A Restricted Subset Selection Rule for Selecting at Least One of the t Best Normal Populations in Terms of Their Means When Their Common Variance is Known,Case II |
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Authors: | Pinyuen Chen Lifang Hsu |
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Institution: | 1. Department of Mathematics, Syracuse University, Syracuse, New York, USA;2. Department of Mathematics, LeMoyne College, Syracuse, New York, USA |
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Abstract: | Consider k( ? 2) normal populations with unknown means μ1, …, μk, and a common known variance σ2. Let μ1] ? ??? ? μk] denote the ordered μi.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 RHPfor 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 μk ? t + 1] ? μk ? 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 RHP 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 μi. The probability requirement in this latter case is termed the subset selection probability requirement. Santner (1976) proposed and investigated a different procedure (RS) 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. |
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Keywords: | Restricted subset size Selecting normal means Subset selection probability requirement |
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