The Fundamentals Of Heavy Tails

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The Fundamentals of Heavy Tails

Author : Jayakrishnan Nair
Publisher : Cambridge University Press
ISBN 13 : 1009062964
Total Pages : 266 pages
Book Rating : 4.0/5 (9 download)

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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 and published by Cambridge University Press. This book was released on 2022-06-09 with total page 266 pages. 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.

Univariate Stable Distributions

Author : John P. Nolan
Publisher : Springer Nature
ISBN 13 : 3030529150
Total Pages : 342 pages
Book Rating : 4.0/5 (35 download)

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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 and published by Springer Nature. This book was released on 2020-09-13 with total page 342 pages. 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.

Limit Distributions for Sums of Independent Random Vectors

Author : Mark M. Meerschaert
Publisher : John Wiley & Sons
ISBN 13 : 9780471356295
Total Pages : 514 pages
Book Rating : 4.3/5 (562 download)

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Book Synopsis Limit Distributions for Sums of Independent Random Vectors by : Mark M. Meerschaert

Download or read book Limit Distributions for Sums of Independent Random Vectors written by Mark M. Meerschaert and published by John Wiley & Sons. This book was released on 2001-07-11 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Die Quintessenz aus über 100 Originalarbeiten! Ausgehend von den Grundpfeilern der modernen Wahrscheinlichkeitstheorie entwickeln die Autoren dieses in sich geschlossenen, gut verständlich formulierten Bandes die Theorie der unendlich teilbaren Verteilungen und der regulären Variation. Im Anschluss erarbeiten sie die allgemeine Grenzwerttheorie für unabhängige Zufallsvektoren. Dabei achten sie sorgfältig darauf, alle Aspekte in den Kontext der Wahrscheinlichkeitslehre und Statistik zu stellen und bieten dafür eine Fülle von Zusatzinformationen an.

Heavy Tails and Copulas

Author : Rustam Ibragimov
Publisher :
ISBN 13 : 9789814689809
Total Pages : 303 pages
Book Rating : 4.6/5 (898 download)

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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 and published by . This book was released on 2017 with total page 303 pages. 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.

Dynamic Models for Volatility and Heavy Tails

Author : Andrew C. Harvey
Publisher : Cambridge University Press
ISBN 13 : 1107328780
Total Pages : pages
Book Rating : 4.1/5 (73 download)

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Book Synopsis Dynamic Models for Volatility and Heavy Tails by : Andrew C. Harvey

Download or read book Dynamic Models for Volatility and Heavy Tails written by Andrew C. Harvey and published by Cambridge University Press. This book was released on 2013-04-22 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The volatility of financial returns changes over time and, for the last thirty years, Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models have provided the principal means of analyzing, modeling and monitoring such changes. Taking into account that financial returns typically exhibit heavy tails - that is, extreme values can occur from time to time - Andrew Harvey's new book shows how a small but radical change in the way GARCH models are formulated leads to a resolution of many of the theoretical problems inherent in the statistical theory. The approach can also be applied to other aspects of volatility. The more general class of Dynamic Conditional Score models extends to robust modeling of outliers in the levels of time series and to the treatment of time-varying relationships. The statistical theory draws on basic principles of maximum likelihood estimation and, by doing so, leads to an elegant and unified treatment of nonlinear time-series modeling.

Foundations of Data Science

Author : Avrim Blum
Publisher : Cambridge University Press
ISBN 13 : 1108617360
Total Pages : 433 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Foundations of Data Science by : Avrim Blum

Download or read book Foundations of Data Science written by Avrim Blum and published by Cambridge University Press. This book was released on 2020-01-23 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.

Closure Properties for Heavy-Tailed and Related Distributions

Author : Remigijus Leipus
Publisher : Springer Nature
ISBN 13 : 3031345533
Total Pages : 99 pages
Book Rating : 4.0/5 (313 download)

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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 and published by Springer Nature. This book was released on 2023-10-16 with total page 99 pages. 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.

Bayesian Data Analysis, Third Edition

Author : Andrew Gelman
Publisher : CRC Press
ISBN 13 : 1439840954
Total Pages : 677 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Bayesian Data Analysis, Third Edition by : Andrew Gelman

Download or read book Bayesian Data Analysis, Third Edition written by Andrew Gelman and published by CRC Press. This book was released on 2013-11-01 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.

