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The Fundamentals of Heavy Tails

2022-06-09 Mathematics
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Release : 2022-06-09
Genre : Mathematics
Kind : eBook
Book Rating : 964/5 ( reviews)

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Book Synopsis The Fundamentals of Heavy Tails by : Jayakrishnan Nair

Download or read book The Fundamentals of Heavy Tails written by Jayakrishnan Nair. This book was released on 2022-06-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Fundamentals of Heavy Tails

2022-06-09 Business & Economics
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Release : 2022-06-09
Genre : Business & Economics
Kind : eBook
Book Rating : 731/5 ( reviews)

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Book Synopsis The Fundamentals of Heavy Tails by : Jayakrishnan Nair

Download or read book The Fundamentals of Heavy Tails written by Jayakrishnan Nair. This book was released on 2022-06-09. Available in PDF, EPUB and Kindle. Book excerpt: An accessible yet rigorous package of probabilistic and statistical tools for anyone who must understand or model extreme events.

Univariate Stable Distributions

2020-09-13 Mathematics
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Release : 2020-09-13
Genre : Mathematics
Kind : eBook
Book Rating : 150/5 ( reviews)

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Book Synopsis Univariate Stable Distributions by : John P. Nolan

Download or read book Univariate Stable Distributions written by John P. Nolan. This book was released on 2020-09-13. Available in PDF, EPUB and Kindle. Book excerpt: This textbook highlights the many practical uses of stable distributions, exploring the theory, numerical algorithms, and statistical methods used to work with stable laws. Because of the author’s accessible and comprehensive approach, readers will be able to understand and use these methods. Both mathematicians and non-mathematicians will find this a valuable resource for more accurately modelling and predicting large values in a number of real-world scenarios. Beginning with an introductory chapter that explains key ideas about stable laws, readers will be prepared for the more advanced topics that appear later. The following chapters present the theory of stable distributions, a wide range of applications, and statistical methods, with the final chapters focusing on regression, signal processing, and related distributions. Each chapter ends with a number of carefully chosen exercises. Links to free software are included as well, where readers can put these methods into practice. Univariate Stable Distributions is ideal for advanced undergraduate or graduate students in mathematics, as well as many other fields, such as statistics, economics, engineering, physics, and more. It will also appeal to researchers in probability theory who seek an authoritative reference on stable distributions.

Heavy Tails and Copulas

2017 BUSINESS & ECONOMICS
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Release : 2017
Genre : BUSINESS & ECONOMICS
Kind : eBook
Book Rating : 809/5 ( reviews)

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Book Synopsis Heavy Tails and Copulas by : Rustam Ibragimov

Download or read book Heavy Tails and Copulas written by Rustam Ibragimov. This book was released on 2017. Available in PDF, EPUB and Kindle. Book excerpt: "This book offers a unified approach to the study of crises, large fluctuations, dependence and contagion effects in economics and finance. It covers important topics in statistical modeling and estimation, which combine the notions of copulas and heavy tails — two particularly valuable tools of today's research in economics, finance, econometrics and other fields — in order to provide a new way of thinking about such vital problems as diversification of risk and propagation of crises through financial markets due to contagion phenomena, among others. The aim is to arm today's economists with a toolbox suited for analyzing multivariate data with many outliers and with arbitrary dependence patterns. The methods and topics discussed and used in the book include, in particular, majorization theory, heavy-tailed distributions and copula functions — all applied to study robustness of economic, financial and statistical models, and estimation methods to heavy tails and dependence."--Publisher's website.

Closure Properties for Heavy-Tailed and Related Distributions

2023-10-16 Mathematics
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Release : 2023-10-16
Genre : Mathematics
Kind : eBook
Book Rating : 533/5 ( reviews)

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Book Synopsis Closure Properties for Heavy-Tailed and Related Distributions by : Remigijus Leipus

Download or read book Closure Properties for Heavy-Tailed and Related Distributions written by Remigijus Leipus. This book was released on 2023-10-16. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a compact and systematic overview of closure properties of heavy-tailed and related distributions, including closure under tail equivalence, convolution, finite mixing, maximum, minimum, convolution power and convolution roots, and product-convolution closure. It includes examples and counterexamples that give an insight into the theory and provides numerous references to technical details and proofs for a deeper study of the subject. The book will serve as a useful reference for graduate students, young researchers, and applied scientists.

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