Application of the Positive Alpha-Stable Distribution

Authors:
Robert D. Pierce
Affiliations:
-
Venue:
SPWHOS '97 Proceedings of the 1997 IEEE Signal Processing Workshop on Higher-Order Statistics (SPW-HOS '97)
Year:
1997

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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; however, when only positive outcomes are possible, then the process would be positive alpha-stable. Phenomena related to energy or power are examples. This paper presents the characteristics and potential applications for the positive alpha-stable distribution. For this distribution all negative-order moments exist, and ratios of these moments are used to estimate alpha. Application areas that will be examined include: seismic activity, ocean wave variability, and radar sea clutter modulation. The correlation properties of these data are examined.