On Estimation of α-Stable Distribution Using L-Moments

The family of stable distributions and, in particular, the α-stable distribution increases its applicability in engineering sciences. Examination of industrial data shows that originally assumed Gaussian properties are not so often observed. Research shows that stable functions can cover much wider spectrum of cases. However, the estimations of α-stable distribution factors may pose some limitations. One of the control engineering aspects, i.e., the assessment of controller performance, may be successfully addressed by L-moments and L-moment ratio diagrams (LMRD). Simultaneously, LMRDs are often used as a method for distribution, fitting with the method of moments (MOM). Unfortunately, the moments do not exist for α-stable distribution. This research shows that, with the use of a Monte-Carlo analysis, this limitation may be overcome, and an efficient method to estimate statistical factors of the α-stable distribution is proposed.