On Tue, 25 Jun 2002, Tom Downing wrote:
> Aside from numerical integration, would anyone
> know if there exist algorithms to calculate the cumulative
> t-distribution density function( implemented via the
> s-plus pt(q,df) function) ? I am looking for something
Yes, there are several. I would look in the (older) books on statistical
computing. The t is a special case of the F and so can be computed from
incomplete beta functions, and you can find algorithms for those on
Abramowitz & Stegun (from memory).
There are the Applied Statistics algorithms AS3 and 27 for lower and upper
tails respectively. I also did a search on netlib (GAMS category L5alt)
with no hits.
> akin to the relatively well-known polynomial
> approximations for the cumulative normal. Or would it
> be quicker to actually do the integration
> with something like gaussian quadrature ?
(Not by a very large margin.)
--
Brian D. Ripley, ripley@stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272860 (secr)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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