Introduction

3In 1915, Schrödinger derived the cumulative probability distribution of what is now regarded as the first passage time of a Wiener process with positive drift. Tweedie (1947) proposed the name Inverse Gaussian for the first passage time distribution, because of the inverse relationship between its cumulative generating function and that of the normal (Gaussian) distribution. The Inverse Gaussian distribution is also known as Wald’s distribution following Wald (1947), who derived it as a limiting form of the distribution of sample size in certain sequential probability ratio tests.