The article explores complex multivariate probability distributions that can be represented as mixtures of stable distributions. New distributions related to the Mittag–Leffler distribution are introduced, and their properties are discussed. The focus is on representing random vectors as products of independent variables, with connections to well-known probability distributions. Examples include generalized Linnik and Mittag–Leffler distributions. The article also proves conditions for the convergence of random sequences to certain multivariate distributions. The findings show how random sums of vectors can converge to a specific distribution called the multivariate generalized Linnik distribution.