Two-Stage and One-Stage Subset Selection Procedures for Exponential Populations under Heteroscedasticity
DOI:
https://doi.org/10.9734/bpi/mcscd/v8/2054Keywords:
Best treatment, multiple comparisons, probability of correct selection, subset selectionAbstract
This paper investigates subset selection procedures for k (k \(\ge\) 2) independent populations, where each population follows a two-parameter exponential distribution E(\(\mu\)i, \(\theta\)i) with unknown and possibly unequal location \(\mu\)i and scale \(\theta\)i parameters. We define a set of good populations, G = (i \(\mu\)i \(\ge\) \(\mu\)[k] - \(\epsilon\)1) where \(\mu\)[k] is the maximum location parameter and \(\epsilon\)1 > 0. The goal is to select a subset S of k populations that contains G with a pre-specified probability P*, i.e., P\(\underline{\delta}\) = (G \(\subseteq\) S| under the proposed procedure)\(\ge\) P*\(\forall\)\(\underline{\delta}\)\(\in\)\(\Omega\), where \(\underline{\delta}\) = (\(\mu\)1, ... , \(\mu\)k, \(\theta\)1, ... , \(\theta\)k) \(\in\) Rk X \(R^k_+\) = \(\Omega\). The paper proposes both two-stage and one-stage subset selection procedures and derives simultaneous confidence intervals for the differences in location parameters \(\mu\)[k] - \(\mu\)i, i = 1, ... ,k and [j]-[i],ij=1,. . . ,k. Further, a subset selection procedure is also introduced to control the probability of omitting a "good" population or selecting a "bad" one, defined by B= (i \(\mu\)i \(\le\) \(\mu\)[k] - \(\epsilon\)2), where \(\epsilon\)2 > \(\epsilon\)1, at1 - P* . The implementation of the proposed procedures is demonstrated using real-life data.
