The parameter that is most important in distinguishing between different members of the Levy family of distributions is the "characteristic exponent," which Levy denoted by the Greek letter a (alpha). Alpha is always greater than zero and no greater than 2. The lower the value of alpha, the more cases fall in the tails of the distribution: in other words, the higher the proportion of events that are extreme, "wild," deviations from the average.

Donald MacKenzie, An Engine, Not a Camera, loc. 479