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How do you determine if an empirical distribution has a heavy tail? What would I have to do in order to determine that? I'm currently using mathematica, so if you know of any coding, that would be very helpful. If not, then that's alright.

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One way to do this is to plot the survival or reliability function of the empirical data on log-log scale. If the resulting graph appears "approximately linear", then one can say that it is likely that heavy-tailed properties may be present. There is a "ton" of literature on this topic. Here is a link to some common techniques... http://onlinelibrary.wiley.com/doi/10.1002/9780470723609.ch1/summary