Re: [S] stable random variable generation

JRG (loesljrg@ican.net)
Tue, 19 May 1998 15:30:05 -0400


At 02:35 PM 190598 EDT, you wrote:
>
>
>> I need to generate a stable random variable. Unfortunately, S+ requires
>> a rather long time. Does anyone know any quicker free package for
>> stable random variable generation?
>>
>> Thank you.
>> Arturas Mazeika
>
>
>generating stable random variables is fairly nontrivial since there are no
>`handles' on the actual distributions other than through integral transforms.
>
>the method of chambers, mallows and stuck (based on transforming a pair of
>uniforms) in the journal of the american statistical association, 1976,
>p340-344, is, to my knowledge, the only practical algorithm and
>implementation for generating arbitrary stables that has been carried out
>to date. this paper contains a brief appendix with fortran code for that
>algorithm. presumably linking this fortran code to s-plus should result
>in being able to generate stables about as fast as is possible within s-plus
>although i would assume that this in fact is what s-plus has already done
>(although i stand to be corrected on this last point).
>
>hope this info helps a little bit; if you should come across any other newer
>algorithms for generating stables, please do let me know.
>
>
>best,
>andrey feuerverger ( andrey@utstat.toronto.edu )
>university of toronto

Seems to be an accurate summary of the situation. There's a compact
discussion of the problem, and possibilities for some special cases, on pp.
458--459 of Devroye, "Non-Uniform Random Variate Generation", Springer
(1986). The new edition of Knuth doesn't mention the problem, so far as I
can see.

---JRG

John R. Gleason

Syracuse University
430 Huntington Hall Voice: 315-443-3107
Syracuse, NY 13244-2340 USA FAX: 315-443-4085
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