A modified rule of three for the one-sided binomial confidence interval

Turpin Lonnie (), Patin Jeanne-Claire (), Jens William () and Turpin Morgan ()
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Turpin Lonnie: McNeese State University, Lake Charles, LA 70605, USA
Patin Jeanne-Claire: McNeese State University, Lake Charles, LA 70605, USA
Jens William: McNeese State University, Lake Charles, LA 70605, USA
Turpin Morgan: McNeese State University, Lake Charles, LA 70605, USA

The International Journal of Biostatistics, 2024, vol. 20, issue 2, 631-639

Abstract: Consider the one-sided binomial confidence interval L , 1 $\left(L,1\right)$ containing the unknown parameter p when all n trials are successful, and the significance level α to be five or one percent. We develop two functions (one for each level) that represent approximations within α / 3 $\alpha /\sqrt{3}$ of the exact lower-bound L = α 1/n . Both the exponential (referred to as a modified rule of three) and the logarithmic function are shown to outperform the standard rule of three L ≃ 1 − 3/n over each of their respective ranges, that together encompass all sample sizes n ≥ 1. Specifically for the exponential, we find that exp − 3 / n $\mathrm{exp}\left(-3/n\right)$ is a better lower bound when α = 0.05 and n

Keywords: one-sided binomial confidence interval; exponential approximation; logarithmic approximation; rule of three; optimization; 62F25; 90C30 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1515/ijb-2022-0061

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