* accuracy of gsl_cdf_binomial_P
@ 2011-06-02 4:50 Z F
2011-06-05 13:04 ` Well Howell
0 siblings, 1 reply; 4+ messages in thread
From: Z F @ 2011-06-02 4:50 UTC (permalink / raw)
To: gsl-discuss
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
^ permalink raw reply [flat|nested] 4+ messages in thread
* Re: accuracy of gsl_cdf_binomial_P
2011-06-02 4:50 accuracy of gsl_cdf_binomial_P Z F
@ 2011-06-05 13:04 ` Well Howell
2011-06-06 2:20 ` Z F
0 siblings, 1 reply; 4+ messages in thread
From: Well Howell @ 2011-06-05 13:04 UTC (permalink / raw)
To: gsl-discuss
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
>
>
^ permalink raw reply [flat|nested] 4+ messages in thread
* Re: accuracy of gsl_cdf_binomial_P
2011-06-05 13:04 ` Well Howell
@ 2011-06-06 2:20 ` Z F
2011-06-06 10:48 ` Well Howell
0 siblings, 1 reply; 4+ messages in thread
From: Z F @ 2011-06-06 2:20 UTC (permalink / raw)
To: gsl-discuss, well
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
> >
> >
>
>
^ permalink raw reply [flat|nested] 4+ messages in thread
* Re: accuracy of gsl_cdf_binomial_P
2011-06-06 2:20 ` Z F
@ 2011-06-06 10:48 ` Well Howell
0 siblings, 0 replies; 4+ messages in thread
From: Well Howell @ 2011-06-06 10:48 UTC (permalink / raw)
To: gsl-discuss
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
>>>
>>>
>>
>
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