In Section 1, we present a number of classical results concerning the Generalized Gamma Convolution ( : GGC) variables, their Wiener-Gamma representations, and relation with the Dirichlet processes.
To a GGC variable, one may associate a unique Thorin measure. Let $G$ a positive r.v. and $\Gamma_t(G)$ (resp. $\Gamma_t(1/G)$ the Generalized Gamma Convolution with Thorin measure $t$-times the law of $G$ (resp. the law of $1/G$). In Section 2, we compare the laws of $\Gamma_t(G)$ and $\Gamma_t(1/G)$.
In Section 3, we present some old and some new examples of GGC variables, among which the lengths of excursions of Bessel processes straddling an independent exponential time.
"Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples." Probab. Surveys 5 346 - 415, 2008. https://doi.org/10.1214/07-PS118