Comparing several exponential populations with more than one control

摘要

Suppose there are k_1 (k_1 ≥ 1) test treatments that we wish to compare with k_2 (k_2≥ 1) control treatments. Assume that the observations from the ith test treatment and the jth control treatment follow a two-parameter exponential distribution E (ξ_i, θ) and E (η_j, θ), where θ is a common scale parameter and ξ_i and η_j are the location parameters of the ith test and the j th control treatment, respectively, i = 1,…, k_i; j = 1,…, k_2. In this paper, simultaneous one-sided and two-sided confidence intervals are proposed for all k_1k_2 differences between the test treatment location and control treatment location parameters, namely ξ_i- η_j, i = 1,…, k_1;rnj = 1,…k_2, and the required critical points are provided. Discussions of multiplerncomparisons of all test treatments with the best control treatment and an optimal sample size allocation are given. Finally, it is shown that the critical points obtained can be used to construct simultaneous confidence intervals for Pareto distribution location parameters.