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A program for maximum likelihood estimation of general stable parameters is described. The Fisher information matrix is computed, making large sample estimation of stable parameters a practical tool. In addition, diagnostics are developed for assessing the stability of a data set. Applications to simulated data, stock price data, foreign exchange rate data, radar data and ocean wave energy are presented. 2 examples. The second reason is the Generalized Central Limit Theorem which states that the only possible non-trivial limit of normalized sums of i.i.d. terms is stable. It has been argued that many observed quantities are the sum of many small terms -the price of a stock, the noise in a communication system, etc. and hence a stable model should be used to describe such systems. The third argument for modeling with stable distributions is empirical: many large data sets exhibit heavy tails and skewness. The strong empirical evidence for these features combined with the Generalized Central Limit Theorem is used by many to justify the use of stable models.

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Mulitvariate stable distributions with elliptical contours are a class of heavy tailed distributions that can be useful for modeling financial data. This paper describes the theory of such distributions, presents formulas for calculating their densities, methods for fitting the data and assessing the fit. Numerical routines are described that work for dimension d ≤ 40. An example looks at a portfolio with 30 assets.