On the Conditional Distribution of the Multivariate t Distribution

As alternatives to the normal distributions, t distributions are widely applied in robust analysis for data with outliers or heavy tails. The properties of the multivariate t distribution are well documented in Kotz and Nadarajah's book, which, however, states a wrong conclusion about the conditional distribution of the multivariate t distribution. Previous literature has recognized that the conditional distribution of the multivariate t distribution also follows the multivariate t distribution. We provide an intuitive proof without directly manipulating the complicated density function of the multivariate t distribution.