Univariate Stable Distributions
Models for Heavy Tailed Data
Authors: Nolan, John P.
Free Preview- Introduces the theory, numerical algorithms, and statistical methods associated with stable distributions with an accessible, non-technical approach
- Highlights the many practical applications of stables distributions, including in finance, statistics, engineering, physics, and more
- Presents a number of helpful exercises, as well as links to free software to apply the models in practice
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- About this Textbook
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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. - About the authors
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John Nolan received his PhD from the University of Virginia, and has taught at the University of Zambia, Kenyon College, and American University. He also worked in a software firm, developing systems for intensive care units. His main research interests are in models for heavy tailed data and extremes.
- Reviews
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“This book is an excellent reference for researchers and practitioners looking to make use of both the rich theory and applicability offered by stable distributions. The text is clear and accessible throughout, including all the necessary mathematical and statistical details to make it both a thorough and practical work on univariate modelling using stable distributions.” (Fraser Daly, zbMATH 1455.62003, 2021)
- Table of contents (7 chapters)
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Basic Properties of Univariate Stable Distributions
Pages 1-23
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Modeling with Stable Distributions
Pages 25-52
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Technical Results for Univariate Stable Distributions
Pages 53-157
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Univariate Estimation
Pages 159-222
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Stable Regression
Pages 223-238
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Table of contents (7 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Univariate Stable Distributions
- Book Subtitle
- Models for Heavy Tailed Data
- Authors
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- John P. Nolan
- Series Title
- Springer Series in Operations Research and Financial Engineering
- Copyright
- 2020
- Publisher
- Springer International Publishing
- Copyright Holder
- The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-52915-4
- DOI
- 10.1007/978-3-030-52915-4
- Hardcover ISBN
- 978-3-030-52914-7
- Series ISSN
- 1431-8598
- Edition Number
- 1
- Number of Pages
- XV, 333
- Number of Illustrations
- 83 b/w illustrations, 21 illustrations in colour
- Topics
