A test for homogeneity of ordered means of inverse Gaussian populations

The inference theory and methodology for the inverse Gaussian (IG) family of right skewed distributions with nonnegative support are well known to bear a striking resemblance to the normal theory and methods. The IG family is therefore increasingly used for modeling and analyzing nonnegative, right skewed data. In this note, we consider the problem of testing homogeneity of order-restricted IG means with a common known scale parameter using the approach used in Mudholkar and McDermott (Biometrika 76 (1989) 161). It is shown that the null hypothesis of equal means in the IG model admits a union-intersection decomposition and, the p-values of the one-tailed Z-like tests used for testing the component hypotheses are independently distributed as in the normal case. This allows testing homogeneity of IG means under a spectrum of order constraints using the classical methods for combining independent p-values. The power properties of this test, for the simple order-restricted case, are empirically examined and compared with the order-restricted likelihood ratio test (Tian and Mudholkar (The likelihood ratio tests for homogeneity of inverse Gaussian means under simple order and simple tree order, submitted for publication)), and the chi-square test which ignores the order restrictions.