An Introduction to Heavy-Tailed and Subexponential Distributions

  • Sergey Foss
  • Dmitry Korshunov
  • Stan Zachary

Part of the Springer Series in Operations Research and Financial Engineering book series (ORFE, volume 38)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Sergey Foss, Dmitry Korshunov, Stan Zachary
    Pages 1-6
  3. Sergey Foss, Dmitry Korshunov, Stan Zachary
    Pages 7-38
  4. Sergey Foss, Dmitry Korshunov, Stan Zachary
    Pages 39-69
  5. Sergey Foss, Dmitry Korshunov, Stan Zachary
    Pages 71-96
  6. Sergey Foss, Dmitry Korshunov, Stan Zachary
    Pages 97-118
  7. Back Matter
    Pages 119-123

About this book


Heavy-tailed probability distributions are an important component in the modeling of many stochastic systems. They are frequently used to accurately model inputs and outputs of computer and data networks and service facilities such as call centers. They are an essential for describing risk processes in finance and also for insurance premia pricing, and such distributions occur naturally in models of epidemiological spread. The class includes distributions with power law tails such as the Pareto, as well as the lognormal and certain Weibull distributions.

 This monograph defines the classes of long-tailed and subexponential distributions in one dimension and provides a complete and comprehensive description of their properties. New results are presented in a simple, coherent and systematic way. This leads to a comprehensive exposition of tail properties of sums of independent random variables whose distributions belong to the long-tailed and subexponential class.

The book includes a discussion of and references to contemporary areas of applications and also contains preliminary mathematical material which makes the book self contained. Modelers in the fields of finance, insurance, network science and environmental studies will find this book to be an essential reference.


environmental modeling financial modeling lognormal distribution long-tailed distribution pareto distribution

Authors and affiliations

  • Sergey Foss
    • 1
  • Dmitry Korshunov
    • 2
  • Stan Zachary
    • 3
  1. 1., Department of Actuarial MathematicsHeriot-Watt UniversityRiccarton, EdinburghUnited Kingdom
  2. 2.Russian Academy of SciencesSobolev Institute of Mathematics of theNovosibirskRussian Federation
  3. 3., Department of Actuarial Mathematics andHeriot-Watt UniversityRiccarton, EdinburghUnited Kingdom

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-9472-1
  • Online ISBN 978-1-4419-9473-8
  • Series Print ISSN 1431-8598
  • Buy this book on publisher's site