Abstract
If we have a collection of copulas then, as a consequence of Sklar’s theorem, we automatically have a collection of bivariate or multivariate distributions with whatever marginal distributions we desire. Clearly this can be useful in modeling and simulation. Furthermore, by virtue of Theorem 2.4.3, the nonparametric nature of the dependence between two random variables, is expressed by the copula. Thus the study of concepts and measures of nonparametric dependence is a study of properties of copulas—a topic we will pursue in Chapter 5. For this study, it is advantageous to have a variety of copulas at our disposal.
Keywords
- Bivariate Distribution
- Continuous Random Variable
- Archimedean Copula
- Joint Distribution Function
- Bivariate Exponential Distribution
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© 1999 Springer Science+Business Media New York
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Nelsen, R.B. (1999). Methods of Constructing Copulas. In: An Introduction to Copulas. Lecture Notes in Statistics, vol 139. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3076-0_3
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DOI: https://doi.org/10.1007/978-1-4757-3076-0_3
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