Abstract. We present a novel algorithm for approximating the parameters of a multivariate t-distribution. At the expense of a slightly decreased accuracy in the estimates, the proposed algorithm is significantly faster and easier to implement compared to the maximum likelihood estimates computed using the expectation-maximization algorithm. The formulation of the proposed algorithm also provides theoretical guidance for solving problems that are intractable with the maximum likelihood equations. In particular, we show how the proposed algorithm can be modified to give an incremental solution for fast online parameter estimation. Finally, we validate the effectiveness of the proposed algorithm by using the approximated t-distribution as a drop in replacement for the conventional Gaussian distribution in two computer vision applications: object recognition and tracking. In both cases the t-distribution gives better performance with no increase in computation.