Multiple-decision procedures for testing the homogeneity of mean for \(k\) exponential distributions (Q2321483)

Summary: In multiple-decision procedures, a crucial objective is to determine the association between the probability of a correct decision (CD) and the sample size. A review of some methods is provided, including a subset selection formulation proposed by Huang and Panchapakesan, a multidecision procedure for testing the homogeneity of means by Huang and Lin, and a similar procedure for testing the homogeneity of variances by Lin and Huang. In this paper, we focus on the use of the Lin and Huang method for testing the null hypothesis \(H_0\) of homogeneity of means for \(k\) exponential distributions. We discuss the decision rule \(R\), evaluation of the critical value \(C\), and the infimum of \(P(\mathrm{CD} \mid R)\) for \(k\) independent random samples from \(k\) exponential distributions. In addition, we also observed that a lower bound for the probability of CD relative to the number of the common sample size is determined based on the desired probability of CD when the largest mean is sufficiently larger than the other means. We explain the results by using two examples.