Clustering via new parsimonious mixtures of heavy tailed distributions

Two families of parsimonious mixture models are used for model-based clustering. They are based on the multivariate shifted exponential normal and the multivariate tail-inflated normal distributions, heavy tailed generalizations of the multivariate normal. Parsimony is achieved via the eigen-decomposition of the component scale matrices, as well as by imposing a constraint on the tailedness parameter. Two variants of the expectation-maximization algorithm are used for parameter estimation. Identifiability conditions are illustrated, and the advantages of our models with respect to other existing parsimonious heavy-tailed mixture models are commented. Our models are firstly tested via simulation studies, and then compared to some competing models in real data applications.