Univariate Stable Distributions

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Univariate Stable Distributions

John P. Nolan
Univariate Stable Distributions Book PDF

Author : John P. Nolan
Publisher : Springer Nature
Page : 342 pages
File Size : 43,9 Mb
Release : 2020-09-13
Category : Mathematics
ISBN : 9783030529154

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Univariate Stable Distributions by John P. Nolan Pdf

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.

Chance and Stability

Vladimir Vasilʹevich Uchaĭkin,Vladimir Michajlovič Zolotarev
Chance and Stability Book PDF

Author : Vladimir Vasilʹevich Uchaĭkin,Vladimir Michajlovič Zolotarev
Publisher : VSP
Page : 606 pages
File Size : 52,6 Mb
Release : 1999
Category : Mathematics
ISBN : 9067643017

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Chance and Stability by Vladimir Vasilʹevich Uchaĭkin,Vladimir Michajlovič Zolotarev Pdf

The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.

Stable Distributions

John Nolan
Stable Distributions Book PDF

Author : John Nolan
Publisher : Birkhauser
Page : 352 pages
File Size : 46,8 Mb
Release : 2007-03-01
Category : Mathematics
ISBN : 0817641599

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Stable Distributions by John Nolan Pdf

Stable distributions model phenomena in a wide range of applications in real systems. Their intriguing mathematical properties have long been of interest, but the lack of computational tools has prevented their practical application. This book, the first to deal with stable distributions as a practical tool, develops an intuition for stable distributions by giving a complete, self-contained derivation of their properties and describing accurate numerical methods for computing stable laws.

One-dimensional Stable Distributions

V. M. Zolotarev
One dimensional Stable Distributions Book PDF

Author : V. M. Zolotarev
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 49,7 Mb
Release : 1986-06-30
Category : Mathematics
ISBN : 9780821845196

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One-dimensional Stable Distributions by V. M. Zolotarev Pdf

This is the first book specifically devoted to a systematic exposition of the essential facts known about the properties of stable distributions. In addition to its main focus on the analytic properties of stable laws, the book also includes examples of the occurrence of stable distributions in applied problems and a chapter on the problem of statistical estimation of the parameters determining stable laws. A valuable feature of the book is the author's use of several formally different ways of expressing characteristic functions corresponding to these laws.

Stable Processes and Related Topics

Cambanis
Stable Processes and Related Topics Book PDF

Author : Cambanis
Publisher : Springer Science & Business Media
Page : 329 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468467789

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Stable Processes and Related Topics by Cambanis Pdf

The Workshop on Stable Processes and Related Topics took place at Cor nell University in January 9-13, 1990, under the sponsorship of the Mathemat ical Sciences Institute. It attracted an international roster of probabilists from Brazil, Japan, Korea, Poland, Germany, Holland and France as well as the U. S. This volume contains a sample of the papers presented at the Workshop. All the papers have been refereed. Gaussian processes have been studied extensively over the last fifty years and form the bedrock of stochastic modeling. Their importance stems from the Central Limit Theorem. They share a number of special properties which facilitates their analysis and makes them particularly suitable to statistical inference. The many properties they share, however, is also the seed of their limitations. What happens in the real world away from the ideal Gaussian model? The non-Gaussian world may contain random processes that are close to the Gaussian. What are appropriate classes of nearly Gaussian models and how typical or robust is the Gaussian model amongst them? Moving further away from normality, what are appropriate non-Gaussian models that are sufficiently different to encompass distinct behavior, yet sufficiently simple to be amenable to efficient statistical inference? The very Central Limit Theorem which provides the fundamental justifi cation for approximate normality, points to stable and other infinitely divisible models. Some of these may be close to and others very different from Gaussian models.

Handbook Of Heavy-tailed Distributions In Asset Management And Risk Management

Michele Leonardo Bianchi,Stoyan V Stoyanov,Gian Luca Tassinari,Frank J Fabozzi,Sergio Focardi
Handbook Of Heavy tailed Distributions In Asset Management And Risk Management Book PDF

Author : Michele Leonardo Bianchi,Stoyan V Stoyanov,Gian Luca Tassinari,Frank J Fabozzi,Sergio Focardi
Publisher : World Scientific
Page : 598 pages
File Size : 40,5 Mb
Release : 2019-03-08
Category : Business & Economics
ISBN : 9789813276215

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Handbook Of Heavy-tailed Distributions In Asset Management And Risk Management by Michele Leonardo Bianchi,Stoyan V Stoyanov,Gian Luca Tassinari,Frank J Fabozzi,Sergio Focardi Pdf

The study of heavy-tailed distributions allows researchers to represent phenomena that occasionally exhibit very large deviations from the mean. The dynamics underlying these phenomena is an interesting theoretical subject, but the study of their statistical properties is in itself a very useful endeavor from the point of view of managing assets and controlling risk. In this book, the authors are primarily concerned with the statistical properties of heavy-tailed distributions and with the processes that exhibit jumps. A detailed overview with a Matlab implementation of heavy-tailed models applied in asset management and risk managements is presented. The book is not intended as a theoretical treatise on probability or statistics, but as a tool to understand the main concepts regarding heavy-tailed random variables and processes as applied to real-world applications in finance. Accordingly, the authors review approaches and methodologies whose realization will be useful for developing new methods for forecasting of financial variables where extreme events are not treated as anomalies, but as intrinsic parts of the economic process.

