Skip to main content Accessibility help
  • Cited by 15
Cambridge University Press
Online publication date:
May 2022
Print publication year:
Online ISBN:

Book description

Heavy tails –extreme events or values more common than expected –emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet after decades of progress, they are still treated as mysterious, surprising, and even controversial, primarily because the necessary mathematical models and statistical methods are not widely known. This book, for the first time, provides a rigorous introduction to heavy-tailed distributions accessible to anyone who knows elementary probability. It tackles and tames the zoo of terminology for models and properties, demystifying topics such as the generalized central limit theorem and regular variation. It tracks the natural emergence of heavy-tailed distributions from a wide variety of general processes, building intuition. And it reveals the controversy surrounding heavy tails to be the result of flawed statistics, then equips readers to identify and estimate with confidence. Over 100 exercises complete this engaging package.


‘Heavy tailed distributions are ubiquitous in many disciplines which use probabilistic models. The book by Nair, Wierman and Zwart is a superb introduction to the topic and presents fundamental principles in a rigorous yet accessible manner. It is a must-read for researchers interested in understanding heavy tails.’

R. Srikant - University of Illinois at Urbana-Champaign

‘As one of the people who keeps discovering heavy tails in computer systems, I'm thrilled to see a book that delves into the deeper foundations behind these ubiquitous distributions. This beautifully written book is both mathematically precise and also full of intuitions and examples which make it accessible to newcomers in the field.’

Mor Harchol-Balter - Carnegie Mellon University

‘The book provides a fresh look at heavy-tailed probability distributions on the real line and their role in applied probability. The authors show that these distributions appear via natural algebraic operations. Their approach, towards understanding properties of these distributions, combines the key mathematical ideas alongside with informal explanations. Physical intuition is also provided, for example, the ‘catastrophe/big jump principle’ for heavy-tailed distributions versus the ‘conspiracy principle’ for light-tailed ones. The book is designed to help the practitioner and includes many interesting examples and exercises that may help to the reader to adjust and enjoy its content.’

Sergey Foss - Heriot-Watt University

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.


  • 2 - Scale Invariance, Power Laws, and Regular Variation
    pp 29-55


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.