Modified generalized p-value and confidence interval by Fisher's fiducial approach

Abstract

In this study, we develop two simple generalized confdence intervalsfor the difierence between means of two normal populations with heteroscedasticvariances which is usually referred to as the Behrens-Fisherproblem. The developed confidence intervals are compared with thegeneralized confidence interval in the literature. We also propose modiedfiducial based approach using Fisher's ducial inference for comparingthe mean of two lognormal distributions and compare them withthe other tests in the literature. A Monte Carlo simulation study isconducted to evaluate performances of the proposed methods underdierent scenarios. The simulation results indicate that the developedconfidences intervals for the Behrens-Fisher problem have shorter intervallengths and they give better coverage accuracy in some cases. Themodified fiducial based approach is the best to provide satisfactory resultsin respect to its type error and power in all sample sizes. Themodified test is applicable to small samples and is easy to compute andimplement. The methods are also applied to two real-life examples.