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Part of the book series: Lecture Notes in Statistics ((LNS,volume 76))

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Abstract

By and laxge this chapter, intended for rapid reading, contains only well-known facts from probability theory and analytic function theory. Much of the probability material can be found in e.g. Feller’s (1971) book. The chapter serves the purpose of giving the background. It also makes it possible to emphasize certain aspects and to fix the terminology. Pick functions are treated in Section 2.4. Since these functions are not well known to probabilists, the exposition is rather careful but much of the material can also be found in, e.g., Donoghue (1974) or Krein & Nudelman (1977). The chapter ends with some rather recent results concerning infinite divisibility of probability distributions.

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© 1992 Springer-Verlag New York, Inc.

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Bondesson, L. (1992). Basic Concepts and Facts. In: Generalized Gamma Convolutions and Related Classes of Distributions and Densities. Lecture Notes in Statistics, vol 76. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2948-3_2

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  • DOI: https://doi.org/10.1007/978-1-4612-2948-3_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97866-6

  • Online ISBN: 978-1-4612-2948-3

  • eBook Packages: Springer Book Archive

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