Exact Group Sequential Methods for Estimating a Binomial Proportion

Algorithm 2

∇ Choose initial step size 𝑑>𝜂.

∇ Let 𝐹←0, 𝑇←0 and 𝑏←𝜃.

∇ While 𝐹=𝑇=0, do the following:

     ⋄ Let st←0 and ℓ←2;

     ⋄ While st = 0, do the following:

     ⋆ Let ℓ←ℓ−1 and 𝑑←𝑑2^ℓ.

     ⋆ If 𝑏−𝑑>𝜃, then let 𝑎←𝑏−𝑑 and 𝑇←0.

      Otherwise, let 𝑎←𝜃 and 𝑇←1.

     ⋆ If 𝐶(𝑎,𝑏)<𝛿, then let st ← 1 and 𝑏←𝑎.

     ⋆ If 𝑑<𝜂, then let st ← 1 and F ← 1.

∇ Return 𝐹.