Cumulant plots and goodness-of-fit tests for the inverse Gaussian distribution

Abstract

This paper uses a standardized version of the logarithm of the empirical moment generating function in order to construct plots for assessing the appropriateness of the inverse Gaussian distribution. Variability is added to the plots by utilizing asymptotic and finite-sample results. The plots have linear scales and do not rely on the use of tables or special functions. In addition, they are equivalent to a goodness-of-fit test whose critical values are obtained from fitted equations involving the sample size and the estimated shape parameter of the inverse Gaussian distribution. Three data sets are used to illustrate the plots. A similar test is also proposed whose critical values are found through parametric bootstrap. An extensive simulation study shows that the new tests maintain good stability in level and high power across a wider range of distributions and sample sizes than other tests. © 2012 Taylor and Francis Group, LLC.