The estimation of stable distribution parameters

This paper concerns the estimation of the parameters that describe a stable distribution. Stable distributions are characterised by four parameters which can be estimated using a number of methods and although approximate maximum likelihood estimation (MLE) techniques do exist, they are computationally intensive. There are a number of techniques that are much faster than MLE and these are the focus of this paper. These techniques are compared and contrasted both for stable random variables and for teletraffic data.