Article,
Some characterizations of the multivariate t distribution
Journal of Multivariate Analysis, 2 (3): 339 - 344 (1972)
DOI: http://dx.doi.org/10.1016/0047-259X(72)90021-8
Abstract
A multivariate t vector X is represented in two different forms, one associated with a normal vector and an independent chi-squared variable, and the other with a normal vector and an independent Wishart matrix. We show that X is multivariate t with mean μ, covariance matrix ν(ν − 2)−1Σ, ν > 2 and degrees of freedom ν if and only if for any a ≠ 0, (a′Σa)−1/2a′(X − μ) has the Student's t distribution with ν degrees of freedom under both representations. Some other characterizations are also obtained.
