Two-Sided Confidence Intervals for Ranked Means

Abstract Suppose given k(≥2) populations π1, ···, πk such that observations from population πi have density function f(x—θi), x∈R, where the location parameter θi is unknown (1 ≤ i ≤ k). Assume Ef ≡ ∫∞ -∞ xf(x)dx < ∞. Let the population means be denoted by μ1, ···, μk and their ranked values by μ[1] ≤ ··· ≤ μ[k]. Dudewicz [1] gave upper and lower confidence intervals for μ[i](1 ≤ i ≤ k). We use these to obtain a class of two-sided intervals. For μ[k] Lal Saxena and Tong [2] previously proposed another two-sided interval. These are compared; e.g., in the case of normal populations ours has smaller length for most values of k.