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Is there a text books or publications that describes multivariate power law/pareto distributions?

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I don't know about any books completely devoted to multivariate power laws or Pareto distributions. However, it is always possible to use Sklar's theorem to construct an arbitrary multivariate distribution from any given set of univariate distributions (that includes power laws and Pareto distributions) using a copula function. For good references on copula functions and how to use to construct arbitrary distributions, there are these two books.

The first one is by Roger B. Nelsen

and the second one is by Harry Joe

For the univariate Pareto and power law distributions, there is this general reference book by Kleiber and Kotz

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