Sequential Analysis, Direct Method

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Abstract
This paper describes from first principles the direct calculation of the operating characteristic function, O.C., the probability of accepting the hypothesis θ = θ0, and the average sample size, A.S.N., required to terminate the test, for any truncated sequential test once the acceptance, rejection, and the continuation regions are specified at each stage. What is needed is to regard a sequential test as a step by step random walk, which is a Markov chain. The method is contrasted with Wald's and two examples are included.

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