Skewness Parameter

A skewness parameter is a shape parameter that controls asymmetry in a specified family of statistical distributions. Its definition and allowed range depend on the family. For a stable distribution, the skewness parameter is . When the index of stability satisfies , gives a symmetric statistical distribution, while positive and negative values favor the right and left tails, respectively. At , the stable distribution is a normal distribution and does not depend on (Nolan 2020).

A skewness parameter is not in general the skewness defined by the standardized third central moment. In particular, a nondegenerate stable distribution with has infinite variance, so its moment-based skewness is undefined even though is well defined.