The fundamentals of heavy tails : properties, emergence, and estimation
著者
書誌事項
The fundamentals of heavy tails : properties, emergence, and estimation
（Cambridge series on statistical and probabilistic mathematics, 53）
Cambridge University Press, 2022
- : hbk
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注記
Includes bibliographical references (p. 240-248) and index
内容説明・目次
内容説明
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.
目次
- 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.
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