Fundamentals of Modern Statistical Methods

Author : Rand R. Wilcox
Publisher : Springer Science & Business Media
ISBN 13 : 1441955240
Total Pages : 255 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Fundamentals of Modern Statistical Methods by : Rand R. Wilcox

Download or read book Fundamentals of Modern Statistical Methods written by Rand R. Wilcox and published by Springer Science & Business Media. This book was released on 2010-03-18 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conventional statistical methods have a very serious flaw. They routinely miss differences among groups or associations among variables that are detected by more modern techniques, even under very small departures from normality. Hundreds of journal articles have described the reasons standard techniques can be unsatisfactory, but simple, intuitive explanations are generally unavailable. Situations arise where even highly nonsignificant results become significant when analyzed with more modern methods. Without assuming the reader has any prior training in statistics, Part I of this book describes basic statistical principles from a point of view that makes their shortcomings intuitive and easy to understand. The emphasis is on verbal and graphical descriptions of concepts. Part II describes modern methods that address the problems covered in Part I. Using data from actual studies, many examples are included to illustrate the practical problems with conventional procedures and how more modern methods can make a substantial difference in the conclusions reached in many areas of statistical research. The second edition of this book includes a number of advances and insights that have occurred since the first edition appeared. Included are new results relevant to medians, regression, measures of association, strategies for comparing dependent groups, methods for dealing with heteroscedasticity, and measures of effect size.

Handbook of Heavy Tailed Distributions in Finance

Author : S.T Rachev
Publisher : Elsevier
ISBN 13 : 9780080557731
Total Pages : 704 pages
Book Rating : 4.5/5 (577 download)

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Book Synopsis Handbook of Heavy Tailed Distributions in Finance by : S.T Rachev

Download or read book Handbook of Heavy Tailed Distributions in Finance written by S.T Rachev and published by Elsevier. This book was released on 2003-03-05 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbooks in Finance are intended to be a definitive source for comprehensive and accessible information in the field of finance. Each individual volume in the series should present an accurate self-contained survey of a sub-field of finance, suitable for use by finance and economics professors and lecturers, professional researchers, graduate students and as a teaching supplement. The goal is to have a broad group of outstanding volumes in various areas of finance. The Handbook of Heavy Tailed Distributions in Finance is the first handbook to be published in this series. This volume presents current research focusing on heavy tailed distributions in finance. The contributions cover methodological issues, i.e., probabilistic, statistical and econometric modelling under non- Gaussian assumptions, as well as the applications of the stable and other non -Gaussian models in finance and risk management.

Fundamental Aspects of Operational Risk and Insurance Analytics

Author : Marcelo G. Cruz
Publisher : John Wiley & Sons
ISBN 13 : 1118573021
Total Pages : 928 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis Fundamental Aspects of Operational Risk and Insurance Analytics by : Marcelo G. Cruz

Download or read book Fundamental Aspects of Operational Risk and Insurance Analytics written by Marcelo G. Cruz and published by John Wiley & Sons. This book was released on 2015-01-20 with total page 928 pages. Available in PDF, EPUB and Kindle. Book excerpt: A one-stop guide for the theories, applications, and statistical methodologies essential to operational risk Providing a complete overview of operational risk modeling and relevant insurance analytics, Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk offers a systematic approach that covers the wide range of topics in this area. Written by a team of leading experts in the field, the handbook presents detailed coverage of the theories, applications, and models inherent in any discussion of the fundamentals of operational risk, with a primary focus on Basel II/III regulation, modeling dependence, estimation of risk models, and modeling the data elements. Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk begins with coverage on the four data elements used in operational risk framework as well as processing risk taxonomy. The book then goes further in-depth into the key topics in operational risk measurement and insurance, for example diverse methods to estimate frequency and severity models. Finally, the book ends with sections on specific topics, such as scenario analysis; multifactor modeling; and dependence modeling. A unique companion with Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk, the handbook also features: Discussions on internal loss data and key risk indicators, which are both fundamental for developing a risk-sensitive framework Guidelines for how operational risk can be inserted into a firm’s strategic decisions A model for stress tests of operational risk under the United States Comprehensive Capital Analysis and Review (CCAR) program A valuable reference for financial engineers, quantitative analysts, risk managers, and large-scale consultancy groups advising banks on their internal systems, the handbook is also useful for academics teaching postgraduate courses on the methodology of operational risk.

