The Fundamentals of Heavy Tails: Properties, Emergence, and Estimation

ISBN-13: 9781316511732 / Angielski / Twarda / 2022

Jayakrishnan Nair; Adam Wierman; Bert Zwart

Opis

An accessible yet rigorous package of probabilistic and statistical tools for anyone who must understand or model extreme events.

Recenzje

'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

Spis treści

Commonly used notation; 1. Introduction; Part I. Properties: 2. Scale invariance, power laws, and regular variation; 3. Catastrophes, conspiracies, and subexponential distributions; 4. Residual lives, hazard rates, and long tails; Part II. Emergence: 5. Additive processes; 6. Multiplicative processes; 7. Extremal processes; Part III. Estimation: 8. Estimating power-law distributions: Listen to the body; 9. Estimating power-law tails: Let the tail do the talking; References; Index.