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.

Keywords:

• Critical points
• Exponential probability model
• Numerical integration
• Simple order alternative
• Simultaneous Confidence intervals
• Uniform probability model

Mathematics Subject Classification:

• 62G10
• 62N02
• 62G30
• 65D30
• 62N01
• 62F25

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.