Copula functions

A neat way of quantifying dependence structures between random variables. Useful in, e.g. Quantitative Risk Management.

The trick is simple: Informally, you look at the marginal iCDF of each of \(n\) variables, and fiddle with the joint distribution of those marginals on \([0,1]^n\). (That’s assuming variables are absolutely continuous w.r.t some underlying measure space; distribution with atoms are more fiddly.)

This is a good trick, although I need to sit down and think it through. I would like to better understand:

  • the relationship between the underlying event space and the instrumental one we “sort of” construct in copula modeling.
  • Is any information lost with non-monotonic coupling in a copula model?
  • conditional copulas and how they work
  • the occasionally-mentioned relationship between copula entropy and mutual information.


For now, see elliptical distributions.

Vine copulas

Hierarchical graphical models, AFAICS.


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