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Copula functions

A neat way of quantifying arbitrary (?) 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 tricky.)

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