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Zbl 1152.62030
Nelsen, Roger B.
An introduction to copulas. 2nd ed. (English)
[B] Springer Series in Statistics. New York, NY: Springer. xiii, 269~p. EUR~62.95 (2006). ISBN 0-387-28659-4/hbk

[For the review of the first edition from 1999 see Zbl 0909.62052.]\par 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.\par 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. \par 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.\par 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.
[Piotr Jaworski (Warszawa)]

MSC 2000:: *62H05 Multivariate structure theory
62H20 Statistical measures of associations
62-01 Textbooks (statistics)
60E05 General theory of probability distributions
60-01 Textbooks (probability theory)

Keywords: copulas; dependence functions; Archimedean copulas; concordance measures

Citations: Zbl 0909.62052

Cited in: Zbl 1207.60010 Zbl 1189.91076

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