Representing a Generalized Pareto with supported factors

I am trying to model the tail of a Gumbel, i.e. a Generalized Pareto.

I understand that the philosophy of Infer.NET is to provide basic distributions and let the user combine them, as discussed in the old forum and in some issues here. Using this approach, how shall I represent a Generalized Pareto?

Assuming my Generalized Pareto has a positive shape parameter, I can encode it as an Exponential-Gamma mixture as described in: https://en.wikipedia.org/wiki/Generalized_Pareto_distribution#GPD_as_an_Exponential-Gamma_Mixture

Gamma factors are supported natively by Infer.NET, so I can use this directly as the parameter of an Exponential.

How shall I encode the Exponential? Shall I simply exponentiate some positive real number drawn from a Uniform using the parameter drawn from a Gamma?