  The generalized gamma convolutions class of distributions appeared in
Thorin's work while looking for the infinite divisibility of the log-Normal and
Pareto distributions. Although these distributions have been extensively
studied in the univariate case, the multivariate case and the dependence
structures that can arise from it have received little interest in the
literature. Furthermore, only one projection procedure for the univariate case
was recently constructed, and no estimation procedures are available. By
expanding the densities of multivariate generalized gamma convolutions into a
tensorized Laguerre basis, we bridge the gap and provide performant estimation
procedures for both the univariate and multivariate cases. We provide some
insights about performance of these procedures, and a convergent series for the
density of multivariate gamma convolutions, which is shown to be more stable
than Moschopoulos's and Mathai's univariate series. We furthermore discuss some
examples.
