Simultaneous Testing for the Successive Differences of Exponential Location Parameters

Abstract

Suppose that k (k ≥ 3) treatments under comparison are ordered in a certain way. For example, the treatments may be increasing dose levels in dose response experiments. The exponential distribution E(μ,Θ) is generally used to model the effective duration of a drug, where the location parameter μ is referred to as latency period that may decrease/increase with the increase in dose level of the drug. In such situations, the experimenter may be interested in the successive comparisons of the treatments. Let E(μ₁,Θ₁),…,E(μ _k ,Θ _k ) be k independent exponential distributions/populations with μ _i (Θ _i ) as the location (scale) parameter of the i th population, i = 1,…,k. In this article, we propose test procedures for simultaneously testing the family of hypotheses

A recursive method for computing the critical constants is discussed. The required tables of critical constants for the implementation of the proposed test procedures are presented. The test procedure is used to derive the simultaneous confidence intervals for the successive differences between the location parameters; that is, μ₂ − μ₁,μ₃ − μ₂,…,μ _k  − μ _k−1. We also extend these simultaneous confidence intervals for successive differences to a larger class of contrasts of the location parameters.

Keywords:

• Contrasts
• Critical constants
• Numerical integration
• Pairwise comparisons
• Simultaneous confidence intervals

Mathematics Subject Classification:

• Primary 62J15, 62F03
• Secondary 62F25, 62N05

Acknowledgments

The authors are grateful to the editor's and referee' comments and suggestions which improved this article.