Fitting Data and Assessing Goodness � of � t with Stable Distributions

There are now several reliable methods for estimating stable pa rameters from data However little attention has been paid to model veri cation i e how to assess whether the stable parameters esti mated actually do a good job of describing the data We analyze sev eral heavy tailed data sets and demonstrate diagnostics for assessing both univariate and multivariate stable ts to data sets Multivari ate stable distributions are characterized in terms of one dimensional projections and new results are given for sub Gaussian stable distri butions