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An Introduction to Copulas
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This book discusses the fundamental properties of copulas and some of their primary applications, which include the study of dependence and measures of association, and the construction of families of bivariate distributions.Abstract:
The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. This book is suitable as a text or for self-study.read more
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Journal ArticleDOI
Multivariate Archimedean copulas, $d$-monotone functions and $\ell_1$-norm symmetric distributions
TL;DR: It is shown that a necessary and sufficient condition for an Archimedean copula generator to generate a $d-dimensional copula is that the generator is a d-monotone function.
Book ChapterDOI
Aggregation operators: properties, classes and construction methods
TL;DR: In this article, the authors restrict their considerations regarding inputs as well as outputs to some fixed interval (scale) I = [a, b] ⊑ [-∞, ∞].
Book
Actuarial Theory for Dependent Risks: Measures, Orders and Models
TL;DR: In this article, the authors provide an essential guide to managing modern financial risk by combining coverage of stochastic order and risk measure theories with the basics of risk management, including dependence concepts and dependence orderings.
Journal ArticleDOI
Multivariate hydrological frequency analysis using copulas
TL;DR: The modeling of multivariate extreme values using copulas allows us to model the dependence structure independently of the marginal distributions, which is not possible with standard classical methods.
Journal ArticleDOI
Multivariate Archimedean copulas, d-monotone functions and ℓ1-norm symmetric distributions
TL;DR: In this paper, it was shown that a necessary and sufficient condition for an Archimedean copula generator to generate a d-dimensional copula is that the generator is a monotone function.