Extending the Thorin class

We prove that the Thorin class $ {T_\kappa }\left( {{\mathbb{R}_{+} }} \right),\kappa > 0 $ {T_\kappa }\left( {{\mathbb{R}_{+} }} \right),\kappa > 0 , is the minimal class of probability distributions on \mathbbR₊ {\mathbb{R}_{+} } that is closed under convolutions and weak limits and contains the Tweedie distributions Tw_(κ+1)/κ (μ, λ), μ > 0, λ > 0.