Assessing the inverse Gaussian distribution assumption

Two easily applied goodness-of-fit tests for the inverse Gaussian distribution are discussed. One of these tests is the familiar Kolmogorov-Smirnov one-sample test that is applied when the form of a probability distribution is completely specified. When the parameters of the distribution are unknown, as is more typical, the Kolmogorov-Smirnov test cannot be directly applied. In this instance, a transformation that uses a distributional result relating the Student-t distribution to the inverse Gaussian distribution allows the Lilliefors test of normality to be adapted to test the inverse Gaussian distribution assumption.>