Overview
- 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
Part of the book series: Springer Series in Operations Research and Financial Engineering (ORFE)
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Table of contents (7 chapters)
Keywords
- Stable distributions
- Univariate stable distributions
- Heavy tailed data
- Heavy tailed data distributions
- Generalized central limit theorem
- Signal processing algorithm
- Univariate estimate
- Stable regression
- Pareto distributions
- Multivariate stable dsitribution
- Stable laws
- Stable random variables
- Brownian motion
- Extreme value estimation
- Stable filter
About this book
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.
Reviews
“The book is a much-welcomed addition to the literature on stable laws and should signifcantly contribute to the further popularization of these laws among practitioners. It is rigorously written without much loss of accessibility to a less technically oriented reader. … The text should be on the bookshelf of any researcher-practitioner or probabilist who is interested in the phenomena characterized by heavy tails.” (Krzysztof Podgorski, Mathematical Reviews, April, 2022)
“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)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Univariate Stable Distributions
Book Subtitle: Models for Heavy Tailed Data
Authors: John P. Nolan
Series Title: Springer Series in Operations Research and Financial Engineering
DOI: https://doi.org/10.1007/978-3-030-52915-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-52914-7Published: 13 September 2020
Softcover ISBN: 978-3-030-52917-8Published: 14 September 2021
eBook ISBN: 978-3-030-52915-4Published: 13 September 2020
Series ISSN: 1431-8598
Series E-ISSN: 2197-1773
Edition Number: 1
Number of Pages: XV, 333
Number of Illustrations: 83 b/w illustrations, 21 illustrations in colour
Topics: Probability Theory and Stochastic Processes, Applications of Mathematics, Statistical Theory and Methods