Singular extended skew-elliptical distributions

Singular vector and matrix extended skew-elliptical distributions are studied in this work. Based on the vectorial case, two alternatives for singular matrix variate extended skew-elliptical distribution are also proposed. In addition, the distributions of a general linear transformation for extended skew-elliptical vectors and matrices are derived along with the corresponding density functions. These results are applied in the distribution of the residuals for a general linear model with extended skew-elliptical errors.