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# A Method for Simulating Stable Random Variables

J. M. Chambers, C. L. Mallows and B. W. Stuck
Journal of the American Statistical Association
Vol. 71, No. 354 (Jun., 1976), pp. 340-344
DOI: 10.2307/2285309
Stable URL: http://www.jstor.org/stable/2285309
Page Count: 5
A new algorithm is presented for simulating stable random variables on a digital computer for arbitrary characteristic exponent $\alpha(0 < \alpha \leq 2)$ and skewness parameter β(-1 ≤ β ≤ 1). The algorithm involves a nonlinear transformation of two independent uniform random variables into one stable random variable. This stable random variable is a continuous function of each of the uniform random variables, and of α and a modified skewness parameter β' throughout their respective permissible ranges.