ABSTRACT
Self-decomposable and stable distributions, as introduced in Section I.5, derive their importance from being limit distributions in the central limit problem. In this chapter, however, self-decomposability and stability will not be studied in this context; we will show that the self-decomposable and stable distributions form interesting subclasses of the class of infinitely divisible distributions, having attractive properties such as unimodality. Again, results for distributions on Z+ and on R+ are much easier obtained than for distributions on R. In this introductory section we collect some general observations, whereas in the subsequent sections the Z+-, R+- and R-case are treated separately.
