Inferences on the coefficient of variation of an inverse gaussian distribution

The likelihood ratio test for a characteristic parameter of the inverse Gaussian distribution is derived. The parameter of interest characterizes the coefficient of variation, the skewness and the kurtosis of the distribution. The distribution of the test statistic is presented in a simplified form. Useful quanfiles of the distribution are given. Methods for constructing confidence bounds for the parameter, including Bayes highest posterior density intervals, are considered.