Goodness-of-fit tests for the inverse Gaussian and related distributions

In this paper, tests of goodness-of-fit for the inverse Gaussian distribution are developed. The distribution involves a shape parameter and, because of this, some test approaches lead to inconsistent strategies. A consistent test is proposed and its properties investigated. A table of critical points is provided and both the level and the power of the test are explored by simulation. It is seen that the test is more powerful than most of its competitors. The framework is widened to cover satellite distributions of the inverse Gaussian and some types of censored data. An example concludes the paper.