Step-Up Tests for Comparing Several Exponential Populations with Control: Location Case

Abstract

SYNOPTIC ABSTRACTLet π1…, πk be k treatments/ populations which are to be compared with a control treatment π0. We assume that an observation from population πi follows exponential distribution with probability density function (pdf) , where IA(.) is an indicator function of event A, θ is the common scale parameter and μi is the location parameter, (i = 0, 1, … k. In this paper, the problem of comparing several exponential populations/treatments with a control, in terms of their location parameters, is addressed by simultaneously testing k hypotheses on differences γi = πi, i = 1, …, k by using a step-up test procedure. A method for computing exact critical constants, which control the Type-I family-wise error rate at a preassigned level α, is discussed for one-sided and two-sided testing problems. The required constants are tabulated for specific values of the Type-I family-wise error rate and application of these constants to Pareto probability model is discussed.