Copulas and Extreme Values

In course

Description

This lecture discusses the use of copulas to measure the strength of dependence in distributions, focusing on distinguishing between different rates of convergence to zero. It covers the concept of X(u) as a measure of dependence level, the scaling chosen for independent and dependent variables, and the distinction between perfectly and asymptotically dependent variables. The lecture also explores the application of copulas in extreme value theory, transforming variables to unit Fréchet margins, and the limiting distribution of componentwise maxima. Examples with bivariate normal and Student t distributions are provided to illustrate the concepts.

Official source

https://mediaspace.epfl.ch/media/0_213z2s2i

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Related lectures (32)

Related concepts (32)

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Folded normal distribution

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Complex normal distribution

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In statistics, the multivariate t-distribution (or multivariate Student distribution) is a multivariate probability distribution. It is a generalization to random vectors of the Student's t-distribution, which is a distribution applicable to univariate random variables. While the case of a random matrix could be treated within this structure, the matrix t-distribution is distinct and makes particular use of the matrix structure.

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