Multivariate dispersion models

We introduce a class of multivariate dispersion models suitable as error di stributions for generalized linear models with multivariate non-normal resp onses. The models preserve some of the main properties of the multivariate normal distribution, and include the elliptically contoured distributions a nd certain other known distributions as special cases. We give explicit met hods for constructing multivariate proper dispersion models. This is exempl ified by constructing multivariate gamma, Laplace, hyperbola, and von Mises distributions. (C) 2000 Academic Press AMS subject classifications: 62H05, 62H11.