Matrix-variate normal mean-variance Birnbaum–Saunders distributions and related mixture models

Matrix-variate data analysis has increasingly attracted interest in the statistical literature over the recent years, especially in the model-based clustering framework. Here, we firstly introduce a new matrix-variate skewed distribution: the matrix-variate normal mean-variance Birnbaum–Saunders distribution. Then, we obtain its symmetric version by constraining the skewness matrix to be a matrix of zeros. Both distributions are then used as components of the corresponding mixture models and used for model-based clustering. Two ECM algorithms are proposed for parameter estimation. By using simulated analyses, we investigate the parameter recovery of our ECM algorithms and the performance of different initialization strategies for our mixture models on several scenarios and under different points of view. Then, our models are compared to other competitors via simulated data as well as in two real data applications.