Prediction Intervals for Future Observations from the Inverse Gaussian Distribution

This paper discusses the problem of predicting a future observation from an inverse Gaussian distribution, based on a sample of size n from that same distribution. Two prediction intervals that have been proposed in the literature, one of which is an approximate prediction interval, are compared using Monte Carlo simulations. In many of the simulated cases the approximate prediction interval is superior with respect to larger estimated coverage probabilities and smaller estimated mean lengths. This is true in particular for n at least 15 and for 95% and 99% prediction intervals.