The first passage time distribution of brownian motion and its applications

Abstract

This paper traces the development of the first passage time distribution of Brownian motion (inverse Gaussian) together with its various applications in inventory problems, usage and storage times, detection theory, labor turnover, money supply, purchasing models, hospital inpatient stay times, strikes duration, biology, … etc. Besides, since the inverse Gaussian distribution arises as the distribution of first passage time of Brownian motion, its applicability to lifetime modeling is a natural consequence. The general characteristics of the inverse Gaussian model which make it attractive for various applications are also identified.