Abstract
This chapter and Chapters 4–7, which treat generalized Gamma convolutions (GGC), form the central body of this work. The class of GGC’s was introduced by 0. Thorin in 1977 as a useful tool for proving ID of particular distributions. This class of distributions, in honor of Thorin often called the ℐ-class, also has its own interest. It is the smallest class of distributions on ℝ+ that contains the Gamma distributions and is closed with respect to convolution and weak limits. The ℐ-class is surprisingly rich, and it has a remarkable structure as will be seen. It should be added that Thorin’s original name for a GGC was “generalized Г-convolution” which is more clear but somewhat hard to abbreviate.
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