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3 - Copulas and Their Properties

from Part One - Theory

Published online by Cambridge University Press:  03 January 2019

Lan Zhang  and
V. P. Singh
Lan Zhang
Affiliation:
Texas A & M University
V. P. Singh
Affiliation:
Texas A & M University
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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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Copulas and their Applications in Water Resources Engineering , pp. 62 - 122
Publisher: Cambridge University Press
Print publication year: 2019

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References

References

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Additional Reading

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  • Copulas and Their Properties
  • Lan Zhang, Texas A & M University, V. P. Singh, Texas A & M University
  • Book: Copulas and their Applications in Water Resources Engineering
  • Online publication: 03 January 2019
  • Chapter DOI: https://doi.org/10.1017/9781108565103.004
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  • Copulas and Their Properties
  • Lan Zhang, Texas A & M University, V. P. Singh, Texas A & M University
  • Book: Copulas and their Applications in Water Resources Engineering
  • Online publication: 03 January 2019
  • Chapter DOI: https://doi.org/10.1017/9781108565103.004
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Copulas and Their Properties
  • Lan Zhang, Texas A & M University, V. P. Singh, Texas A & M University
  • Book: Copulas and their Applications in Water Resources Engineering
  • Online publication: 03 January 2019
  • Chapter DOI: https://doi.org/10.1017/9781108565103.004
Available formats
×