Re: accuracy of gsl_cdf_binomial_P

[Well Howell <whowell at superlink dot net>]

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<whowell@superlink.net>  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