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Selection of good populations and related confidence intervals using sample quasi-ranges

机译：使用样本准范围选择良好的总体和相关的置信区间

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The authors consider k (k > = 2) independent populations or treatments such that an observation from population pi_i follows an absolutely continuous distribution which is a member of a location-scale family with location parameter mu_i (-infinity < mu_i < 00) and scale parameter theta_i (theta_i > 0), i = 1,...k. For a given sigma_1 (sigma_1 > 1) the population pi_i is considered 'good' if theta_i < sigma_1 theta_[1] i= 1,...k, where theta_[1] = min(theta_1,..., theta_k). A class of selection procedures, based on sample quasi-ranges, is proposed to select a subset of k populations which includes all good populations with probability at least P* (a preassigned value). Bofinger and Mengersen (Ref. 1) considered k (k > 2) treatments possibly differing in location parameters theta_1,..., theta_k and proposed a subset selection procedure to obtain the conservative results for the goals of selecting all the good or only good treatments, where 'good' means having a location parameter among the largest t (1 < t < k). vander Laan (Refs. 2, 3), retricting to location setting of Chen and Dudewicz (Ref. 4), proposed a subset selection procedure to select a subset which contains at least one eppsion-best treatment, where the treatment pi_i with location parameter theta_i was termed eppsion-best when theta_i > = theta_[k] - eppsion, eppsion > = 0. The author has also tabulated the efficiency results as compared to the subset selection procedure of Gupta (Ref. 5) for various choices of e, P' and k. Gill, Sharma and Misra (Ref. 6) extended Lam's (Ref. 7) approach to the scale parameters. All these procedures are applicable only when complete samples are available from each of the k populations. McDonald (Ref. 8), and Singh, Gill and Mishra (Ref. 9) proposed subset selection procedures based on sample quasi-ranges, under different probability settings, to select a subset which contains the best population associated with the smallest scale parameter, whereas the goal in this is to select which contains the set of good populations.
机译：作者考虑了k（k> = 2）个独立的种群或处理方法，以便从种群pi_i观察到的结果遵循绝对连续分布，该分布是具有位置参数mu_i（-infinity 0），i = 1，... k。对于给定的sigma_1（sigma_1> 1），如果theta_i 2）种处理可能在位置参数theta_1，...，theta_k上有所不同，并提出了一个子集选择程序来获得保守的结果，以选择所有优良或唯一优良的目标。处理，其中“好”表示在最大t（1 = theta_ [k]-eppsion，eppsion> = 0时，theta_i被称为最佳爆发。作者还列出了针对e的各种选择与Gupta的子集选择程序（参考5）相比的效率结果， P'和k。 Gill，Sharma和Misra（参考文献6）将Lam（参考文献7）的方法扩展到比例参数。所有这些程序仅在从k个群体中的每个群体中都有完整的样本可用时才适用。麦当劳（参考文献8）和辛格，吉尔和米斯拉（参考文献9）提出了基于样本准范围的子集选择程序，该方法在不同的概率设置下选择了包含与最小尺度参数相关的最佳总体的子集，而这样做的目的是选择包含一组良好人口的人群。

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