By Zakkula Govindarajulu
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Extra resources for Sequential statistics
This formula is valid if the starting points of the test are not near either boundary and if the mean paths are inclined to the. boundaries at not more than a small angle so that the overshoot beyond the boundary at the end of the test is negligible. Page (1954) derived expressions for the OC function and the ASN of a SPRT that are closer to the true values. Kemp (1958) obtains even better approximations by using the same method of Page (1954) but different assumptions and we will present Kemp’s results.
However, if the SPRT (B’,A’) is used instead of ( B ,A ) it is not obvious whether the error probabilities are decreased or increased. , a(1-p’) p(1-a’) 2 a’(1-P) L: P’(1 - a ) - Adding these two we obtain a + p 2 a’+ P’. That is, at most one of the error probabilities could be larger than the nominal error probability. 2. SPRT: IT’S FINITE TERMINATION AND BOUNDS 17 + hence any increase in error size in a’ [p’] is not beyond a factor of 1 p [1+a]. These factors are close to unity when a and ,8 are small.
A possible excess of f l / f o beyond the boundaries A and B at termination of the test procedure is caused by the discontinuity of the number of observations. If n were continuous then f1/ fo would be continuous in n and the ratio could exactly achieve A and B at the time of the termination. 9) has shown that increase in the expected sample number using the inequalities is slight. A nice feature of the SPRT is that the approximations to A and B are only functions of a and /3 and can be computed once and for all free of f;whereas the critical values in Neyman and Pearson formulations of fixed-sample procedures depend on f and a.