A new generalized p-value for testing equality of inverse Gaussian means under heterogeneity

For the problem of comparing the means of k inverse Gaussian (IG) populations, a new generalized pivot quantity is defined and the generalized p-value based on this generalized pivot quantity is also given. Numerical results indicate that the proposed test has excellent type I error control for both balanced and unbalanced cases, and tends to be robust for the number of populations, whereas the type I error probability of the Tian’s generalized test can be much larger than the nominal level for a bigger value of k. The proposed procedure is illustrated using two examples.