Efficient Numerical Methods for Stable Distributions

"Stable distributions are a broad parameterized class of heavy-taileddistributions, containing the Gaussian distribution at one end and theCauchy distribution in the middle, which have been shown to be atheoretically justifiable model for a large class of impulsiveinterference. Researchers have successfully used stable distributionsto model real-life radar data sets, including clutter in sea data andforest canopy data.Nevertheless, practical considerations have hindered their use. Inparticular, general stable distribution probability density functions(PDF) and cumulative distribution functions (CDF) do not haveclosed-form expressions.In the last 5-10 years, however, a variety of algorithms have beenproposed for PDF and CDF approximations, random vector generation,parameter estimates, diagnostic tests, and inference for univariateand multivariate stable distributions. These methods have been usedfor real-time calculations in optimum and sub-optimum detectors. Butcurrently there are no reliable, commercial-quality implementations ofthese algorithms.The purpose of this research is to fill that gap. The ultimate goal isto 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 firstcommercial software library for stable distribution calcula