Mathematics for Machine Learning

Author : Marc Peter Deisenroth
Publisher : Cambridge University Press
ISBN 13 : 1108569323
Total Pages : 392 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Mathematics for Machine Learning by : Marc Peter Deisenroth

Download or read book Mathematics for Machine Learning written by Marc Peter Deisenroth and published by Cambridge University Press. This book was released on 2020-04-23 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

Probability for Statistics and Machine Learning

Author : Anirban DasGupta
Publisher : Springer Science & Business Media
ISBN 13 : 1441996346
Total Pages : 796 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Probability for Statistics and Machine Learning by : Anirban DasGupta

Download or read book Probability for Statistics and Machine Learning written by Anirban DasGupta and published by Springer Science & Business Media. This book was released on 2011-05-17 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a versatile and lucid treatment of classic as well as modern probability theory, while integrating them with core topics in statistical theory and also some key tools in machine learning. It is written in an extremely accessible style, with elaborate motivating discussions and numerous worked out examples and exercises. The book has 20 chapters on a wide range of topics, 423 worked out examples, and 808 exercises. It is unique in its unification of probability and statistics, its coverage and its superb exercise sets, detailed bibliography, and in its substantive treatment of many topics of current importance. This book can be used as a text for a year long graduate course in statistics, computer science, or mathematics, for self-study, and as an invaluable research reference on probabiliity and its applications. Particularly worth mentioning are the treatments of distribution theory, asymptotics, simulation and Markov Chain Monte Carlo, Markov chains and martingales, Gaussian processes, VC theory, probability metrics, large deviations, bootstrap, the EM algorithm, confidence intervals, maximum likelihood and Bayes estimates, exponential families, kernels, and Hilbert spaces, and a self contained complete review of univariate probability.

A Modern Introduction to Probability and Statistics

Author : F.M. Dekking
Publisher : Springer Science & Business Media
ISBN 13 : 1846281687
Total Pages : 488 pages
Book Rating : 4.8/5 (462 download)

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Book Synopsis A Modern Introduction to Probability and Statistics by : F.M. Dekking

Download or read book A Modern Introduction to Probability and Statistics written by F.M. Dekking and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books

Bandit Algorithms

Author : Tor Lattimore
Publisher : Cambridge University Press
ISBN 13 : 1108486827
Total Pages : 537 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Bandit Algorithms by : Tor Lattimore

Download or read book Bandit Algorithms written by Tor Lattimore and published by Cambridge University Press. This book was released on 2020-07-16 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and rigorous introduction for graduate students and researchers, with applications in sequential decision-making problems.

Performance Modeling and Design of Computer Systems

Author : Mor Harchol-Balter
Publisher : Cambridge University Press
ISBN 13 : 1107027500
Total Pages : 573 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Performance Modeling and Design of Computer Systems by : Mor Harchol-Balter

Download or read book Performance Modeling and Design of Computer Systems written by Mor Harchol-Balter and published by Cambridge University Press. This book was released on 2013-02-18 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written with computer scientists and engineers in mind, this book brings queueing theory decisively back to computer science.

Advances in Heavy Tailed Risk Modeling

Author : Gareth W. Peters
Publisher : John Wiley & Sons
ISBN 13 : 1118909534
Total Pages : 667 pages
Book Rating : 4.1/5 (189 download)

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Book Synopsis Advances in Heavy Tailed Risk Modeling by : Gareth W. Peters

Download or read book Advances in Heavy Tailed Risk Modeling written by Gareth W. Peters and published by John Wiley & Sons. This book was released on 2015-05-26 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: ADVANCES IN HEAVY TAILED RISK MODELING A cutting-edge guide for the theories, applications, and statistical methodologies essential to heavy tailed risk modeling Focusing on the quantitative aspects of heavy tailed loss processes in operational risk and relevant insurance analytics, Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk presents comprehensive coverage of the latest research on the theories and applications in risk measurement and modeling techniques. Featuring a unique balance of mathematical and statistical perspectives, the handbook begins by introducing the motivation for heavy tailed risk processes. A companion with Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk, the handbook provides a complete framework for all aspects of operational risk management and includes: Clear coverage on advanced topics such as splice loss models, extreme value theory, heavy tailed closed form loss distribution approach models, flexible heavy tailed risk models, risk measures, and higher order asymptotic approximations of risk measures for capital estimation An exploration of the characterization and estimation of risk and insurance modeling, which includes sub-exponential models, alpha-stable models, and tempered alpha stable models An extended discussion of the core concepts of risk measurement and capital estimation as well as the details on numerical approaches to evaluation of heavy tailed loss process model capital estimates Numerous detailed examples of real-world methods and practices of operational risk modeling used by both financial and non-financial institutions Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk is an excellent reference for risk management practitioners, quantitative analysts, financial engineers, and risk managers. The handbook is also useful for graduate-level courses on heavy tailed processes, advanced risk management, and actuarial science.