Modeling with Stable Distributions

Abstract

Stable distributions have been proposed as a model for many types of physical and economic systems. There are several reasons for using a stable distribution to describe a system. The first is where there are solid theoretical reasons for expecting a non-Gaussian stable model, e.g. reflection off a rotating mirror yielding a Cauchy distribution, hitting times for a Brownian motion yielding a Lévy distribution, the gravitational field of stars yielding the Holtsmark distribution; see below for these and other examples.