Mixtures of multivariate power exponential distributions

Summary

An expanded family of mixtures of multivariate power exponential distributions is introduced. While fitting heavy‐tails and skewness have received much attention in the model‐based clustering literature recently, we investigate the use of a distribution that can deal with both varying tail‐weight and peakedness of data. A family of parsimonious models is proposed using an eigen‐decomposition of the scale matrix. A generalized expectation–maximization algorithm is presented that combines convex optimization via a minorization–maximization approach and optimization based on accelerated line search algorithms on the Stiefel manifold. Lastly, the utility of this family of models is illustrated using both toy and benchmark data.