Tail behavior, modes, and other characteristics of stable distributions

Stable distributions have heavy tails that are asymptotically Paretian. Accurate computations of stable densities and distribution functions are used to analyze when the Paretian tail actually appears. Implications for estimation procedures are discussed. In addition to numerically locating the mode of a general stable distribution, analytic and numeric results are given for the mode. Extensive tables of stable percentiles have been computed; aspects of these tables and the appropriateness of infinite variance stable models are discussed.