below \(1-\alpha\). In addition, the endpoints of the interval are strictly increasing functions of the observed variable. An easy-to-program algorithm is provided for computing this interval.

MSC:

62F25 Parametric tolerance and confidence regions
62-04 Software, source code, etc. for problems pertaining to statistics
65C30 Numerical solutions to stochastic differential and integral equations
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Casella, Statistical Inference. (1990)
[2] Casella, Refining poisson confidence intervals, The Canadian Journal of Statistics 17 pp 45– (1989) · Zbl 0672.62046
[3] Crow, Confidence intervals for the expectation of a Poisson variable, Biometrika 46 pp 441– (1959) · Zbl 0093.32202 · doi:10.1093/biomet/46.3-4.441
[4] Kulkarni, Maximum (Max) and mid-P confidence intervals and pvalues for the standard mortality and incidence ratios, American Journal of Epidemiology 147 pp 83– (1998) · doi:10.1093/oxfordjournals.aje.a009371
[5] Sahai, Confidence intervals for the mean of a Poisson distribution: A review, Biometrical Journal 35 pp 857– (1993)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.