Generating Random Variables from the Inverse Gaussian and First-Passage-Two-Barrier Distributions

We investigate a naive method for generating pseudo-random variables from two distributions, the inverse Gaussian and the First-PassageTwo-Barrier distribution. These are the first passage time distributions of a Wiener process with non-zero drift to one and two barriers respectively. The method consists of simulating a path (a realization of the Wiener process) by constructing a step function which jumps by a normally distributed amount at successive time intervals. The time at which the path breaches a barrier (the first passage time) is taken as a realization of the desired random variable. We show that this method is unsatisfactory, at least for some combinations of parameter values and time intervals between jumps, and suggest possible areas for future work.