Operating Characteristic and Expected Sample Size of a Sequential Probability Ratio Test for the Simple Exponential Distribution

Summary

For the problem of testing the simple hypothesis H : θ = θ₁ against the simple alternative K : θ = θ₂ with θ₂ > θ₁ , where θ is the unknown parameter of the simple exponential distribution, the familar Wald's Sequential Probability ratio test may be adopted. It is shown in the present paper that for a class of sequential probability ratio tests, exact expressions for the operating characteristic and the expected sample size can be given. The nature of the expected sample size function and the effect of Walo's approximations to the stopping bounds of the sequential probability ratio test are also studied.