Univariate Stable Distributions: Models for Heavy Tailed Data de John P. Nolan

Univariate Stable Distributions: Models for Heavy Tailed Data: Springer Series in Operations Research and Financial Engineering

Autor John P. Nolan

en Limba Engleză Paperback – 14 sep 2021

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.

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Specificații

ISBN-13: 9783030529178
ISBN-10: 3030529177
Pagini: 333
Ilustrații: XV, 333 p. 104 illus., 21 illus. in color.
Dimensiuni: 155 x 235 mm
Ediția:1st ed. 2020
Editura: Springer International Publishing
Colecția Springer
Seria Springer Series in Operations Research and Financial Engineering

Locul publicării:Cham, Switzerland

Cuprins

Basic Properties of Univariate Stable Distributions.- Modeling with Stable Distributions.- Technical Results for Univariate Stable Distributions.- Univariate Estimation.- Stable Regression.- Signal Processing with Stable Distributions.- Related Distributions.- Appendix A: Mathematical Facts.- Appendix B: Stable Quantiles.- Appendix C: Stable Modes.- Appendix D: Asymptotic Standard Deviations of ML Estimators.

Recenzii

“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)

Notă biografică

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.

Textul de pe ultima copertă

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 methodsinto 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.

Caracteristici

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