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Biometrika 1971 58(3):615-623; doi:10.1093/biomet/58.3.615
© 1971 by Biometrika Trust
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A technique for obtaining probabilities of correct selection in a two-stage selection problem

PAUL N. SOMERVILLE

RCA International Service Corporation, Patrick Air Force Base, Florida and Florida Institute of Technology Melbourne, Florida

Suppose one has several normal populations, identically distributed except for their means. At stage one a sample of size n1 is taken from each population. At stage two, a sample of size n2 is taken from the two populations producing the largest means in stage one and the population having the largest cumulative mean selected as best. For the least favourable configuration of means an algorithm is developed for calculating pn, the probability of ‘correct’ selection. The technique involves using a finite representation of the standard normal distribution, counting methods and the use of a high-speed computer both for enumeration and for later smoothing and filtering.

Key Words: Ranking • Selection • Multivariate normal intergral • Combinatorial methods • Enumerative techniques • Finite representation


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