Comparing exponential location parameters with several controls under heteroscedasticity

Suppose that random samples are taken from <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$k$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>k</mi> </math> </EquationSource> </InlineEquation> treatment groups and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$l$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>l</mi> </math> </EquationSource> </InlineEquation> control groups, where the observations in each group have a two-parameter exponential distribution. We consider the problem of constructing simultaneous confidence intervals for the differences between location parameters of the treatment groups and the control groups when the scale parameters may be unequal. Using the parametric bootstrap approach, we develop a new multiple comparisons procedure when the scale parameters and sample sizes are possibly unequal. We then present a simulation study in which we compare the performance of our proposed procedure with two other procedures. The results of our simulations indicate that our proposed procedure performs better than other procedures. The usefulness of our proposed procedure is illustrated with an example. Copyright Springer-Verlag Berlin Heidelberg 2014