Data Analysis and Applications 4

Andreas Makrides,Alex Karagrigoriou,Christos H. Skiadas
Data Analysis and Applications 4 Book PDF

Author : Andreas Makrides,Alex Karagrigoriou,Christos H. Skiadas
Publisher : John Wiley & Sons
Page : 241 pages
File Size : 46,9 Mb
Release : 2020-04-09
Category : Mathematics
ISBN : 9781119721581

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Data Analysis and Applications 4 by Andreas Makrides,Alex Karagrigoriou,Christos H. Skiadas Pdf

Data analysis as an area of importance has grown exponentially, especially during the past couple of decades. This can be attributed to a rapidly growing computer industry and the wide applicability of computational techniques, in conjunction with new advances of analytic tools. This being the case, the need for literature that addresses this is self-evident. New publications are appearing, covering the need for information from all fields of science and engineering, thanks to the universal relevance of data analysis and statistics packages. This book is a collective work by a number of leading scientists, analysts, engineers, mathematicians and statisticians who have been working at the forefront of data analysis. The chapters included in this volume represent a cross-section of current concerns and research interests in these scientific areas. The material is divided into three parts: Financial Data Analysis and Methods, Statistics and Stochastic Data Analysis and Methods, and Demographic Methods and Data Analysis- providing the reader with both theoretical and applied information on data analysis methods, models and techniques and appropriate applications.

Lévy Processes

Ole E Barndorff-Nielsen,Thomas Mikosch,Sidney I. Resnick
L vy Processes Book PDF

Author : Ole E Barndorff-Nielsen,Thomas Mikosch,Sidney I. Resnick
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201977

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Lévy Processes by Ole E Barndorff-Nielsen,Thomas Mikosch,Sidney I. Resnick Pdf

A Lévy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Lévy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Lévy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Lévy processes and their enormous flexibility in modeling tails, dependence and path behavior. This volume, with an excellent introductory preface, describes the state-of-the-art of this rapidly evolving subject with special emphasis on the non-Brownian world. Leading experts present surveys of recent developments, or focus on some most promising applications. Despite its special character, every topic is aimed at the non- specialist, keen on learning about the new exciting face of a rather aged class of processes. An extensive bibliography at the end of each article makes this an invaluable comprehensive reference text. For the researcher and graduate student, every article contains open problems and points out directions for futurearch. The accessible nature of the work makes this an ideal introductory text for graduate seminars in applied probability, stochastic processes, physics, finance, and telecommunications, and a unique guide to the world of Lévy processes.

Tempered Stable Distributions

Michael Grabchak
Tempered Stable Distributions Book PDF

Author : Michael Grabchak
Publisher : Springer
Page : 118 pages
File Size : 49,9 Mb
Release : 2016-01-26
Category : Mathematics
ISBN : 9783319249278

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Tempered Stable Distributions by Michael Grabchak Pdf

This brief is concerned with tempered stable distributions and their associated Levy processes. It is a good text for researchers interested in learning about tempered stable distributions. A tempered stable distribution is one which takes a stable distribution and modifies its tails to make them lighter. The motivation for this class comes from the fact that infinite variance stable distributions appear to provide a good fit to data in a variety of situations, but the extremely heavy tails of these models are not realistic for most real world applications. The idea of using distributions that modify the tails of stable models to make them lighter seems to have originated in the influential paper of Mantegna and Stanley (1994). Since then, these distributions have been extended and generalized in a variety of ways. They have been applied to a wide variety of areas including mathematical finance, biostatistics,computer science, and physics.

Trends in Partial Differential Equations of Mathematical Physics

José-Francisco Rodrigues,Gregory Seregin
Trends in Partial Differential Equations of Mathematical Physics Book PDF

Author : José-Francisco Rodrigues,Gregory Seregin
Publisher : Birkhauser
Page : 282 pages
File Size : 53,9 Mb
Release : 2005-01-01
Category : Mathematics
ISBN : 081767165X

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Trends in Partial Differential Equations of Mathematical Physics by José-Francisco Rodrigues,Gregory Seregin Pdf

This book consists of contributions originating from a conference in Obedo, Portugal, which honoured the 70th birthday of V.A. Solonnikov. A broad variety of topics centering on nonlinear problems is presented, particularly Navier-Stokes equations, viscosity problems, diffusion-absorption equations, free boundaries, and Euler equations.

