January 2019 Archives

Archimedean Review

In the last couple of posts we've been taking a look at Archimedean copulas which define the dependency between the elements of vector values of a multivariate random variable by applying a generator function φ to the values of the cumulative distribution functions, or CDFs, of their distributions when considered independently, known as their marginal distributions, and applying the inverse of the generator to the sum of the results to yield the value of the multivariate CDF.
We have seen that the densities of Archimedean copulas are rather trickier to calculate and that making random observations of them is trickier still. Last time we found an algorithm for the latter, albeit with an implementation that had troubling performance and numerical stability issues, and in this post we shall add an improved version to the ak library that addresses those issues.

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