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Generalized Gamma Convolutions and Related Classes of Distributions and Densities

  • Book
  • © 1992

Overview

Authors:
  1. Lennart Bondesson

    1. Department of Forest Biometry, Swedish University of Agricultural Sciences, Umeå, Sweden

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction and Summary

    • Lennart Bondesson
    Pages 1-6

  3. Basic Concepts and Facts

    • Lennart Bondesson
    Pages 7-28

  4. Generalized Gamma Convolutions

    • Lennart Bondesson
    Pages 29-48

  5. Densities of Generalized Gamma Convolutions

    • Lennart Bondesson
    Pages 49-67

  6. Hyperbolically Completely Monotone Densities

    • Lennart Bondesson
    Pages 68-89

  7. Back to ℐ

    • Lennart Bondesson
    Pages 90-104

  8. Extended Generalized Gamma Convolutions

    • Lennart Bondesson
    Pages 105-125

  9. Generalized Negative Binomial Convolutions

    • Lennart Bondesson
    Pages 126-136

  10. The ℐ2-Class of Distributions

    • Lennart Bondesson
    Pages 137-151

  11. Shot-Noise Distributions

    • Lennart Bondesson
    Pages 152-159

  12. Back Matter

    Pages 160-177
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Keywords

About this book

Generalized Gamma convolutions were introduced by Olof Thorin in 1977 and were used by him to show that, in particular, the Lognormal distribution is infinitely divisible. After that a large number of papers rapidly appeared with new results in a somewhat random order. Many of the papers appeared in the Scandinavian Actuarial Journal. This work is an attempt to present the main results on this class of probability distributions and related classes in a rather logical order. The goal has been to be on a level that is not too advanced. However, since the field is rather technical, most readers will find difficult passages in the text. Those who do not want to visit a mysterious land situated between the land of probability theory and statistics and the land of classical analysis should not look at this work. When some years ago I submitted a survey to a journal it was suggested by the editor, K. Krickeberg, that it should be expanded to a book. However, at that time I was rather reluctant to do so since there remained so many problems to be solved or to be solved in a smoother way than before. Moreover, there was at that time some lack of probabilistic interpretations and applications. Many of the problems are now solved but still it is felt that more applications than those presented in the work could be found.

Authors and Affiliations

  • Department of Forest Biometry, Swedish University of Agricultural Sciences, Umeå, Sweden

    Lennart Bondesson

Bibliographic Information

  • Book Title: Generalized Gamma Convolutions and Related Classes of Distributions and Densities

  • Authors: Lennart Bondesson

  • Series Title: Lecture Notes in Statistics

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

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1992

  • Softcover ISBN: 978-0-387-97866-6Published: 06 August 1992

  • eBook ISBN: 978-1-4612-2948-3Published: 06 December 2012

  • Series ISSN: 0930-0325

  • Series E-ISSN: 2197-7186

  • Edition Number: 1

  • Number of Pages: XIV, 585

  • Topics: Applications of Mathematics

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