Computational aspects of stable distributions

Abstract

Stable distributions are a class of probability distributions that generalize the normal distribution. They are the only possible limits of normalized sums of independent, identically distributed terms, so sums of a large number of such terms have to approach a stable law. The non‐Gaussian stable distributions have heavy tails with infinite variance, and can be skewed. In most cases, there are no known formulas for the density or cumulative distribution function of these laws, so using them in practice requires significant computational methods. This paper explains some of the computations used to make stable laws useful in practical problems.