How We Tend To Overestimate Powerlaw Tail Exponents
  In the presence of a layer of metaprobabilities (from uncertainty concerning the parameters), the asymptotic tail exponent corresponds to the lowest possible tail exponent regardless of its probability. The problem explains "Black Swan" effects, i.e., why measurements tend to chronically underestimate tail contributions, rather than merely deliver imprecise but unbiased estimates. 
Nassim N. Taleb
q-fin.RM math.ST physics.data-an stat.TH