%0 Journal Article %1 Lin1972339 %A Lin, Pi-Erh %D 1972 %J Journal of Multivariate Analysis %K multivariate statistics t-distribution %N 3 %P 339 - 344 %R http://dx.doi.org/10.1016/0047-259X(72)90021-8 %T Some characterizations of the multivariate t distribution %U http://www.sciencedirect.com/science/article/pii/0047259X72900218 %V 2 %X 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.

@article{Lin1972339, 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. }, added-at = {2015-05-13T00:55:49.000+0200}, author = {Lin, Pi-Erh}, biburl = {https://www.bibsonomy.org/bibtex/21479258169426b332922690bef611be0/shabbychef}, description = {Some characterizations of the multivariate t distribution}, doi = {http://dx.doi.org/10.1016/0047-259X(72)90021-8}, interhash = {8f4e5732d0e9c5631b869c2f67d8c6ea}, intrahash = {1479258169426b332922690bef611be0}, issn = {0047-259X}, journal = {Journal of Multivariate Analysis }, keywords = {multivariate statistics t-distribution}, number = 3, pages = {339 - 344}, timestamp = {2015-05-13T00:55:49.000+0200}, title = {Some characterizations of the multivariate t distribution }, url = {http://www.sciencedirect.com/science/article/pii/0047259X72900218}, volume = 2, year = 1972 }