Two approaches to adaptation of sample myriad to characteristics of SαS distribution data

This paper deals with theoretical and numerical simulation based analysis of sample myriad properties for a family of symmetric α-stable (SαS) distributions often used for modeling noise in natural environments. The theoretically optimal values of a sample myriad tunable parameter k in the sense of minimal asymptotic variance are obtained. Two practical approaches are proposed to adapt the parameter k to SαS distribution characteristics for data samples of a limited size. Statistical properties of the developed approaches are studied for cases of a priori unknown parameters of SαS distribution. A practical application where the proposed approaches can be useful is considered.