On Fri, 30 Jan 2004, David Smith wrote:
> > Unless Insightful wants to tell you exactly how they
> > compute the gamma function, you may be out of luck.
>
> Insightful is quite happy to do so. :) The details are right there in
> help(gamma):
That's not what help(gamma) gives on my Linux S-PLUS 6.1 system, and it
does give help on gamma and not [dpq]gamma (which are in help(GAMMA)).
Under Windows, neither give useful information, and I suspect David was
using 6.2 under Windows and that has got a case-insensitivity problem ....
Most OSes have gamma and lgamma as functions in libc, and indeed the
current C standard requires that. My guess is that Insightful call the
standard C functions where available.
There are lots of C implementations of gamma around. Spencer has
mentioned that R has one, and I recall locfit as having one ....
> For shape less than 10^8 pgamma(q,shape) is computed using formulae 6.5.31
> and 6.5.32 of Abramowitz and Stegun (1970). For these values of shape dgamma
> is computed based on the lgamma function. For larger values of shape pgamma
> and dgamma use a normal approximation, adjusted for skewness only. See
> formulae 26.2.48 and 26.1.32 of Abramowitz and Stegun. There may be slight
> discontinuities in higher derivatives at shape==10^8.
--
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 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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