Many real problems in finance and hydrology involve data sets with power law tails. For multivariable data, the power law tail index usually varies with the coordinate, and the coordinates may be dependent. This paper surveys nonparametric methods for modeling such data sets. These models are based on a generalized central limit theorem. The limit laws in the generalized central limit theorem are operator stable, a class that contains the multivariate Gaussian as well as marginally stable random vectors with different tail behavior in each coordinate. Modeling this kind of data requires choosing the right coordinates, estimating the tail index for those coordinates, and characterizing dependence between the coordinates. We illustrate the practical application of these methods with several example data sets from finance and hydrology. 1.
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