Re: accuracy of gsl_cdf_binomial_P

[Well Howell <whowell at superlink dot net>]

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.

Mean absolute deviations for these 40 tests, comparing pbinom with
gsl_cdf_binomial_P and with binomCDF, show  MAD of 2.319E-15 and 3.296E-15
respectively.

My "commend"?  Looks as if we all have to decide when to STOP
accumulating small terms, and some stop earlier than others.  While I always
test functions in Excel against other sources before release in a report,
anything showing a MAD below 4E-15 sure beats using my slide rule
(which didn't have an incomplete beta function anyway ~;).

Well Howell




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