Multivariate T Distribution: Introduction

Multivariate versions of the Student's t distribution derive through Studentization from multivariate normal models. Multivariate t distributions are useful to model errors of a random experiment offering greater flexibility and heavier tails than multivariate normal models. There are two types of multivariate t distributions. Type I distributions are derived by scaling each component of a normal vector by a single random scalar. Type II distributions involve separate scalings by elements of a further random vector, itself having a joint multivariate distribution.