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Stable distributions are a rich class of probability distributions that allow skewness and heavy tails and have many intriguing mathematical properties. The class was characterized by Paul Levy in his study of sums of independent identically distributed terms in the 1920’s. The lack of closed formulas for densities and distribution functions for all but a few stable distributions (Gaussian, Cauchy and Levy) Alpha-stable distributions arise naturally in the study of heavy-tailed distributions, and have found applications in economics and physics as models of rare, but extreme events (such as earthquakes or stock market crashes) ,We'll start with some background about alpha-stable distributions, and then go through the functions. |
