Two-Stage and One-Stage Subset Selection Procedures for Exponential Populations under Heteroscedasticity

his paper investigates subset selection procedures for k (k
2) independent populations, where each population follows a two-parameter exponential distribution E(
i, i) with unknown and possibly unequal location
i and scale i parameters. We define a set of good populations,[k] - 1) where [k] is the maximum location parameter and 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 = (G S| under the proposed procedure)
P*where = (1, ... , k, 1, ... , k) Rk X The paper proposes both two-stage and one-stage subset selection procedures and derives simultaneous confidence intervals for the differences in location parameters
[k] - 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 i [k] - 2), where 2 >
1, at1 - P* . The implementation of the proposed procedures is demonstrated using real-life data.