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An introduction to copulas. 2nd ed. (English) Zbl 1152.62030
Springer Series in Statistics. New York, NY: Springer (ISBN 0-387-28659-4/hbk). xiii, 269 p. (2006).
[For the review of the first edition from 1999 see Zbl 0909.62052.]
Copulas (or copulae) are functions that join multivariate distribution functions to their one-dimensional margins. Since this notion is scale invariant, it captures scale invariant dependence properties of distributions. On the other side copulas proved to be a are very useful tool in multivariate modelling when the marginal one-dimensional distributions are already known. Therefore the study of copulas and their role in statistics is a vigorously growing field.
The book begins with the basic properties of copulas and then proceeds to present methods for constructing copulas and to discuss the role played by copulas in modeling and study of dependence. The focus is on bivariate copulas, although most chapters conclude with a discussion of the general multivariate case.
This introductory and informative text on copulas is clearly written and from an educational standpoint well presented. With more than hundred examples and over 160 exercises, this book is suitable as a textbook or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics.
The second edition maintains the basic organization of the material and the general level of presentation as the first one from 1999. The major additions are sections on: copula transformation methods; extreme value copulas; copulas with specific analytic or functional properties; tail dependence and quasi-copulas. Some exercises and examples were also added and about 30 new entries referred to in the text were inserted in the bibliography.

MSC:
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H20 Measures of association (correlation, canonical correlation, etc.)
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
60E05 Probability distributions: general theory
60-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
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