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Principles of copula theory

By: Durante, Fabrizio.
Contributor(s): Sempi, Carlo.
Publisher: Boca Raton CRC Press 2016Description: xvi, 315 p.ISBN: 9781439884423.Subject(s): Copulas - Mathematical statistics | Multivariate analysis | CopulaDDC classification: 519.535 Summary: 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. (https://www.crcpress.com/Principles-of-Copula-Theory/Durante-Sempi/p/book/9781439884423)
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Slot 1424 (0 Floor, East Wing) Non-fiction 519.535 D8P7 (Browse shelf) Available 192550

Table of Contents:

1.Copulas: Basic Definitions and Properties

2.Copulas and Stochastic Dependence

3.Copulas and Measures

4.Copulas and Approximation

5.The Markov Product of Copulas

6.A Compendium of Families of Copulas

7.Generalizations of Copulas: Quasi-Copulas

8.Generalizations of Copulas: Semi-Copulas

Bibliography
Index

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.

(https://www.crcpress.com/Principles-of-Copula-Theory/Durante-Sempi/p/book/9781439884423)

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