Quadratic statistics for the goodness-of-fit test of the inverse Gaussian distribution

The problem of using a quadratic test to examine the goodness-of-fit of an inverse Gaussian distribution with unknown parameters is discussed. Tables of approximate critical values of Anderson-Darling, Cramer-von Mises, and Watson test statistics are presented in a format requiring only the sample size and the estimated value of the shape parameter. A relationship is found between the sample size and critical values of these test statistics, thus eliminating a need to interpolate among sample sizes given in the table. A power study showed that the proposed modified goodness-of-fit procedures have reasonably good power.>