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A test for the homogeneity of normal variances was proposed by Liu and Xu [Liu, X.H., Xu, X.Z., 2010. A generalized p-value approach for testing the homogeneity of variances. Statistics and Probability Letters 80, 1486–1491]. For testing the homogeneity of inverse Gaussian scale-like parameters, a parallel test is developed in this article. The proposed test is proved to have exact frequent property...