Adaptation of sample myriad tunable parameter to characteristics of SαS distribution

Abstract

Processes obeying heavy-tailed symmetric alpha-stable (SalphaS) distributions have been shown to describe well many natural phenomena in radio engineering, acoustics, communications, etc. For processing such data, one needs to apply robust estimators and the methods based on a sample myriad are considered quasi-optimal ones. Sample myriad estimation requires setting a tunable parameter k. However, only quite approximate and impractical recommendations concerning its selection exist. Thus, in this paper we consider some approaches to deal with setting k in practical applications. It is shown that they are to be adaptive to data sample scale and tail heaviness.