Step-Down Procedure for Comparison between Successive Exponential Populations

Abstract

This article deals with the comparison between successive two-parameter exponential populations with respect to the location parameter when it is reasonable to assume that the populations are ordered in some natural way. It is well reported in the literature that if the interest of the experimenter is only in testing the significance of differences, the stepwise procedures are more powerful than the simultaneous confidence intervals procedures. This fact motivated us to extend the simultaneous confidence intervals procedure, for the differences between the location parameters of successive exponential populations, of Singh et al. (2006) to a stepwise procedure by proposing step-down tests for simultaneously testing the significance of the differences of the location parameters of successive two-parameter exponential populations. For a given type-I family-wise error rate (FWER), the critical constants are tabulated for the implementation of the proposed procedure by the practitioners. The advantage of the proposed procedure in comparison to the Singh et al. (2006) procedure is demonstrated by using a numerical example.