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

Author

Listed:
  • 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)

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

Suggested Citation

  • Turpin Lonnie & Patin Jeanne-Claire & Jens William & Turpin Morgan, 2024. "A modified rule of three for the one-sided binomial confidence interval," The International Journal of Biostatistics, De Gruyter, vol. 20(2), pages 631-639.
    • Handle: RePEc:bpj:ijbist:v:20:y:2024:i:2:p:631-639:n:1002
    DOI: 10.1515/ijb-2022-0061
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