Elements of Copula Modeling with R

verfasst von: Marius Hofert, Ivan Kojadinovic, Martin Mächler, Jun Yan

Verlag: Springer International Publishing

Buchreihe : Use R!

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

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.