Univariate Stable Distributions
Springer International Publishing (Verlag)
978-3-030-52914-7 (ISBN)
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.
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.
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.
"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)
| Erscheinungsdatum | 15.09.2020 |
|---|---|
| Reihe/Serie | Springer Series in Operations Research and Financial Engineering |
| Zusatzinfo | XV, 333 p. 104 illus., 21 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 691 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | Brownian motion • Extreme value estimation • Generalized central limit theorem • Heavy tailed data • Heavy tailed data distributions • Multivariate stable dsitribution • Pareto distributions • Signal processing algorithm • Stable Distributions • Stable filter • Stable Laws • Stable random variables • Stable regression • Univariate estimate • Univariate stable distributions |
| ISBN-10 | 3-030-52914-2 / 3030529142 |
| ISBN-13 | 978-3-030-52914-7 / 9783030529147 |
| Zustand | Neuware |
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