An approximate prediction linterval for the mean of future observations from the inverse gaussian distribution

The problem of predicting, on the basis of an observed sample from an inverse Gaussian distribution, the mean of a future random sample from the same distribution is considered. Approximate prediction intervals are proposed, and their accuracy is investigated via extensive Monte Carlo simulations. The results are useful for predicting the mean of future first passage times for a Brownian motion with positive drift or mean failure time of m future items having inverse Gaussian life distribution.