Equal probability of correct selection for bernoulli selection procedures

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Abstract

The problem of selecting the Bernoulli population which has the highest “success” probability is considered. It has been noted in several articles that the probability of a correct selection is the same, uniformly in the Bernoulli p-vector (p1, p2., pk), for two or more different selection procedures. We give a general theorem which explains this phenomenon. An application of particular interest arises when “strong” curtailment of a single-stage procedure (as introduced by Bechhofer and Kulkarni (1982a)) is employed; the corresponding result for “weak” curtailment of a single-stage procedure needs no proof. The use of strong curtailment in place of weak curtailment requires no more (and usually many less) observations to achieve the same probability of a correct selection. Similar general results hold for the analogous multinomial selection problems.

Original languageEnglish
Pages (from-to)2887-2896
Number of pages10
JournalCommunications in Statistics - Theory and Methods
Volume12
Issue number24
DOIs
Publication statusPublished - 1 Jan 1983

Keywords

  • Bermoullie selection problem
  • probability of correct selection
  • sequential selection procedures
  • strong curtailment
  • weak curtailment

ASJC Scopus subject areas

  • Statistics and Probability

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