### Abstract

Consider k(2) normal populations with unknown means _{1},., _{k}, and a common known variance σ^{2}. Let _{[1]} ṡṡṡ _{[k]} denote the ordered _{i}.The populations associated with the t(1 t k-1) largest means are called the t best populations. Hsu and Panchapakesan (2004) proposed and investigated a procedure RH_{p}for selecting a non empty subset of the k populations whose size is at most m(1 m k-t) so that at least one of the t best populations is included in the selected subset with a minimum guaranteed probability P* whenever [k-t + _{1]}-[k-_{t]} δ*, where P* and δ* are specified in advance of the experiment. This probability requirement is known as the indifference-zone probability requirement. In the present article, we investigate the same procedure RH_{p} for the same goal as before but when k-t < m k-1 so that at least one of the t best populations is included in the selected subset with a minimum guaranteed probability P* whatever be the configuration of the unknown _{i}. The probability requirement in this latter case is termed the subset selection probability requirement. Santner (1976) proposed and investigated a different procedure (R_{S}) based on samples of size n from each of the populations, considering both cases, 1 m k-t and k-t < m k. The special case of t = 1 was earlier studied by Gupta and Santner (1973) and Hsu and Panchapakesan (2002) for their respective procedures.

Original language | English (US) |
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Pages (from-to) | 2250-2259 |

Number of pages | 10 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 43 |

Issue number | 10-12 |

DOIs | |

State | Published - May 15 2014 |

### Keywords

- Restricted subset size
- Selecting normalmeans
- Subset selection probability requirement

### ASJC Scopus subject areas

- Statistics and Probability

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## Cite this

*Communications in Statistics - Theory and Methods*,

*43*(10-12), 2250-2259. https://doi.org/10.1080/03610926.2013.827717