## 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 (p_{1}, p_{2}., p_{k}), 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 language | English |
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Pages (from-to) | 2887-2896 |

Number of pages | 10 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 12 |

Issue number | 24 |

DOIs | |

Publication status | Published - 1 Jan 1983 |

### Bibliographical note

Copyright:Copyright 2015 Elsevier B.V., All rights reserved.

## Keywords

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

## ASJC Scopus subject areas

- Statistics and Probability