On Tests Based on Sample Quasi Ranges for Ordered Alternative (Scale Case of Exponential Distribution)

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 (2004) 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.