24 Recent developments in the inverse Gaussian distribution

Abstract

This chapter describes the principal developments in inverse Gaussian theory. An important application of this model is in reliability theory, which has spurred considerable progress in regression for the inverse Gaussian model. The widely applicable physical basis for this model and its analytical tractability make the search for a useful multidimensional generalization important. The chapter discusses the various proposals for a multivariate inverse Gaussian; a variety of special results such as estimation, characterization theorems, and Bayesian methods; the generalized inverse Gaussian distribution; and various applications of the inverse Gaussian. The inverse Gaussian is a competitor to other well-known parametric families, such as the gamma or the Weibull. The inverse Gaussian model arises out of a spatially homogeneous random walk or diffusion, plus a constant drift towards a linear barrier. There are several ways to generalize these constructions, and these generalizations are most convincing if they are motivated by physical considerations. The analytical tractability of the inverse Gaussian is sufficient reason to use it for curve fitting. As the hazard function for the inverse Gaussian increases and then decreases, it serves as a good model for accelerated life tests.