Volume 9, Issue 4
Tricks of the Trade
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Stable Distributions in Mathematica
The direct use of Mathematica for data analysis can be slow. For in-depth analysis of data, STABLE is an excellent MathLink package that includes many more functions and parameterizations. The MathLink program consists of compiled Fortran routines that are passed to Mathematica with wrapper functions that are compatible with the functions in the StableDistribution package. It solves the problem of the shape of the Zolotarev integrand by dividing it into intervals. The peak is found numerically and a narrow interval on either side of the peak is handled with a more involved routine than the other parts. Its compiled code can thus use simpler and faster numerical integration routines for greater speed than possible with Mathematica's very versatile but complicated NIntegrate function. It is also bulletproof, at the cost of not allowing calculations when but rounding to , and not permitting calculations when . It is limited to double-precision calculations. The interface can perform maximum likelihood calculations many times faster than the Mathematica package described earlier, using a very fast interpolation method. These fits are usually a minimum of 50 times faster than possible with the package described in this paper. The MathLink interface has been used with Mathematica's J/Link to download stock market data from internet databases and automatically analyze the time series of thousands of stocks. The MathLink interface is available (currently for Windows only) from www.robustanalysis.com. The package described in this paper is designed so that both programs can be run simultaneously turning Mathematica into a powerful, stable workstation.
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