Nair J. The Fundamentals of Heavy Tails. Properties, Emergence, Estimation 2022 torrent

Textbook in PDF format

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.
Frontmatter
Preface
Acknowledgments
Introduction
Properties
Scale Invariance, Power Laws, and Regular Variation
Catastrophes, Conspiracies, and Subexponential Distributions
Residual Lives, Hazard Rates, and Long Tails
Emergence
Additive Processes
Multiplicative Processes
Extremal Processes
Estimation
Estimating Power-Law Distributions: Listen to the Body
Estimating Power-Law Tails: Let the Tail Do the Talking
Commonly Used Notation
References
Index