A closed testing procedure for comparing successive exponential populations with respect to location parameter

ABSTRACT

Consider k independent random samples such that i^th sample is drawn from a two-parameter exponential population with location parameter μ_i and scale parameter θ_i, i = 1, …, k. For simultaneously testing differences between location parameters of successive exponential populations, closed testing procedures are proposed separately for the following cases (i) when scale parameters are unknown and equal and (ii) when scale parameters are unknown and unequal. Critical constants required for the proposed procedures are obtained numerically and the selected values of the critical constants are tabulated. Simulation study revealed that the proposed procedures has better ability to detect the significant differences and has more power in comparison to exiting procedures. The illustration of the proposed procedures is given using real data.

KEYWORDS:

• Type I family-wise error rate
• Power comparison
• Simultaneous confidence intervals
• Critical constants

Acknowledgments

The authors are deeply grateful to the referees and the editors for their valuable comments and suggestions, which led to an appreciable improvement in the quality of the manuscript.