Springer Series in Operations Research and Financial Engineering

An Introduction to Heavy-Tailed and Subexponential Distributions

Authors: Foss, Sergey, Korshunov, Dmitry, Zachary, Stan

Free Preview
  • Provides a complete and comprehensive introduction to the theory of long
  • tailed and subexponential distributions
  • Discusses where the areas of applications currently stand -Includes preliminary mathematical material
see more benefits

Buy this book

eBook n/a
  • ISBN 978-1-4419-9473-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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.

Reviews

From the reviews:

“The book An Introduction to Heavy-Tailed and Subexponential Distributions … presents numerous ideas of ‘heaviness’ for probability distribution tails. It gives precise definitions to common terms such as heavy-tailed and long-tailed, as well as more esoteric terms such as subexponential or h-insensitive. … This book is small, self-contained monograph. There are some examples and applications, but the emphasis is on basic properties and classification.” (John D. Cook, The Mathematical Association of America, August, 2011)

“This monograph provides a comprehensive introduction to the theory of long-tailed and sub-exponential distributions. … Every chapter ends with historical comments on the topics that it covers, and the book ends with a list of references. Most of the material covered is appearing for the first time in book form, and the book will serve as a valuable reference for researchers interested in tail properties of sums and maxima of independent random variables having long-tailed/sub-exponential distributions.” (Sreenivasan Ravi, Mathematical Reviews, Issue 2012 f)


Table of contents (5 chapters)

Table of contents (5 chapters)
  • Introduction

    Pages 1-6

    Foss, Sergey (et al.)

  • Heavy-Tailed and Long-Tailed Distributions

    Pages 7-38

    Foss, Sergey (et al.)

  • Subexponential Distributions

    Pages 39-69

    Foss, Sergey (et al.)

  • Densities and Local Probabilities

    Pages 71-96

    Foss, Sergey (et al.)

  • Maximum of Random Walk

    Pages 97-118

    Foss, Sergey (et al.)

Buy this book

eBook n/a
  • ISBN 978-1-4419-9473-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices

Services for this book

Loading...

Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Heavy-Tailed and Subexponential Distributions
Authors
Series Title
Springer Series in Operations Research and Financial Engineering
Series Volume
38
Copyright
2011
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science + Business Media, LLC
eBook ISBN
978-1-4419-9473-8
DOI
10.1007/978-1-4419-9473-8
Series ISSN
1431-8598
Edition Number
1
Number of Pages
IX, 123
Number of Illustrations
1 b/w illustrations
Topics