Application of the positive alpha-stable distribution

Abstract

Many physical phenomena are non-Gaussian and if the observed data have frequently occurring extreme values, then the phenomena may be modeled as a random process with an alpha-stable distribution. When positive and negative outcomes are equally likely, then the process would be symmetric alpha-stable (S/spl alpha/S); however when only positive outcomes are possible, then the process would be positive alpha-stable (P/spl alpha/S). Phenomena related to energy or power are examples. This paper presents the characteristics and potential applications for the P/spl alpha/S distribution. For this distribution all negative-order moments exist, and ratios of these moments are used to estimate alpha. Application areas that are examined include: seismic activity, ocean wave variability, and radar sea clutter modulation. The correlation properties of these data are examined.