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A Modified Play-the-Winner Rule for Sequential Trials

Bartholomew P. Hsi and Thomas A. Louis
Journal of the American Statistical Association
Vol. 70, No. 351 (Sep., 1975), pp. 644-647
DOI: 10.2307/2285948
Stable URL: http://www.jstor.org/stable/2285948
Page Count: 4
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A Modified Play-the-Winner Rule for Sequential Trials
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Abstract

The two-arm bandit type of Play-the-Winner rule is modified to sample simultaneously the two competing sequences of trials until the first "failure" occurs. Then the sequence without a failure is sampled until it fails, and the process is repeated. This modification leads to the direct application of the sequential probability ratio test on two paired geometric variables. A further modification leads to a scheme which avoids overshooting the stopping boundaries and reduces the total sample size. Exact formulas for the boundary limits, operating characteristics and ASN function for the proposed methods are presented.

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