dependence modeling with copulas chapman hall crc monographs on statistics applied probability

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Dependence Modeling With Copulas

Author : Harry Joe
ISBN : 9781466583221
Genre : Mathematics
File Size : 71. 68 MB
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Dependence Modeling with Copulas covers the substantial advances that have taken place in the field during the last 15 years, including vine copula modeling of high-dimensional data. Vine copula models are constructed from a sequence of bivariate copulas. The book develops generalizations of vine copula models, including common and structured factor models that extend from the Gaussian assumption to copulas. It also discusses other multivariate constructions and parametric copula families that have different tail properties and presents extensive material on dependence and tail properties to assist in copula model selection. The author shows how numerical methods and algorithms for inference and simulation are important in high-dimensional copula applications. He presents the algorithms as pseudocode, illustrating their implementation for high-dimensional copula models. He also incorporates results to determine dependence and tail properties of multivariate distributions for future constructions of copula models.

Multivariate Models And Multivariate Dependence Concepts

Author : Harry Joe
ISBN : 0412073315
Genre : Mathematics
File Size : 62. 26 MB
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This book on multivariate models, statistical inference, and data analysis contains deep coverage of multivariate non-normal distributions for modeling of binary, count, ordinal, and extreme value response data. It is virtually self-contained, and includes many exercises and unsolved problems.

Dependence Modeling

Author : Dorota Kurowicka
ISBN : 9789814299886
Genre : Mathematics
File Size : 21. 26 MB
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This book is a collaborative effort from three workshops held over the last three years, all involving principal contributors to the vine-copula methodology. Research and applications in vines have been growing rapidly and there is now a growing need to collate basic results, and standardize terminology and methods. Specifically, this handbook will trace historical developments, standardizing notation and terminology, summarize results on bivariate copulae, summarize results for regular vines, and give an overview of its applications. In addition, many of these results are new and not readily available in any existing journals. New research directions are also discussed.

Principles Of Copula Theory

Author : Fabrizio Durante
ISBN : 9781439884447
Genre : Mathematics
File Size : 49. 61 MB
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Principles of Copula Theory explores the state of the art on copulas and provides you with the foundation to use copulas in a variety of applications. Throughout the book, historical remarks and further readings highlight active research in the field, including new results, streamlined presentations, and new proofs of old results. After covering the essentials of copula theory, the book addresses the issue of modeling dependence among components of a random vector using copulas. It then presents copulas from the point of view of measure theory, compares methods for the approximation of copulas, and discusses the Markov product for 2-copulas. The authors also examine selected families of copulas that possess appealing features from both theoretical and applied viewpoints. The book concludes with in-depth discussions on two generalizations of copulas: quasi- and semi-copulas. Although copulas are not the solution to all stochastic problems, they are an indispensable tool for understanding several problems about stochastic dependence. This book gives you the solid and formal mathematical background to apply copulas to a range of mathematical areas, such as probability, real analysis, measure theory, and algebraic structures.

Simulating Copulas

Author : Jan-Frederik Mai
ISBN : 9781848168749
Genre : Mathematics
File Size : 82. 72 MB
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This book provides the reader with a background on simulating copulas and multivariate distributions in general. It unifies the scattered literature on the simulation of various families of copulas (elliptical, Archimedean, Marshall-Olkin type, etc.) as well as on different construction principles (factor models, pair-copula construction, etc.). The book is self-contained and unified in presentation and can be used as a textbook for advanced undergraduate or graduate students with a firm background in stochastics. Alongside the theoretical foundation, ready-to-implement algorithms and many examples make this book a valuable tool for anyone who is applying the methodology.Errata(s)Errata (128 KB)

Copulas And Dependence Models With Applications

Author : Manuel Úbeda Flores
ISBN : 9783319642215
Genre : Mathematics
File Size : 33. 19 MB
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This book presents contributions and review articles on the theory of copulas and their applications. The authoritative and refereed contributions review the latest findings in the area with emphasis on “classical” topics like distributions with fixed marginals, measures of association, construction of copulas with given additional information, etc. The book celebrates the 75th birthday of Professor Roger B. Nelsen and his outstanding contribution to the development of copula theory. Most of the book’s contributions were presented at the conference “Copulas and Their Applications” held in his honor in Almería, Spain, July 3-5, 2017. The chapter 'When Gumbel met Galambos' is published open access under a CC BY 4.0 license.

