The Fundamentals of Heavy Tails

Properties, Emergence, and Estimation

Jayakrishnan Nair, Adam Wierman, Bert Zwart

• Publisher: Cambridge University Press
• Year: 2022
• Print ISBN:
  9781316511732
• eBook ISBN:
  9781009062961
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

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.

Table of contents

• Cover
• Half-title Page
• Series Page
• Title Page
• Copyright Page
• Contents
• Preface
• Acknowledgments
• 1 Introduction
• Part I Properties
• Part II Emergence
• Part III Estimation
• Commonly Used Notation
• References
• Index