Book contents
- Copulas and Their Applications in Water Resources Engineering
- Copulas and Their Applications in Water Resources Engineering
- Copyright page
- Dedication
- Contents
- Preface
- Acknowledgments
- Part One Theory
- 1 Introduction
- 2 Preliminaries
- 3 Copulas and Their Properties
- 4 Symmetric Archimedean Copulas
- 5 Asymmetric Copulas
- 6 Plackett Copula
- 7 Non-Archimedean Copulas
- 8 Entropic Copulas
- 9 Copulas in Time Series Analysis
- Part Two Applications
- Index
- References
3 - Copulas and Their Properties
from Part One - Theory
Published online by Cambridge University Press: 03 January 2019
Book contents
- Copulas and Their Applications in Water Resources Engineering
- Copulas and Their Applications in Water Resources Engineering
- Copyright page
- Dedication
- Contents
- Preface
- Acknowledgments
- Part One Theory
- 1 Introduction
- 2 Preliminaries
- 3 Copulas and Their Properties
- 4 Symmetric Archimedean Copulas
- 5 Asymmetric Copulas
- 6 Plackett Copula
- 7 Non-Archimedean Copulas
- 8 Entropic Copulas
- 9 Copulas in Time Series Analysis
- Part Two Applications
- Index
- References
Summary
The term copula is derived from the Latin verb copulare, meaning “to join together.” In the statistics literature, the idea of a copula can be dated back to the nineteenth century in modeling multivariate non-Gaussian distributions. By formulating a theorem, now called Sklar theorem, Sklar (1959) laid the theoretical foundation for the modern copula theory. In general, copulas couple multivariate distribution functions to their one-dimensional marginal distribution functions, which are uniformly distributed in [0, 1]. In other words, copula functions enable us to represent a multivariate distribution with the use of univariate probability distributions (sometimes simply called marginals, or margins), regardless of their forms or types. In this chapter, we will discuss the general concepts of copulas, including their definition, properties, composition and construction, dependence structure, and tail dependence.
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- Publisher: Cambridge University PressPrint publication year: 2019
References
References
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