I do see a testing function (beta_series) that only tries sample sizes
smaller than
n=512, but I can't easily find any use of a gaussian approximation in
the source
code for the 1.14 version of GSL.
I don't expect some of the other sources I tested against to use the
gaussian
either, so my finding that all 4 methods agree within about ten times
the IEEE
eps value of 2.2204E-16 would be proof enough for me to NOT fully read the
beta_inc.c source code.
Funny history - I was first asked if I was using the gaussian
approximation to
the binomial in the mid 60's, and was able to answer that I was using
the exact
binomial ~;)
On 6/5/2011 10:19 PM, Z F wrote:
Dear Well Howell,
--- On Sun, 6/5/11, Well Howell<[email protected]> wrote:
An interesting (but "homework-like"
~;) question - and fun to answer too.
Anyway, I'd probably compare GSL results with those from
other sources.
I had easy access to gsl_cdf_binomial_P (v 1.14), R
pbinom(k,n,p),
binomCDF
(Excel 2007) and dcdflib (Fortran - Brown, Lovato&
Russel; U. Texas;
November, 1997).
For a sample size of n=1000, a trial probability of p=0.01
and number of
successes of
s=1 thru 40, the CDF values from dcdclib and the R 2.13.0
stats package
pbinom()
function (http://cran.r-project.org/) show no
difference.
Thank you very much for your reply.
It seems I was not clear with my question. I am not looking for a
comparison with other libraries, but rather for information regarding
the approximations used to obtain the values of CDF. What I am afraid of
is that a Gaussian approximation is used for a large sample, rendering
values in the tails of the distribution error-prone.
I someone could provide any info on the subject or maybe point in the "right
direction" , I would highly appreciate it.
Thanks again
ZF
On 6/2/2011 12:49 AM, Z F wrote:
Hello everybody,
I was wondering if someone could comment on the
accuracy of gsl_cdf_binomial_P() function gsl implementation
for large n (n is about a few thousand).
for different values of p and when the result of cdf
is in the tails ( small less then 0.05 and large -- above
0.95)
Thank you very much
ZF
