Abstract
Consider k (k ≥ 3) treatments or competing firms such that observations from ith treatment or firm follows a two-parameter exponential probability distribution E(μ i ,θ i ), where μ i is the location parameter and θ i (θ i > 0) is the scale parameter, i = 1,…,k. Singh and Gill (Citation2004) proposed a class of one-sided tests, based on sample quasi-ranges, for testing the null hypothesis of homogeneity against the simple ordered alternative for doubly censored data, as well as for data contaminated with outlier. In this article, a class of tests, based on sample quasi-ranges, for testing the null hypothesis H o :θ1 =···= θ k against the U-shaped alternative H u :θ1 ≥···≥ θ h ≤···≤ θ k with at least one strict inequality, a generalization of Singh and Liu's procedure is proposed. The required critical constants for the implement of the proposed procedures are computed using a recursive integration technique. A simulation study is carried to examine the robustness of our presently proposed tests based on sample quasi-ranges. An optimum selection criterion of a member from the proposed class is also considered.
Acknowledgments
The author gratefully acknowledges the helpful suggestions of referees and the associate editor, which have led to an appreciable improvement in the quality of the article.