Elements of Copula Modeling with R

Copulas

Copulas are multivariate distribution functions with standard uniform univariate margins. They are increasingly applied to modeling dependence among random variables in probabilistic and statistical models arising in fields such as risk management, actuarial science, insurance, finance, engineering, hydrology, climatology, meteorology, to name a few. The relatively recent enthusiasm for the use of copulas finds its origin in a representation theorem from 1959 due to Abe Sklar. This result suggests to view a multivariate distribution function as a coupling of its univariate margins by means of the underlying copula. Important consequences are, for example, that more flexible multivariate distributions can be constructed and that their statistical inference is simplified, especially in high dimensions.

About the book

The aim of this book is to introduce the main theoretical results about copulas and to show how statistical modeling of multivariate continuous distributions using copulas can be carried out in the R statistical environment using the package copula (among others). The book targets statisticians, actuaries, risk managers, engineers and environmental scientists alike, who would like to learn about the theory and practice of copula modeling with R without an overwhelming amount of mathematics.

In the spirit of other monographs in the Springer Use R! series, each chapter combines key theoretical definitions or results with illustrations in R. The book may also be used for teaching a course on copula modeling.

List of features

• Offers a basic introduction to copulas and their main properties, along with the most important theoretical results.
• Introduces the most widely used copula classes, their corresponding sampling procedures, along with selected copula transformations that are important for practical purposes.
• Tackles the estimation of copulas from a parametric, semi-parametric and non-parametric perspective.
• Discusses graphical diagnostics, statistical tests and model selection.
• Addresses more advanced topics such as the handling of ties, time series and covariates (in a regression-like setting).
• Illustrates the presented concepts by stand-alone and reproducible R examples involving either synthetic or real data.