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Stable Distributions in Mathematica
Robert H. Rimmer
John P. Nolan

References

[1] P. Levy, Calcul des Probabilites, Paris: Gauthier-Villars, 1925.

[2] J. P. Nolan, Stable Distributions: Models for Heavy Tailed Data, Boston: Birkhauser, 2005. Chapter 1 provides a good introduction and is available at the American University Stable website academic2.american.edu/~jpnolan/stable/stable.html.

[3] B. B. Mandelbrot, "The Variation of Certain Speculative Prices," Journal of Business, 36(4), 1963 pp. 394-419.

[4] B. B. Mandelbrot, "Correction of an Error in "The Variation of Certain Speculative Prices" (1963)," Journal of Business, 45(4), 1972 pp. 542-543.

[5] B. B. Mandelbrot, Fractals and Scaling in Finance: Discontinuity, Concentration, Risk, New York: Springer-Verlag, 1997.

[6] C. Rose and M. D. Smith, Mathematical Statistics with Mathematica, Springer Texts in Statistics, New York: Springer-Verlag, 2002.

[7] J. P. Nolan, "Numerical Calculation of Stable Densities and Distribution Functions," Communications in Statistics-Stochastic Models, 13(4), 1997 pp. 759-774.

[8] J. M. Chambers, C. L. Mallows, and B. W. Stuck, "A Method for Simulating Stable Random Variables," Journal of the American Statistical Association, 71(354), 1976 pp. 340-344.

[9] S. T. Rachev and S. Mittnik, Stable Paretian Models in Finance, New York: John Wiley, 2000.

[10] J. P. Nolan, "Stable MathLink Package," (Mar 18, 2005) www.robustanalysis.com.

[11] V. M. Zolotarev, "One-Dimensional Stable Distributions," Translation of Mathematical Monographs, Vol. 65, American Mathematical Society, 1986. (Translation of the original 1983 Russian).



     
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