<p>The classical Laplace distribution and its skewed generalizations have played an increasingly vital role in modeling univariate and multivariate data across diverse application areas. In this study, we explore an extension of the multivariate generalized asymmetric laplace (GAL) distribution to accommodate variable shape parameters along each coordinate. This novel class of multivariate marginally generalized asymmetric laplace (MGAL) distributions offers enhanced flexibility in modeling multidimensional data that may exhibit varying degrees of skewness or tail behavior across dimensions. We present fundamental properties of MGAL distributions and discuss parameter estimation through various computational schemes, leveraging the expectation maximization (EM) algorithm and its variants. The efficacy of these estimation methods is demonstrated on simulated data, while real data examples showcase the modeling capabilities of this innovative stochastic model.</p>