| Created by Mathematica (October 27, 2005) |  |
Stable PDF
The shape and skewness of the stable probability density function are controlled by two parameters, {α, β}. α determines the relative weight of the tails and the mid distribution; it is always in the range (0, 2]. If α = 2, the distribution has the shape of a normal distribution. As α decreases toward 1, the tails progressively have more weight; at α = 1, it becomes a Cauchy distribution. As α becomes smaller the tails become very heavy. When α is greater than 1, the mean of the distribution exists, when α is 1 or less the tails are so heavy that the mean does not exist. β is the skewness parameter with a range, [-1, 1]. When it is negative, the left tail is heavier than the right and vice versa, when it is 0, the distribution is symmetric. γ is the scale parameter in the range (0, ∞], and δ is the location parameter. In the 1-parameterization used here it is the mean when α > 1.