title: A distance between elliptical distributions based in an embedding into the Siegel group
abstract: This paper describes two different embeddings of the manifolds corresponding to many elliptical probability distributions with the informative geometry into the manifold of positive-definite matrices with the Siegel metric, generalizing a result published previously elsewhere. These new general embeddings are applicable to a wide class of elliptical probability distributions, in which the normal, t-Student and Cauchy are specific examples. A lower bound for the Rao distance is obtained, which is itself a distance, and, through these embeddings, a number of statistical tests of hypothesis are derived
keyphrases: elliptical distributions Siegel group elliptical probability distributions informative geometry positive-definite matrices lower bound manifolds embeddings