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Abstract
In 1977 Thorin introduced the class of generalized Γ-convolutions and proved that the Pareto distribution belongs to this class. In subsequent papers Thorin, Bondesson and others have shown that several important distributions are generalized Γ-convolutions.
The purpose of the present paper is to provide a very short proof of Thorin's result that the Pareto distribution is a generalized Γ-convolution. The proof is based on an old stability property of the Stieltjes cone due to Reuter (1956) and Itô (1974).