Confidence intervals of the ratio of means of two independent inverse Gaussian distributions

The inverse Gaussian (IG) distribution is an ideal candidate for modeling positive, right-skewed data. However, there have always been reservations about the use of the IG distribution in data analysis, partially due to the fact the exact confidence interval involving two IG means is not available when the shape parameters are not equal. In this paper, we present an approach based on the modified directed likelihood ratio statistic to obtain the approximate confidence interval of the ratio of two inverse Gaussian means. As assessed by simulation, the coverage probability of the proposed approach is found to be very accurate even for very small sample sizes.