Multivariate θ-generalized normal distributions

A new family of continuous multivariate distributions is introduced, generalizing the canonical form of the multivariate normal distribution. The well-known univariate version of this family, as developed by Box, Tiao and Lund, among others, has proven a valuable tool in Bayesian analysis and robustness studies, as well as serving as a unified model for least θ's and maximum likelihood estimates. The purpose of the family introduced here is to extend, to a degree of generality which will permit practical applications, the useful role played by the univariate family to a multidimensional setting.