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From: Beliavsky on 5 Mar 2010 10:10
Is there a public domain Fortran code to compute the expectation value
of the Mth largest out of N standard normal variates? I can simulate
this, of course, but maybe there are fast but accurate approximations.
From: Lurker on 5 Mar 2010 10:28
You might find someting here...

http://jblevins.org/mirror/amiller/

"Beliavsky" <beliavsky(a)aol.com> wrote in message
news:6c4a11a7-dff5-4529-8225-6adc5b18a4bd(a)q15g2000yqj.googlegroups.com...
> Is there a public domain Fortran code to compute the expectation value
> of the Mth largest out of N standard normal variates? I can simulate
> this, of course, but maybe there are fast but accurate approximations.


From: Gordon Sande on 5 Mar 2010 10:56
On 2010-03-05 11:10:19 -0400, Beliavsky <beliavsky(a)aol.com> said:

> Is there a public domain Fortran code to compute the expectation value
> of the Mth largest out of N standard normal variates? I can simulate
> this, of course, but maybe there are fast but accurate approximations.

Google yielded

Algorithm AS 177: Expected Normal Order Statistics (Exact and Approximate)
J. P. Royston
Journal of the Royal Statistical Society. Series C (Applied Statistics),
Vol. 31, No. 2 (1982), pp. 161-165 (article consists of 5 pages)

when asked for "normal order statistics". I have often been told that order
statistics are an example of a computation requiring very high precision due
to extreme cancelation so one should use one of the symbolic manipualtion
packages and be patient. It is the sort of thing that may have approxiamtion
formulae of varying accurracy. The title of this algorithm reinforces these
notions.



From: Beliavsky on 5 Mar 2010 11:45
On Mar 5, 10:28 am, "Lurker" <spamk...(a)spamkill.co.uk> wrote:
> You might find someting here...
>
> http://jblevins.org/mirror/amiller/

Thanks to you and to Gordon Sande. The relevant code is at
http://jblevins.org/mirror/amiller/as177.f90 .
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