Calculations Involving the Multivariate Normal and Multivariate t Distributions with and without Truncation

Clustering Multivariate Normal Distributions

In this paper, we consider the task of clustering multivariate normal distributions with respect to the relative entropy into a prescribed number, k, of clusters using a generalization of Lloyd’s k-means algorithm [1]. We revisit this information-theoretic clustering problem under the auspices of mixed-type Bregman divergences, and show that the approach of Davis and Dhillon [2] (NIPS*06) can a...

The entropic centers of multivariate normal distributions

In this paper, we seek for a single best representative of a set of statistical multivariate normal distributions. To define the “best” center, we consider either minimizing the average or the maximum relative entropy of the center to the given set of normal distributions. Since the relative entropy is an asymmetric divergence, this yields the notion of leftand right-sided, and symmetrized entr...

Multivariate t Distributions and Their Applications

Shape mixtures of multivariate skew-normal distributions

Classes of shape mixtures of independent and dependent multivariate skew-normal distributions are considered and some of their main properties are studied. If interpreted from a Bayesian point of view, the results obtained in this paper bring tractability to the problem of inference for the shape parameter, that is, the posterior distribution can be written in analytic form. Robust inference fo...

Multivariate extremes of generalized skew-normal distributions

We explore extremal properties of a family of skewed distributions extended from the multivariate normal distribution by introducing a skewing function π . We give sufficient conditions on the skewing function for the pairwise asymptotic independence to hold. We apply our results to a special case of the bivariate skew-normal distribution and finally support our conclusions by a simulation stud...