[S] Summary:stable random variable generation

Arturas Mazeika (arturas@ieva.maf.vu.lt)
Thu, 21 May 1998 19:53:57 +0200 (MET DST)

Thanks very much to John P. Nolan, Andrey Feuerverger, John R. Gleason,
Matt Calder and others, who respond about stable r.v. simulation

Some notes:

1) The simulation of stable r.v. in S+ is one of the quickest one.

2) The algorithm is described in the journal of the American
Statistical Association, 1976, p340-344.

3) The compact discussion of the problem is on pp 458-459 of Devroye,
"Non-Uniform Random Variate Generation", Springer.

4) If you'd like simply to simulate symmetric stable r.v. you can
use formula:

X = ((sin(ag)/(cos(g)^(1/a))) * ((cos((1-a)g)/W)^((1-a)/a))

where, a = alpha, g ~ Uniform(-pi/2, pi/2), W ~ Exponential(1).

Arturas Mazeika
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