Suppose that there are k ≥ 2 independent populations (treatments or systems), where the worth of the i-th population is measured in terms of an unknown location parameter μi, i = 1 . . ., k. For a pre-assigned level P*, we construct 100P*% simultaneous two-sided confidence intervals for parameters minj ≠ i μj − μi, μi − maxj≠i μj, i = 1, . . ., k, for the location-scale probability models by assuming that the k populations have the same scale parameter θ. We call these comparisons as multiple comparisons with the worst and best. We also construct 100P*% simultaneous upper and two-sided confidence intervals for parameters μ[i] − μ[1], i≠1, μ[k] − μ[i], i ≠ k, where μ[1] ≤ . . . ≤ μ[k] denote the ranked values of μis. The cases of known and unknown scale parameter θ are dealt with separately. Results are applied to exponential populations model and, for this case, tables for implementation of proposed confidence intervals are provided. Finally, implementation of proposed confidence intervals is illustrated through an example.
