a.k. from thus spake a.k.

Last time we took a look at how we could define copulas to represent the dependency between random variables by summing the results of a generator function to that sum.

These are known as Archimedean copulas and are valid whenever[0,1] , equal to zero when its argument equals one and have derivatives that are non-negative over that interval when

Whilst such copulas are relatively easy to implement we saw that their densities are a rather trickier job, in contrast to Gaussian copulas where the reverse is true. In this post we shall see how to draw random vectors from Archimedean copulas which is also much more difficult than doing so from Gaussian copulas.

*φ*applied to the results of their cumulative distribution functions, or CDFs, and then applying the inverse of that function*φ*

^{-1}

These are known as Archimedean copulas and are valid whenever

*φ*is strictly decreasing over the interval*n*

^{th}

*n*is even and non-positive when it is odd, for*n*up to the number of random variables.Whilst such copulas are relatively easy to implement we saw that their densities are a rather trickier job, in contrast to Gaussian copulas where the reverse is true. In this post we shall see how to draw random vectors from Archimedean copulas which is also much more difficult than doing so from Gaussian copulas.