A proof for the existence of multivariate singular generalized skew-elliptical density functions

We derive the density functions of multivariate singular generalized skew-elliptical distributions, present their characteristic function, and derive explicit formulas for the expectation and the covariance matrix. This letter generalizes results given in Díaz-García et al. (2002) and Young et al. (2016) about the existence of multivariate singular elliptical and multivariate singular skew-normal density functions, respectively.