The Fundamentals of Heavy Tails: Properties, Emergence, and Estimation (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 53) - Hardcover

Nair, Jayakrishnan; Wierman, Adam; Zwart, Bert

Hardcover

ISBN 10: 1316511731 ISBN 13: 9781316511732

Publisher: Cambridge University Press, 2022

Synopsis

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.

About this title

About the Author

Jayakrishnan Nair is an Associate Professor in Electrical Engineering at IIT Bombay. His research focuses on modeling, performance evaluation, and design issues in online learning environments, communication networks, queueing systems, and smart power grids. He is the recipient of best paper awards at IFIP Performance (2010 and 2020), and ACM e-Energy (2020).

Adam Wierman is a Professor of Computing and Mathematical Sciences at the California Institute of Technology (Caltech). His research develops tools in machine learning, optimization, control, and economics with the goal of making the networked systems that govern our world sustainable and resilient. He is best known for his work spearheading the design of algorithms for sustainable data centers and is the recipient of numerous awards including the ACM Sigmetrics Rising Star award, the IEEE Communication Society William Bennet Prize, and multiple teaching awards. 

Bert Zwart is a mathematician with expertise in stochastic operations research, queueing theory, and large deviations. In the context of heavy tails, Bert has focused on sample path properties, designing Monte-Carlo methods and applications to computer communication and energy networks. Bert was area editor of Operations Research, the flagship journal of his profession, from 2009-2017, and was the recipient of the INFORMS Applied Probability Society Erlang prize, awarded every two years to a young applied probabilist.

From the Back Cover

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.

Reviews

'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

Edition details

• Publisher: Cambridge University Press
• Publication date: 2022
• Language: English
• ISBN 10: 1316511731
• ISBN 13: 9781316511732
• Binding: Hardcover
• Number of pages: 264