A Comparison of Five Tests for the Equality of Inverse Gaussian Means under Heteroscedasticity of Scale Parameters

Abstract

Analysis of Reciprocals F-test developed by Miura [1] is used to test the equality of InverseGaussian (IG) means based on the assumption of homogeneity of scale parameters. However,this method is not valid when this assumption is not satisfied. There are some methodsdeveloped for comparing the equality of the IG means under heteroscedasticity of scaleparameters. In this study, the goal of this study is to compare these methods under differentcombinations of parameters and various sample sizes. We compare the performances of the fivecommonly used tests in the literature via Monte Carlo simulation study. The tests considered areanalysis of reciprocals (ANORE) F-test, parametric bootstrap approach (PBA), generalized pvalueapproach proposed by Tian (GPA), generalized p-value approach proposed by Shi and Lv(GPSL) and computational approach test (CAT). According to simulation results, GPSL andCAT have satisfactory type I error rates for all parameter combinations. Except for the numberof groups is k=7, when the sample sizes are different and scale parameters are both different andinversely proportional, the power of GPA is higher than the other tests.