The Fundamentals Of Heavy Tails
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The Fundamentals Of Heavy Tails
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Author : Jayakrishnan Nair
language : en
Publisher: Cambridge University Press
Release Date : 2022-06-09
The Fundamentals Of Heavy Tails written by Jayakrishnan Nair and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-09 with Business & Economics categories.
An accessible yet rigorous package of probabilistic and statistical tools for anyone who must understand or model extreme events.
Heavy Tail Phenomena
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Author : Sidney I. Resnick
language : en
Publisher: Springer Science & Business Media
Release Date : 2007
Heavy Tail Phenomena written by Sidney I. Resnick and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Business & Economics categories.
This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavy-tail analysis. It is uniquely devoted to heavy-tails and emphasizes both probability modeling and statistical methods for fitting models. Prerequisites for the reader include a prior course in stochastic processes and probability, some statistical background, some familiarity with time series analysis, and ability to use a statistics package. This work will serve second-year graduate students and researchers in the areas of applied mathematics, statistics, operations research, electrical engineering, and economics.
Univariate Stable Distributions
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Author : John P. Nolan
language : en
Publisher: Springer Nature
Release Date : 2020-09-13
Univariate Stable Distributions written by John P. Nolan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-13 with Mathematics categories.
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.
Nonparametric Analysis Of Univariate Heavy Tailed Data
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Author : Natalia Markovich
language : en
Publisher: John Wiley & Sons
Release Date : 2008-03-11
Nonparametric Analysis Of Univariate Heavy Tailed Data written by Natalia Markovich and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-11 with Mathematics categories.
Heavy-tailed distributions are typical for phenomena in complex multi-component systems such as biometry, economics, ecological systems, sociology, web access statistics, internet traffic, biblio-metrics, finance and business. The analysis of such distributions requires special methods of estimation due to their specific features. These are not only the slow decay to zero of the tail, but also the violation of Cramer’s condition, possible non-existence of some moments, and sparse observations in the tail of the distribution. The book focuses on the methods of statistical analysis of heavy-tailed independent identically distributed random variables by empirical samples of moderate sizes. It provides a detailed survey of classical results and recent developments in the theory of nonparametric estimation of the probability density function, the tail index, the hazard rate and the renewal function. Both asymptotical results, for example convergence rates of the estimates, and results for the samples of moderate sizes supported by Monte-Carlo investigation, are considered. The text is illustrated by the application of the considered methodologies to real data of web traffic measurements.
Advances In Heavy Tailed Risk Modeling
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Author : Gareth W. Peters
language : en
Publisher: John Wiley & Sons
Release Date : 2015-05-05
Advances In Heavy Tailed Risk Modeling written by Gareth W. Peters and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-05 with Mathematics categories.
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 in high consequence low frequency loss modeling. With a companion, Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk, the book 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 distributional 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 modelling, 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 book is also a useful handbook for graduate-level courses on heavy tailed processes, advanced risk management, and actuarial science.
Handbook Of Heavy Tailed Distributions In Finance
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Author : S.T Rachev
language : en
Publisher: Elsevier
Release Date : 2003-03-05
Handbook Of Heavy Tailed Distributions In Finance written by S.T Rachev and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-05 with Business & Economics categories.
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.
Dynamic Models For Volatility And Heavy Tails
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Author : Andrew C. Harvey
language : en
Publisher: Cambridge University Press
Release Date : 2013-04-22
Dynamic Models For Volatility And Heavy Tails written by Andrew C. Harvey and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Business & Economics categories.
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.
Elements Of Distribution Theory
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Author : Thomas A. Severini
language : en
Publisher: Cambridge University Press
Release Date : 2005-08-08
Elements Of Distribution Theory written by Thomas A. Severini and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-08 with Business & Economics categories.
This detailed introduction to distribution theory uses no measure theory, making it suitable for students in statistics and econometrics as well as for researchers who use statistical methods. Good backgrounds in calculus and linear algebra are important and a course in elementary mathematical analysis is useful, but not required. An appendix gives a detailed summary of the mathematical definitions and results that are used in the book. Topics covered range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distribution and the central limit theorem to more advanced concepts such as exchangeability, models with a group structure, asymptotic approximations to integrals, orthogonal polynomials and saddlepoint approximations. The emphasis is on topics useful in understanding statistical methodology; thus, parametric statistical models and the distribution theory associated with the normal distribution are covered comprehensively.
Introduction To Probability For Computing
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Author : Mor Harchol-Balter
language : en
Publisher: Cambridge University Press
Release Date : 2023-09-28
Introduction To Probability For Computing written by Mor Harchol-Balter and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-28 with Computers categories.
Learn about probability as it is used in computer science with this rigorous, yet highly accessible, undergraduate textbook. Fundamental probability concepts are explained in depth, prerequisite mathematics is summarized, and a wide range of computer science applications is described. Throughout, the material is presented in a “question and answer” style designed to encourage student engagement and understanding. Replete with almost 400 exercises, real-world computer science examples, and covering a wide range of topics from simulation with computer science workloads, to statistical inference, to randomized algorithms, to Markov models and queues, this interactive text is an invaluable learning tool whether your course covers probability with statistics, with stochastic processes, with randomized algorithms, or with simulation. The teaching package includes solutions, lecture slides, and lecture notes for students.
Economic Networks
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Author : Thomas J. Sargent
language : en
Publisher: Cambridge University Press
Release Date : 2024-04-25
Economic Networks written by Thomas J. Sargent and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-25 with Business & Economics categories.
It has become increasingly clear that economies can fruitfully be viewed as networks, consisting of millions of nodes (households, firms, banks, etc.) connected by business, social, and legal relationships. These relationships shape many outcomes that economists often measure. Over the past few years, research on production networks has flourished, as economists try to understand supply-side dynamics, default cascades, aggregate fluctuations, and many other phenomena. Economic Networks provides a brisk introduction to network analysis that is self-contained, rigorous, and illustrated with many figures, diagrams and listings with computer code. Network methods are put to work analyzing production networks, financial networks, and other related topics (including optimal transport, another highly active research field). Visualizations using recent data bring key ideas to life.