Finite mixtures of multivariate skew tail-inflated normal distributions

Finite mixtures are a flexible and common tool for modelling underlying group structures in the data. It is often the case that groups in the data present non-normal features, such as asymmetry and heavy tails. To accommodate these aspects, in this work, we first introduce a new distribution: the multivariate skew tail-inflated normal. Then, we use this distribution in a mixture modelling setting. An AECM algorithm is disclosed for maximum-likelihood parameter estimation. A simulation study is conducted to assess the goodness of the proposed algorithm in recovering the model parameters and data classification. Furthermore, we analyze two real datasets: one concerning log-returns of four cryptocurrencies, and the other regarding performance indicators of university courses across Italy.