The likelihood ratio tests for homogeneity of inverse Gaussian means under simple order and simple tree order

The inverse Gaussian (IG) family is now widely used for modeling non negative skewed measurements. In this article, we construct the likelihood-ratio tests (LRTs) for homogeneity of the order constrained IG means and study the null distributions for simple order and simple tree order cases. Interestingly, it is seen that the null distribution results for the normal case are applicable without modification to the IG case. This supplements the numerous well known and striking analogies between Gaussian and inverse Gaussian families.