Efficient Numerical Methods for Stable Distributions

Period of Performance: 10/10/2002 - 04/10/2003


Phase 1 SBIR

Recipient Firm

Insightful Corporation
Seattle, WA 98109
Principal Investigator


Stable distributions are a broad parameterized class of heavy-tailed distributions, containing the Gaussian distribution at one end and the Cauchy distribution in the middle, which have been shown to be a theoretically justifiable model for a large class of impulsive interference. Researchers have successfully used stable distributions to model real-life radar data sets, including clutter in sea data and forest canopy data. Nevertheless, practical considerations have hindered their use. In particular, general stable distribution probability density functions (PDF) and cumulative distribution functions (CDF) do not have closed-form expressions. In the last 5-10 years, however, a variety of algorithms have been proposed for PDF and CDF approximations, random vector generation, parameter estimates, diagnostic tests, and inference for univariate and multivariate stable distributions. These methods have been used for real-time calculations in optimum and sub-optimum detectors. But currently there are no reliable, commercial-quality implementations of these algorithms. The purpose of this research is to fill that gap. The ultimate goal is to turn these new methods and ideas into a coherent, user-friendly, fast and accurate C++ library for stable distribution calculations, and to demonstrate their use for signal processing applications. The proposed research will lead to the development of the first commercial software library for stable distribution calculations and analyses. The software will be incorporated into our flagship product, S-PLUS, a premier platform for statistical research and analysis. A core market for Insightful is finance, where stable distributions have important applications. We intend to enchance S+FinMetrics, a popular S-PLUS add-on module for financial data analysis, to include stable distribution models in the areas of portfolio optimization, value at risk calculations, regression and forecasting, and option pricing. We also anticipate that our expertise developed during the implementation of this research will open the way for further consulting opportunities.