On some characterizations of the t-distribution

In this paper we discuss three different characterizations of the generalized t-distribution within the class of the eliptical distributions. We show that this distribution can be characterized in terms of its unconditional and conditional marginals and in terms of quadratic forms. Similar results have been proved for the normal distribution. An additional characterization of the t distribution within the subclass of the compound normal distributions (or scale mixture of normal distributions) is also studied.