Copula Modeling

Author : P. K. Trivedi
ISBN : 9781601980205
Genre : Business & Economics
File Size : 60. 71 MB
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Copula Modeling explores the copula approach for econometrics modeling of joint parametric distributions. Copula Modeling demonstrates that practical implementation and estimation is relatively straightforward despite the complexity of its theoretical foundations. An attractive feature of parametrically specific copulas is that estimation and inference are based on standard maximum likelihood procedures. Thus, copulas can be estimated using desktop econometric software. This offers a substantial advantage of copulas over recently proposed simulation-based approaches to joint modeling. Copulas are useful in a variety of modeling situations including financial markets, actuarial science, and microeconometrics modeling. Copula Modeling provides practitioners and scholars with a useful guide to copula modeling with a focus on estimation and misspecification. The authors cover important theoretical foundations. Throughout, the authors use Monte Carlo experiments and simulations to demonstrate copula properties

Introduction To Credit Risk Modeling Second Edition

Author : Christian Bluhm
ISBN : 9781584889939
Genre : Mathematics
File Size : 81. 85 MB
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Contains Nearly 100 Pages of New Material The recent financial crisis has shown that credit risk in particular and finance in general remain important fields for the application of mathematical concepts to real-life situations. While continuing to focus on common mathematical approaches to model credit portfolios, Introduction to Credit Risk Modeling, Second Edition presents updates on model developments that have occurred since the publication of the best-selling first edition. New to the Second Edition An expanded section on techniques for the generation of loss distributions Introductory sections on new topics, such as spectral risk measures, an axiomatic approach to capital allocation, and nonhomogeneous Markov chains Updated sections on the probability of default, exposure-at-default, loss-given-default, and regulatory capital A new section on multi-period models Recent developments in structured credit The financial crisis illustrated the importance of effectively communicating model outcomes and ensuring that the variation in results is clearly understood by decision makers. The crisis also showed that more modeling and more analysis are superior to only one model. This accessible, self-contained book recommends using a variety of models to shed light on different aspects of the true nature of a credit risk problem, thereby allowing the problem to be viewed from different angles.

Analysis Of Mixed Data

Author : Alexander R. de Leon
ISBN : 9781439884720
Genre : Mathematics
File Size : 82. 90 MB
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A comprehensive source on mixed data analysis, Analysis of Mixed Data: Methods & Applications summarizes the fundamental developments in the field. Case studies are used extensively throughout the book to illustrate interesting applications from economics, medicine and health, marketing, and genetics. Carefully edited for smooth readability and seamless transitions between chapters All chapters follow a common structure, with an introduction and a concluding summary, and include illustrative examples from real-life case studies in developmental toxicology, economics, medicine and health, marketing, and genetics An introductory chapter provides a "wide angle" introductory overview and comprehensive survey of mixed data analysis Blending theory and methodology, this book illustrates concepts via data from different disciplines. Analysis of Mixed Data: Methods & Applications traces important developments, collates basic results, presents terminology and methodologies, and gives an overview of statistical research applications. It is a valuable resource to methodologically interested as well as subject matter-motivated researchers in many disciplines.

Graphical Models With R

Author : Søren Højsgaard
ISBN : 9781461422990
Genre : Mathematics
File Size : 68. 98 MB
Format : PDF
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Graphical models in their modern form have been around since the late 1970s and appear today in many areas of the sciences. Along with the ongoing developments of graphical models, a number of different graphical modeling software programs have been written over the years. In recent years many of these software developments have taken place within the R community, either in the form of new packages or by providing an R interface to existing software. This book attempts to give the reader a gentle introduction to graphical modeling using R and the main features of some of these packages. In addition, the book provides examples of how more advanced aspects of graphical modeling can be represented and handled within R. Topics covered in the seven chapters include graphical models for contingency tables, Gaussian and mixed graphical models, Bayesian networks and modeling high dimensional data.

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