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This book introduces the main theoretical findings related to copulas and shows how statistical modeling of multivariate continuous distributions using copulas can be carried out in the R statistical environment with the package copula (among others).

Copulas are multivariate distribution functions with standard uniform univariate margins. They are increasingly applied to modeling dependence among random variables in fields such as risk management, actuarial science, insurance, finance, engineering, hydrology, climatology, and meteorology, to name a few.

In the spirit of the Use R! series, each chapter combines key theoretical definitions or results with illustrations in R. Aimed at statisticians, actuaries, risk managers, engineers and environmental scientists wanting to learn about the theory and practice of copula modeling using R without an overwhelming amount of mathematics, the book can also be used for teaching a course on copula modeling.

### Chapter 1. Introduction

Assume that one is given the two bivariate data sets displayed in Fig. 1.1 and asked to compare them in terms of the “dependence” between the two underlying variables. The first (respectively, second) data set, denoted by (x i1, x i2), i ∈{1, …, n} (respectively, (y i1, y i2), i ∈{1, …, n}), is assumed to consist of n = 1000 independent observations (that is, a realization of independent copies) of a bivariate random vector (X 1, X 2) (respectively, (Y 1, Y 2)). Roughly speaking, comparing the two data sets in terms of dependence means comparing the way X 1 and X 2 are related with the way Y 1 and Y 2 are related.
Marius Hofert, Ivan Kojadinovic, Martin Mächler, Jun Yan

### Chapter 2. Copulas

This chapter offers a basic introduction to copulas and presents their main properties along with the most important theoretical results such as the Fréchet-Hoeffding bounds, Sklar’s Theorem, and the invariance principle.
Marius Hofert, Ivan Kojadinovic, Martin Mächler, Jun Yan

### Chapter 3. Classes and Families

This chapter introduces the main copula classes and the corresponding sampling procedures, along with some copula transformations that are important for practical purposes.
Marius Hofert, Ivan Kojadinovic, Martin Mächler, Jun Yan

### Chapter 4. Estimation

This chapter addresses the estimation of copulas from a parametric, semi-parametric, and nonparametric perspective.
Marius Hofert, Ivan Kojadinovic, Martin Mächler, Jun Yan

### Chapter 5. Graphical Diagnostics, Tests, and Model Selection

This chapter presents graphical diagnostics and statistical tests, and discusses model selection for copulas.
Marius Hofert, Ivan Kojadinovic, Martin Mächler, Jun Yan

### Chapter 6. Ties, Time Series, and Regression

This chapter is concerned with more advanced topics in copula modeling such as the handling of ties, time series, and covariates (in a regression-like setting).
Marius Hofert, Ivan Kojadinovic, Martin Mächler, Jun Yan