An Estimation Method for the Excess over the Boundaries In the SPRT and Its Application

Abstract

Since Wald developed the sequential probability ratio test, many studies have been done to approximate the characteristics of the test. One of the major efforts among them is to approximate the excess over the boundaries used in the test. In this paper the excess is approximated as a simple function of the parameter to be tested by using the condition of the test statistic immediately before the stopping time in normal and exponential cases. The use of the estimated excess shows good performances in estimating the operating characteristic function, the average sample number, and the probability mass function of the sarnple number. It also make it possible to determine the boundary values which can give the error probabilities close to the desired ones.