Stable Non-Gaussian Random Processes

Gennady Samoradnitsky
Stable Non Gaussian Random Processes Book PDF

Author : Gennady Samoradnitsky
Publisher : Routledge
Page : 632 pages
File Size : 43,9 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351414807

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Stable Non-Gaussian Random Processes by Gennady Samoradnitsky Pdf

This book serves as a standard reference, making this area accessible not only to researchers in probability and statistics, but also to graduate students and practitioners. The book assumes only a first-year graduate course in probability. Each chapter begins with a brief overview and concludes with a wide range of exercises at varying levels of difficulty. The authors supply detailed hints for the more challenging problems, and cover many advances made in recent years.

Continuous Multivariate Distributions, Volume 1

Samuel Kotz,N. Balakrishnan,Norman L. Johnson
Continuous Multivariate Distributions Volume 1 Book PDF

Author : Samuel Kotz,N. Balakrishnan,Norman L. Johnson
Publisher : John Wiley & Sons
Page : 752 pages
File Size : 48,8 Mb
Release : 2004-04-05
Category : Mathematics
ISBN : 9780471654032

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Continuous Multivariate Distributions, Volume 1 by Samuel Kotz,N. Balakrishnan,Norman L. Johnson Pdf

Continuous Multivariate Distributions, Volume 1, Second Edition provides a remarkably comprehensive, self-contained resource for this critical statistical area. It covers all significant advances that have occurred in the field over the past quarter century in the theory, methodology, inferential procedures, computational and simulational aspects, and applications of continuous multivariate distributions. In-depth coverage includes MV systems of distributions, MV normal, MV exponential, MV extreme value, MV beta, MV gamma, MV logistic, MV Liouville, and MV Pareto distributions, as well as MV natural exponential families, which have grown immensely since the 1970s. Each distribution is presented in its own chapter along with descriptions of real-world applications gleaned from the current literature on continuous multivariate distributions and their applications.

A Practical Guide to Heavy Tails

Robert Adler,Raya Feldman,Murad Taqqu
A Practical Guide to Heavy Tails Book PDF

Author : Robert Adler,Raya Feldman,Murad Taqqu
Publisher : Springer Science & Business Media
Page : 560 pages
File Size : 55,8 Mb
Release : 1998-10-26
Category : Mathematics
ISBN : 0817639519

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A Practical Guide to Heavy Tails by Robert Adler,Raya Feldman,Murad Taqqu Pdf

Twenty-four contributions, intended for a wide audience from various disciplines, cover a variety of applications of heavy-tailed modeling involving telecommunications, the Web, insurance, and finance. Along with discussion of specific applications are several papers devoted to time series analysis, regression, classical signal/noise detection problems, and the general structure of stable processes, viewed from a modeling standpoint. Emphasis is placed on developments in handling the numerical problems associated with stable distribution (a main technical difficulty until recently). No index. Annotation copyrighted by Book News, Inc., Portland, OR

Statistical Tools for Finance and Insurance

Pavel Čižek,Wolfgang Härdle,Rafał Weron
Statistical Tools for Finance and Insurance Book PDF

Author : Pavel Čižek,Wolfgang Härdle,Rafał Weron
Publisher : Springer Science & Business Media
Page : 534 pages
File Size : 47,6 Mb
Release : 2005
Category : Business & Economics
ISBN : 3540221891

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Statistical Tools for Finance and Insurance by Pavel Čižek,Wolfgang Härdle,Rafał Weron Pdf

Statistical Tools in Finance and Insurance presents ready-to-use solutions, theoretical developments and method construction for many practical problems in quantitative finance and insurance. Written by practitioners and leading academics in the field, this book offers a unique combination of topics from which every market analyst and risk manager will benefit. Covering topics such as heavy tailed distributions, implied trinomial trees, support vector machines, valuation of mortgage-backed securities, pricing of CAT bonds, simulation of risk processes and ruin probability approximation, the book does not only offer practitioners insight into new methods for their applications, but it also gives theoreticians insight into the applicability of the stochastic technology. Additionally, the book provides the tools, instruments and (online) algorithms for recent techniques in quantitative finance and modern treatments in insurance calculations. Written in an accessible and engaging style, this self-instructional book makes a good use of extensive examples and full explanations. Thenbsp;design of the text links theory and computational tools in an innovative way. All Quantlets for the calculation of examples given in the text are supported by the academic edition of XploRe and may be executed via XploRe Quantlet Server (XQS). The downloadable electronic edition of the book enables one to run, modify, and enhance all Quantlets on the spot.

Stable Non-Gaussian Random Processes

Gennady Samoradnitsky
Stable Non Gaussian Random Processes Book PDF

Author : Gennady Samoradnitsky
Publisher : Routledge
Page : 519 pages
File Size : 53,6 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351414791

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Stable Non-Gaussian Random Processes by Gennady Samoradnitsky Pdf

This book serves as a standard reference, making this area accessible not only to researchers in probability and statistics, but also to graduate students and practitioners. The book assumes only a first-year graduate course in probability. Each chapter begins with a brief overview and concludes with a wide range of exercises at varying levels of difficulty. The authors supply detailed hints for the more challenging problems, and cover many advances made in recent years.