This textbook highlights the many practical uses of stable distributions, exploring the theory, numerical algorithms, and statistical methods used to work with stable laws. Because of the author's accessible and comprehensive approach, readers will be able to understand and use these methods....

In this paper we describe methods and evaluate programs for linear regression by maximum likelihood when the errors have a heavy tailed stable distribution. The asymptotic Fisher information matrix for both the regression coefficients and the error distribution parameters are derived, giving...

In this paper, we explore tail dependence modeling in multivariate extreme value distributions. The measure of dependence chosen is the scale function, which allows combinations of distributions in a very flexible way. The correspondences between the scale function and the spectral measure or...

This paper unifies and extends results on a class of multivariate extreme value (EV) models studied by Hougaard, Crowder and Tawn. In these models, both unconditional and conditional distributions are themselves EV distributions, and all lower-dimensional marginals and maxima belong to the...

We describe a method for calculating simultaneous prediction intervals for ARMA times series with heavy-tailed stable innovations. The spectral measure of the vector of prediction errors is shown to be discrete. Direct computation of high-dimensional stable probabilities is not feasible, but we...