Error Probabilities and Average Sample Number of the Sequential Probability Ratio Test

Summary Let x 1, x 2, ... be independent random variables which under p θ have probability density function of the form exp (θx – Ψ(θ)} relative to some measure v, where Ψ is normalized so that Ψ(0) = Ψ‘(0) = 0. Let a ≤ 0 < b, sn = ∑1 n x k, and T=inf{n:sn∉(a,b)}. Approximations are given for p θ{sT ≥; b} and E θ(T) based on asymptotic considerations arising in renewal theory. The accuracy of these approximations is discussed for normally distributed x‘s. It is shown that for θ = 0 these approximations give complete asymptotic expansions as b → ∞ in powers of b −1 with exponentially small remainder.